1

BASIC OPTICAL CONCEPTS A course in programmed instruction

AO AMERICAN OPTICAL OPTICAL PRODUCTS DIVISION

SOUTHBRIDGE, MA 01550

Copyright © 1972 by AMERICAN OPTICAL CORPORATION

Book 1 of 4

2

AN INTRODUCTION TO PROGRAMMED INSTRUCTION This book is written in the form of programmed instruction. The purpose of P.I. (programmed instruction) is to help you to learn. People learn best when they are involved most, and to keep you actively involved while reading this book we have written it in short steps, called frames. Each frame is numbered, and separated from the next frame by a row of asterisks. In each frame you’ll be given some information, and then asked to answer a question – either about the information in that frame, or about information contained in a previous frame. An answer – not necessarily the answer, because many times we’ll ask a question that could be answered in many ways – to the question asked in each frame is given immediately below a heavy black line. To avoid inadvertently seeing our answer before you have written your answer, use the cardboard shield that comes with this book. (If you can’t find your shield, any piece of paper will do.) Use the shield to cover the answer by putting it over the page as soon as you turn to it, and then sliding the shield down the page until you come to a heavy black line. Stop the shield there, so everything below the line is obscured. It’s important to write your answer in each frame – not just to think it – because things stick in your mind more readily after you’ve written them down. So be sure to have a supply of sharp pencils, or a pen, handy before starting this book. If the answer we’re looking for calls for just one, two, or three words, we may leave one, two, or three blank spaces for you to write the answer in. The length of the space will give you some idea about the length of the missing word. We won’t give you three spaces this long: “___ ___ ___,” and expect you to write the answer “Compound hyperopic astigmatism” in them. Neither will we give you a space this long: “________________,” when the word we’re looking for is “Eye.” Leaving you the right number of spaces, of approximately the right length, may give you more of a hint about the answer than we care to give. Also, many times, we’ll be looking for an answer in your own words … maybe requiring four or five lines. In these cases we’ll provide a blank line, or several blank lines, that start with an asterisk (like this: * ________________). The asterisk means “start writing your answer here, in your own words.” If you need more room than we give you, write wherever you can find the space … sideways up the margin if necessary. Sometimes you’ll be asked to make a choice between several answers, only one of which is correct. The choices will be shown in parentheses, and underlined. Your job will be to draw a circle around the (correct/incorrect) answer. If you make an incorrect response, correct it … after making sure you understand why it was incorrect. This book is yours, and you will want to refer to it many times in the future. If a response you have written is incorrect, you may be misled at some later date when you glance through the book in order to recall some facts.

3

Programmed instruction has many advantages over other methods of learning. One, we’ve mentioned … in making frequent responses, you learn more readily. Other advantages are: you get immediate feedback, through the answer to the question asked in each frame, on whether or not you’re absorbing the information; if your answer to a question is wrong, it’s easy to go back a few frames to see why you were wrong; finally, you go at your own speed, without having to wait for people who learn more slowly than you, or trying to keep up with people who learn more quickly than you. One last word … this book is not a test. It’s very easy to go through it looking at our answer to each frame before writing your answer. If you do this, you’ll remember little of the contents, and you’ll have wasted a lot of time. Use the book as it is designed to be used, to help you to learn, and you’ll be the chief beneficiary.

INDEX Section Page I The Composition of Light 1 II The Measurement of Light 15 III Refraction 22 IV Dispersion 34 V Review 44

4

SECTION I

THE COMPOSITION OF LIGHT 1. When you switch on the electric light in a room, how does the light travel from the lamp to the

corners of the room … and out of the door, and through the window?

There are two theories on how light travels. One is called the corpuscular theory, and the other is called the electromagnetic wave theory.

The theory that light is composed of a stream of invisible particles, or corpuscles, emitted by objects and gathered by the eye, is called the ________________ theory. corpuscular * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

2. Think of a still pond … toss a stone into that pond, and you’ll see waves move outward across the surface of the water. The theory that light travels in this way – in a series of waves moving outward from the source of light – is called the ___________________________ _____________ theory.

electromagnetic wave * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

3. The reason why two totally different theories are accepted is that each theory explains certain phenomena about light that the other theory cannot explain.

The corpuscular theory, for example, explains how light can be used to create electrical energy. Light, entering an exposure meter that you use to adjust your camera, moves a needle across a dial. The impact of particles of light – called photons – releases charged particles called electrons … which create an electric current.

The corpuscular theory on how light travels states that light is composed of a stream of invisible ________________, or ________________, emitted by objects and gathered by the eye.

Particles, corpuscles (either order) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

5

4. The electromagnetic wave theory explains (when the corpuscular theory cannot explain) how a rainbow is formed, and how light is broken up into bands of colored light when it passes through a prism, and how a telescope works.

The electromagnetic wave theory on how light travels states that light travels in ___________ moving _____________ from the source of light.

waves, outward (or away) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

5. In this program we’re going to be discussing the way in which light enters the eye, or passes

through a glass lens … both of which happen when you look through a simple telescope. We are, therefore, going to consider only one of the two theories about light. That theory is the * ___________________________________________. electromagnetic wave theory * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

6. The electromagnetic wave theory on how light travels states that light travels in * ____________

______________________________________________________________________________

waves, moving outward from the source of light (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

7. Electromagnetic waves travel in much the same way as a wave on the surface of a pond travels. The up-and-down motion of the wave is at 90 degrees to the direction of travel.

6

Light is measured by the length of its waves. (By this you can deduce that there is more than one form of light.) The wave length is the distance traveled forward by the light as it goes through one complete vibration … i.e. the distance from the crest of one wave to the crest of the next.

What is the wave length of the electromagnetic wave shown in the diagram above?

(a) 2 cms. (b) 4 cms.

(c) 14 cms. (b) 4 cms. (The distance from A to C, or C to E, etc.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

8. Light is just one form of electromagnetic radiation – but it is the only visible form. Other forms

of electromagnetic radiation are radio waves, infra-red and ultra-violet rays, x-rays and cosmic rays. They differ from one another only in the length of their waves.

This very simple diagram shows the whole range of electromagnetic radiation. The figures on the diagram, ranging from 4 ten trillionths of an inch up to 18 ½ miles, show the wavelengths of the different forms of radiation. You can see that the radiation shown in the diagram in frame 7 – with a wavelength of 4 cms. (just over 1 ½ inches) – was ultra-short-wave broadcasting radiation … at the very low end of the ultra-short-wave band. (This band is used for television and radar.)

7

What wavelengths limit the range of electromagnetic radiation visible to the human eye?

16 millionths inch to 32 millionths inch * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

9. Because the wavelengths of visible light are so very short, they are measured in special units,

called nanometers.

The prefix nano- comes from the Greek word nanos, dwarf, and means a billionth part of whatever the prefix is attached to. You can have nanoseconds – which is one billionth of a second – as well as nanometers.

How long is one nanometer? * ___________________________________________________ _____________________________________________________________________________

one billionth of a meter * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

10. One nanometer is one billionth of a meter, or – in simpler terms for those of us who don’t think in meters – there are approximately 25 million nanometers in one inch.

Visible light has wavelengths that range from 380 nanometers to 800 nanometers. The color of the light we see depends upon the wavelength of the light.

Think of the colors of a rainbow … red, orange, yellow, green, blue, violet. What, do you suppose, is the approximate wavelength of red light? Is it approximately 380 nanometers? Or is it approximately 800 nanometers? And what, do you suppose is the approximate wavelength of violet light? 380 nanometers, or 800 nanometers? (There’s a clue in the diagram in frame 8, if you look at the relative positions of infra-red rays and ultra-violet rays on the scale.) Write your answers here:

Color Approximate wave length ________ _____________________ ________ _____________________

Red light 800 nanometers Violet light 380 nanometers * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

8

11. Red light has a longer wavelength than violet light. You might have guessed this from the fact that infra-red rays are shown in the diagram in frame 8 to have a longer wavelength than ultra-violet rays. Both infra-red rays and ultra-violet rays are electromagnetic waves that are invisible to the human eye.

The electromagnetic wave theory on how light travels states that

* ___________________________________________________________________________

_____________________________________________________________________________

light travels in waves, moving outward from the source of light. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

12. How would you define the term wavelength as it is applied to light?

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Wave length is the distance traveled forward by the light as it goes through one complete vibration … OR … the distance from the crest of one wave to the crest of the next. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

13. Just as we have collective words to describe a whole lot of sheep or a whole lot of lions (a flock, and a pride), so we have collective words to describe a whole lot of light waves. A ray is a single band of visible light (made up of radiation of all wave lengths … from 380

nanometers to 800 nanometers). If we were using the corpuscular theory, we’d say that a ray was the path taken by a single corpuscle of light.

A pencil of light is a group of rays, coming from a single point on a light source. Because they come from a single point, the rays in a pencil of light are diverging.

9

A beam of light is a group of pencil coming from all the points on a light source. (An electric light bulb is a single source of light, but not a single point. A light bulb contains thousands of points of light from which rays emanate.)

When you see a search-light in the sky at night, probably advertising a new super-market, are you looking at a ray, a pencil, or a beam? (Please explain your choice.)

* ___________________________________________________________________________

_____________________________________________________________________________

A beam. The source of light of a search-light is made up by an enormous number of points of light. It is not a single point of light. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

14. If a beam of light is intercepted by an object, a shadow will be formed.

In this diagram, we’ve drawn only two rays – despite the fact that light is emitted in all directions from a source. We’ve drawn only the rays that just touch the outer edges of the ball, and so mark the outer edges of the ball’s shadow.

10

Because the light in the diagram above is shown to come from a single point, the edges of the shadow are shown as being sharply defined. But light seldom – if ever, under natural conditions – comes from a single point.

Below, we’ve drawn a lamp, showing just four of the many points on the filament from which light is emitted. Again, we’ve drawn only two rays from each of the points on the light source … each ray touching just the outer edges of the ball.

On this diagram, shade in the area on the screen covered by the shadow. Then, on the blank lines below, answer this question: why, if a light source is fairly large, will the shadow cast by an object be indistinctly defined at the edges?

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Your diagram should look something like this:

11

Each pencil of rays from each point on the light source casts its own shadow. The shadow you see, therefore, is a group of many overlapping shadows. Where the most shadows overlap – in the center of the group – the shadow you see is darkest. At the edges of the group – where unintercepted rays are striking the screen – the shadow you see is indistinctly defined. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

15. A ray of light is a ____________ band of visible light, made up of radiation of * __________________________________.

single all wave lengths * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

16. A pencil of light is a group of __________ coming from a _____________

rays single * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

17. A beam of light is a group of __________ coming from ________________________________

pencils all the points on a light source * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

18. Because rays of light diverge from every point on a source of light, any normal object (from the

size of a pin to the size of the Washington Monument) is not going to intercept all of the rays coming in its direction. Some rays are going to pass it … and it’s these rays that get past an object that cause the edges of its shadow to be indistinctly defined.

12

Only a pencil of light coming from a single point of light will give a precisely defined edge to a shadow – and we’ve already agreed that single points of light are seldom, if ever, found naturally. In the diagrams above, however, the shadow cast by the ball in diagram B is more sharply defined than the shadow cast by the ball in diagram A. Why is B’s shadow sharper than A’s?

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Because the screen on which the shadow falls is closer to the ball in diagram B than it is in diagram A.

OR

Because in diagram A the intercepted rays have diverged farther by the time the shadow is formed than they have in diagram B. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

19. One rule for forming a sharply defined shadow, therefore, is that the screen must be relatively close to the object. Now look at these two diagrams:

13

In these two diagrams, the shadow cast by the ball in diagram A is more sharply defined than the shadow cast by the ball in diagram B. Why is this?

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Because the source of the light in diagram A is farther from the object than it is in diagram B.

OR

Because the rays of light being intercepted in diagram B are traveling on more sharply diverging paths than are the rays of light in diagram A. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

20. Another rule for forming a sharply defined shadow, therefore, is that the source of light must be relatively far from the object.

In each of the last two frames, the diagram showing the formation of the more sharply defined shadow was the diagram in which the rays intercepted by the outer limits of the ball had diverged the least amount. (Diagram B in frame 18, and diagram A in frame 19.)

If the rays that are intercepted by an object are very nearly parallel (i.e. are hardly diverging at all) at the point of interception, the shadow will be sharply defined. Since rays are emitted in all directions from all the points on a source of light, this means either that all the points on the source must be very close together (which means a very small source of light) or that the source must be very far away from the object.

14

Which of the two lamps shown above will create the more clearly defined shadow behind the ball … the lamp in diagram A, or the lamp in diagram B? Why.

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

The lamp in diagram A, because the source of light is smaller. The rays from lamp A, when intercepted by ball A, will be more nearly parallel than the rays from lamp B, when intercepted by ball B. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

21. A single band of visible light, of all wavelengths, is called a ______.

ray * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

22. Groups of diverging rays, coming from all the points on a light source, are called a __________. A group of diverging rays, coming from a single point on a light source is called a __________.

beam pencil * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

23. Why does a very large source of light, such as the sun, cause the Washington Monument to cast a

sharply defined shadow in bright sunlight?

15

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Because the sun is so far away that the beam intercepted by the Washington Monument is composed of practically parallel rays. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

24. What does the electromagnetic wave theory state?

* ___________________________________________________________________________

_____________________________________________________________________________

Light travels in waves, moving outward from the source of light. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

25. Give definitions of the terms ray, pencil, and beam.

Ray: *______________________________________________________________________

_____________________________________________________________________________

Pencil: *______________________________________________________________________

_____________________________________________________________________________

Beam: *______________________________________________________________________

_____________________________________________________________________________

Ray: a single band of visible light, of all wavelengths. Pencil: a group of diverging rays, coming from a single point on a light source. Beam: a group of pencils, coming from all the points on a light source. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

16

SECTION II

THE MEASUREMENT OF LIGHT 26. Electromagnetic radiation waves are measured in three ways. We’ve already discussed one way

… wavelength. The other two are frequency and velocity.

Frequency is the number of times a wave of radiation vibrates in one second. Thinking again of the pond, after the stone has been tossed into it … frequency is the number of times a leaf, floating on the surface of the pond, bobs up and down in one second as the waves (caused by the stone) pass underneath it.

There is a mathematical relationship between the wavelength, the frequency and the velocity of radiation waves. If a wave vibrates ten times each second (its frequency) and it travels forward one meter each time it vibrates (i.e. the distance from the crest of one wave to the crest of the next is one meter – which is its wavelength), what is the velocity of that wave? Answer: ____ meters per second.

10 meters per second. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

27. Velocity, frequency, and wavelength. If we know the value of any two of these for any form of electromagnetic radiation, we can calculate the third. Write the formula for this calculation. (You just used the formula in the previous frame.) Velocity =

Velocity = Frequency X Wavelength. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

28. One vibration of a wave is called a cycle. On the A.M. band of your radio dial you’ll find a

station that broadcasts at 1,200 kilocycles. (1 kilocycle = 1,000 cycles.) If the wavelength of the radio signals used by that station are approximately .155 miles (check the long-range broadcast band on the diagram in frame 8), at what speed do those radio signals travel from the broadcasting station to your receiver? Do your calculations here … and give your answer in miles per second.

Answer =

17

Velocity = Frequency X Wavelength = 1,200,000 cycles per second X .155 miles = 186,000 miles per second * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

29. Define frequency, as the term is applied to light:

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Frequency is the number of times a wave of light vibrates in one second. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

30. What is a nanometer?

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

A unit of measure applied to visible light, equal to one billionth of a meter. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

31. The velocity of all electromagnetic waves – of any wavelength – is the same in air. Light travels

in air at 186,325 miles a second. Radio waves, television waves, x-rays, and cosmic rays all travel in air at the same speed (so the answer we got in frame 28 wasn’t quite right … but it was close).

We know that the wave lengths of electromagnetic waves vary enormously (in the diagram in

frame 8 we can see the variation to be from 4 ten trillionths of an inch to 18 miles) and we know that the velocity is equal to the frequency multiplied by the wavelength. If the velocity of electromagnetic waves in air is always the same, what can we say about the frequency of radiation A, which has a wavelength of one inch, compared to the frequency of radiation B that has a wavelength of two inches?

18

(a) A and B have the same frequency. (b) A’s frequency is twice that of B. (c) B’s frequency is twice that of A. Which?

(b) A’s frequency is twice that of B. (Because B’s wavelength is twice that of A.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

32. Define velocity, frequency, and wavelength in terms of electromagnetic waves:

Velocity: * __________________________________________________________________

_____________________________________________________________________________

Frequency:* __________________________________________________________________

_____________________________________________________________________________

Wavelength: * __________________________________________________________________

_____________________________________________________________________________

Velocity: the speed at which electromagnetic waves travel. Frequency: the number of times a wave vibrates in one second. Wavelength: the distance traveled forward by the wave as it goes through one complete

vibration. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

33. In air, light travels at 186,325 miles a second – but, to simplify the math we’re about to do, we’ll

round it off to the figure we got in frame 28 … 186,000 miles a second.

19

When light enters any other substance – such as water, or glass – it slows down. The speed of light in water is (in round figures) 140,000 miles a second. In one particular crown glass, the speed of light is 122,000 miles a second. The chemical composition of the substance through which the light is passing determines how fast the light will travel.

Different types of glass, therefore, with different chemical compositions, permit light to pass through them at _________________ speeds.

different * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

34. A comparison of the speed of light in air with the speed of light after it has entered a substance is

known as the index of refraction (or refractive index) of that substance. The formula to determine the index of refraction of a substance is:

Index of refraction Speed of light in air_____ of the substance = Speed of light in the substance

The speed of light in water is 140,000 miles/second. What is the index of refraction of water? Write down the formula (using 186,000 miles/second as the speed of light in air) and do your calculations here …

Answer:

Index of refraction 186,000 of water = 140,000 = 1.3286 The index of refraction of water is 1.33.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

20

35. The speed of light in air is 1.33 times the speed of light in water. What is the index of refraction of the crown glass in which light travels at 122,000 miles/second? Answer:

1.52.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 36. The index of refraction of a particular flint glass is 1.65. Does light travel faster in this flint glass

than in the crown glass with an index of refraction of 1.52 … or slower? * _____________.

Slower. (The speed of light in air is 1.52 times as fast as the speed of light in the crown glass, yet it is 1.65 times as fast as the speed of light in the flint glass … where it is 113,000 miles/second.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 37. If the speed of light is reduced in glass A by a greater amount than it is reduced in glass B, which

glass has the higher index of refraction? Glass A, or glass B? * _____________.

Glass A.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 38. What is the formula for determining the index of refraction of a substance?

Index of refraction Speed of light in air_____ of the substance = Speed of light in the substance

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

21

SECTION III

REFRACTION 39. When a beam of light passes from a substance with one index of refraction into a substance with

another index of refraction … such as from air into water, from one type of glass into another … the beam will bend – so long as it strikes the surface of the new substance at any angle other than 90 degrees.

In this diagram the rays in the beam of light strike the surface of the glass vertically … at an angle of 90 degrees. The beam, therefore, does not bend.

In this diagram, the rays in the beam of light strike the surface of the glass at an angle. Ray A enters the glass first, and slows down … next, ray B slows down, then C, then D. The effect on the beam is exactly the same effect that you get in your car if you put your foot on the brake pedal, and only the brakes on one side of the car respond. The beam is pulled towards the slower moving ray; it is bent towards ray A.

What do you suppose happens when the beam of light passes through the opposite surface of the glass, and re-enters the air? Complete the diagram below by drawing the paths that rays A, B, C, and D will take as they pass through the glass block and into the air … (use a ruler).

22

The diagram should now look like this:

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

40. The beam of light in frame 39 was made to slow down on entering the glass block. Because it met the surface of the glass at an angle, the beam was turned from its original path. When it passed right through the glass block, entering the air again caused the speed at which the light was traveling to increase. Ray A entered the air first; again, the effect was to pull the beam towards the slower moving ray, but this time ray D was moving more slowly than ray A. So the beam was pulled back into its original course (assuming that the sides of the glass block were parallel).

The amount of the angle through which the beam is turned on entering the glass is dependent upon two factors. One – the angle at which the beam strikes the surface of the glass, and two – the index of refraction of the glass. We say that, in being turned from the original path, the beam is refracted, and the angle through which it is turned is called the angle of deviation.

A few frames back we mentioned two types of glass: a crown glass with an index of refraction of 1.52 and a flint glass with an index of refraction of 1.65. Assuming a constant angle at which the beam strikes the surface of the glass, in which type of glass, do you suppose, is light refracted through the greater angle of deviation … the crown glass, or the flint glass … and why?

23

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Flint glass produces a greater angle of deviation than crown glass. The higher the index of refraction, the slower the speed of light in that substance, and the greater the angle of deviation. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

41. A ray of light will be refracted, and turned through an angle of deviation, whenever it passes from a substance with one index of refraction into a substance with another index of refraction. Define the term index of refraction.

* ___________________________________________________________________________

_____________________________________________________________________________

A comparison of the speed of light in air with the speed of light after it has entered a substance. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

42. What is the formula for determining the index of refraction of a substance?

Index of refraction Speed of light in air_____ of the substance = Speed of light in the substance

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

24

43. Define angle of deviation.

* ___________________________________________________________________________

_____________________________________________________________________________

The angle through which light is refracted (or turned) as it passes from a substance with one index of refraction into a substance with another index of refraction. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

44. The angle of deviation … the amount by which a ray of light is refracted as it passes, say, from

air into glass … depends upon two factors. We mentioned them both in frame 40. Without looking back … what are those two factors?

* ___________________________________________________________________________

_____________________________________________________________________________

The index of refraction of the glass, and the angle at which the ray of light strikes the surface of the glass. (Either order.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

45. Although it might seem logical to measure the angle at which a ray of light strikes the surface of

a piece of glass – which is called the angle of incidence – as the angle between the ray and the glass, it’s not done that way. It’s measured, instead, as the angle between the ray and a line perpendicular to the surface of the glass, at the point of contact.

Identify the angle of incidence in this diagram by marking it with the letter I …

25

This … is the angle of incidence.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

46. If we draw a dotted line along the path that the ray of light would have taken if it had not been

refracted, we can see the angle of deviation … identified by the letter ‘d’ in the diagram below.

The angle between the ray of light inside the glass and the line perpendicular to the surface of the glass is called the angle of refraction. It’s identified by the letter r.

As you can see from this diagram (if you remember your basic geometry from school), the angle of refraction and the angle of deviation are together equal to the angle of incidence.

26

What two factors affect the angle of deviation?

* ___________________________________________________________________________

_____________________________________________________________________________

The index of refraction of the glass, and the angle of incidence. (Either order.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

47. Do these two factors – the index of refraction of the glass, and the angle of incidence – affect the angle of refraction also? (Yes / No) Why?

* ___________________________________________________________________________

_____________________________________________________________________________

Yes. Because the angle of refraction together with the angle of deviation equals the angle of incidence. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

48. Here’s the diagram you looked at in frame 46 again.

Keeping in mind the two factors on which the amount by which a ray of light is refracted as it passes from air into glass depends, and keeping an eye on the diagram above to help you remember which angle is what, answer these questions …

27

(a) What happens to the angle of refraction when the angle of incidence increases?

* ____________________________

(b) What happens to the angle of refraction if the angle of incidence remains the same, but the glass is replaced by a substance with a lower index of refraction?

* ____________________________

(c) What happens to the angle of refraction when the angle of incidence decreases?

* ____________________________

(a) It increases. (b) It increases. (c) It decreases. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

49. When a ray passes from air into glass (or from any substance with a low index of refraction into

a substance with a higher index of refraction) the ray is always refracted towards the line perpendicular to that surface of the glass.

When the ray passes from glass into air, the ray is always refracted ___________ __________ the line perpendicular to that surface of the glass.

away from * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

50. When a ray passes right through a piece of glass with parallel sides, the two refractions that take place are equal and opposite.

28

In this diagram, the ray has passed right through the glass and is now traveling in the same direction as it was before it entered the glass, but it has been slightly displaced sideways. Notice that the angles inside the glass – between the ray and the perpendicular – are both referred to as the angle of refraction, and the angles outside the glass – between the ray and the perpendicular – are both referred to as the angle of incidence.

Would you expect a ray of light to be traveling in the same direction after passing through a piece of glass as it was before passing through that piece of glass, if the sides of the glass were not parallel? Why?

* ___________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________ _____________________________________________________________________________

No … but read on to see if your reason why is correct. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

51. If we tilt one surface of the glass, we’ll tilt the line perpendicular to that surface. We will, therefore, alter the angle of refraction at that surface.

You can see in this diagram that if we’d tilted the surface of the glass to a position where it was at exactly 90 degrees to the ray inside the glass, there would have been no refraction at all when the ray passed from the glass into the air.

29

In altering the angle of refraction, we’ve altered the angle of incidence, and so altered the direction of travel of the ray after it’s left the glass.

The trigonometric relationship between the index of refraction, the angle of incidence, and the angle of refraction is called Snell’s Law. We don’t need to go into the mathematical details of Snell’s Law, but you should remember the name. Define angle of refraction and angle of incidence Angle of refraction: *________________________________________________________

_____________________________________________________________________________

Angle of incidence: *________________________________________________________

_____________________________________________________________________________

Angle of refraction: the angle inside a piece of glass between the path taken by a ray of light at a surface of the glass and a line perpendicular to that surface. Angle of incidence: the angle outside a piece of glass between the path taken by a ray of light as it meets or leaves a surface of the glass and a line perpendicular to that surface. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

52. When a ray of light passes obliquely from air into glass – that is, at an angle less than 90o to the

surface – the direction in which the ray is refracted at the surface of the glass is always * ____________________________________________________________________________

______________________________________________________________________________ And when a ray of light passes obliquely from glass into air, the direction in which the ray is

refracted at the surface of the glass is always * ________________________________________

______________________________________________________________________________

towards a line perpendicular to that surface. away from a line perpendicular to that surface. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

30

53. In which direction will the ray of light be refracted as it either enters (diagrams 1 and 4) or leaves (diagrams 2 and 3) the pieces of glass in each of these diagrams? In the direction of arrow A … or arrow B?

1. A 2. B 3. A 4. A

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 54. Snell’s Law describes a trigonometric relationship between three variables: if we know the value of any two of the three variables, we can determine the third.

31

What are those three variables? * _____________________________________________ * _____________________________________________

* _____________________________________________

Index of refraction. Angle of incidence. Angle of refraction. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

32

SECTION IV

DISPERSION

55. Much earlier in this program we said that light waves of all frequencies – in fact, any

electromagnetic radiation – travel at the same speed … in air. All light waves do not, however, travel at the same speed in glass.

In glass, different wavelengths of light travel at different speeds. The longer wavelengths of light travel faster (or are slowed down less) than the shorter wavelengths.

Since the angle through which light is bent as it passes from air into glass is dependent, partially, on the deceleration experienced by the light, which, do you suppose, is bent through the greater angle … red light or violet light … and why? (Look back to the diagram in frame 8, in Section I, if you need help on this one.)

* ___________________________________________________________________________

_____________________________________________________________________________

Violet light is bent through the greater angle. Violet light has a shorter wavelength than red. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

56. The direction in which light bends as it passes from air into glass, or from glass into air, is

always the same, no matter what the wavelength might be. Red, orange, yellow, green, blue, or violet … it bends in the same direction. Violet light merely bends more than the other wavelengths.

In which direction does light bend as it passes from air into glass?

* ___________________________________________________________________________ And in which direction does light bend as it passes from glass into air?

* ___________________________________________________________________________

Towards a line perpendicular to the surface. Away from a line perpendicular to the surface. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

33

57. You’ll remember that we defined a ray as a single band of visible light – made up of radiation of all wave lengths. That band of visible light is “white” light, made up of separate waves of red, orange, yellow, green, blue, and violet light … which, together, are called the spectrum.

In this diagram the ray is greatly magnified to show the spectrum … which will appear as white light so long as all the waves are traveling in the same direction.

If the spectrum, shown in the diagram above, passes right through the glass with parallel sides, the individual waves will be refracted back onto their original course. In the diagram below, you can see what happens … (the ray, in this diagram, is no longer magnified so that the individual waves of the spectrum can be seen before it enters the glass.)

All the wavelengths in the diagram above emerge on paths which are parallel to the direction in which the ray was traveling before it entered the glass, but they’ve all been displaced sideways by varying amounts.

Will the waves emerging from the glass be seen as white light, or as bands of colored light? Why?

* ___________________________________________________________________________

_____________________________________________________________________________

34

White light, because all the waves are traveling in the same direction. (If you object to this answer, remember that there is not one solitary ray passing through the glass … there are millions, packed closely together. So the emerging red wave, though separated from the orange wave it started out with, is nevertheless closely packed to orange, yellow, green, blue and violet waves from other rays, all traveling along a parallel path.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

58. Now let’s consider what will happen when a single ray passes through a piece of glass that does

not have parallel sides …

When the piece of glass does not have parallel sides, the waves will emerge traveling in diverging directions.

Will the waves emerging from the glass be seen as white light, or as a spectrum … bands of colored light? Why?

* ___________________________________________________________________________

_____________________________________________________________________________

A spectrum. All of the red waves from the entering rays will emerge on parallel paths; all of the orange waves will emerge on other (different) parallel paths, etc. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

59. On what two factors does the direction of the path taken by a ray of light, as it emerges from

glass into air, depend?

35

* ___________________________________________________________________________

_____________________________________________________________________________

1. The index of refraction. 2. The angle between the path of the ray inside the glass and a line perpendicular to the surface

of the glass. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

60. What law states the trigonometric relationship between the index of refraction, the angle of

incidence, and the angle of refraction? * _______________________

Snell’s Law. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

61. What color wavelengths are refracted through the greatest angle – and what color wavelengths are refracted through the least angle – when white light passes from air into glass? Greatest refraction: * _______________ Least refraction: * _______________

Violet Red * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

62. Why is violet light refracted through a greater angle than red light when it passes from air into glass?

* ___________________________________________________________________________

_____________________________________________________________________________

36

Because the speed of violet light in glass is slower than the speed of red light in glass.

OR

Because violet light slows down by a greater amount than red light when it passes from air into glass.

OR Because violet light has a shorter wavelength than red light, and the shorter wavelengths of light travel more slowly in glass than the longer wavelengths of light.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

62. Look at the diagram below, and decide which wavelengths of light (represented by the arrows)

have been refracted through the greatest angle, and which have been refracted through the least angle.

Now identify the color of the light of each of the wavelengths by labeling the appropriate arrow.

Reading from top to bottom, the arrows represent violet, blue, green, yellow, orange and red light. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

64. The effect that a piece of glass without parallel sides has on a ray of light … that of separating

the ray into bands of the various wavelengths, to appear as a spectrum … is called dispersion.

37

Dispersion is found to some degree in all glass, no matter what its chemical composition happens to be. You’ll recall that the chemical composition of glass determines its index of refraction. The chemical composition also determines the dispersion properties of the glass, but not in direct proportion to its index of refraction.

Two types of glass, of different chemical composition, with different indices of refraction, may have the same dispersion properties.

Similarly, two types of glass, of different chemical composition, but with the same index of refraction, may have different dispersion properties.

The difference between high dispersion properties and low dispersion properties is apparent in these diagrams.

“Dispersion High” means * ______________________________________________________ _____________________________________________________________________________ “Dispersion Low” means * ______________________________________________________ _____________________________________________________________________________

38

there is wide variation in the angles through which the different wave lengths are refracted. there is only slight variation in the angles through which the different wave lengths are refracted. (In your own words.) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

65. What is the meaning of the term dispersion:

* ___________________________________________________________________________

_____________________________________________________________________________

Dispersion is the effect that a piece of glass without parallel sides has on a ray of light … that of separating the ray into bands of the various wavelengths, to appear as a spectrum. (In your own words.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

66. What does the index of refraction measure? (Think carefully about the formula before you write down your answer.)

* ___________________________________________________________________________

_____________________________________________________________________________

The speed of light in the substance compared with the speed of light in air.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

67. Measuring the speed of light over very short distances is obviously extremely difficult. Clearly,

it’s much easier to measure the angle of refraction within a piece of glass and then, by comparing that angle to the angle of incidence (with the aid of Snell’s Law), to calculate the index of refraction.

39

But one ray of light, on entering a piece of glass, is dispersed into a variety of wavelengths, each one producing a different angle of refraction. To avoid the confusion that could result from this situation, we measure the angle of refraction of only one wavelength – of 590 nanometers, which we see as yellow light.

In each of the four diagrams in frame 64, only the yellow wave is identified. You can see that the angle of incidence of the yellow wave, as it emerges from each of the two pieces of glass with an index of refraction of 1.60, is the same in each case. The angles of incidence of the other waves, however, differ. The angle of incidence of the yellow wave, as it emerges from each of the two pieces of glass with an index of refraction of 1.50, is also the same in each case. With this piece of information in mind, we should, perhaps, reword our definition of the index of refraction. How could you reword the answer you gave in frame 60 so that the method by which the index of refraction of a substance is measured is absolutely clear?

* ___________________________________________________________________________

_____________________________________________________________________________

The speed of yellow light (wavelength, 590 nanometers) in the substance, compared with the speed of light in air.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

68. Why is there no need, in the answer to the question posed in frame 67, to specify “the speed of

yellow light in air?”

* ___________________________________________________________________________

_____________________________________________________________________________

Because all wavelengths of light travel at the same speed in air.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

69. Demonstrate your understanding of dispersion by drawing the approximate paths taken by the

different wavelengths of visible light as a ray passes through the pieces of glass represented in the diagrams below. Label each wavelength. Under each diagram write “white light” or “spectrum” to indicate how the emerging waves would appear to the human eye.

40

Your diagrams should look something like this …

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

41

SECTION V

REVIEW 70. What does the electromagnetic wave theory state?

* ___________________________________________________________________________

_____________________________________________________________________________

Light travels in waves, moving outward from the source of light.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

71. What is the difference between a ray of light, a pencil of light, and a beam of light?

* ___________________________________________________________________________

_____________________________________________________________________________ _____________________________________________________________________________

_____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

A ray is a single band of visible light, of all wavelengths, coming from a single point on a light source. A pencil is a group of diverging rays, coming from a single point on a light source. A beam is a group of pencils coming from all the points on a light source. (In your own words.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

42

72. What is the mathematical relationship between the wavelength, the velocity, and the frequency of light?

Velocity = Frequency X Wavelength

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 73. Define frequency and wavelength as the terms are applied to electromagnetic radiation. Frequency: * __________________________________________________________________ ______________________________________________________________________________ Wavelength: * __________________________________________________________________ ______________________________________________________________________________

Frequency: the number of times a wave of radiation vibrates in one second. Wavelength: the distance traveled forward by a wave as it goes through one complete vibration. (In your own words.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 74. The angle between the path taken by a ray of light before it strikes the surface of a piece of glass and a line perpendicular to that surface is called the * __________________________________.

The angle through which that ray (strictly speaking, the yellow wavelength) is bent as it enters the piece of glass is called the * __________________________________. The angle between the path taken by the ray inside the piece of glass and a line perpendicular to the surface of the glass is called the * __________________________________.

43

angle of incidence angle of deviation angle of refraction

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 75. What is the formula for determining the index of refraction of a substance?

Index of refraction Speed of light in air_____ of the substance = Speed of light in the substance

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 76. In which direction is a ray of light refracted as it passes from air into glass … and from glass into air? From air into glass: * ___________________________________________________________ _____________________________________________________________________________ From glass into air: * ___________________________________________________________ _____________________________________________________________________________

towards a line perpendicular to that surface of the glass. away from a line perpendicular to that surface of the glass.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

44

77. What is the meaning of the term dispersion? * _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

The effect that glass has upon light, to separate white light into it’s separate wavelengths, so that it appears as a spectrum. (In your own words.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

78. Why does dispersion take place in glass? * _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

Because, although all wavelengths of light travel at the same speed in air, the various wavelengths are slowed down to different speeds in glass … therefore the various wavelengths refract by different amounts, and follow diverging paths. (In your own words.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

79. What color visible light refracts the least as it enters glass … and why does it refract less than the other colors? * _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

45

Red light refracts least because it has the longest wavelength of any visible light. Longer wavelengths travel faster in glass than shorter wavelengths. (In your own words.)

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Identify the angles of incidence (with an ‘I’), deviation (with a ‘d’), and refraction (with an ‘r’) in this diagram. Be sure to identify all angles.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *