Light - The Photonic Storm

Sandeep Kar

Light - The TutorialLight - The Tutorial 22

IntroductioIntroductionn Light is a form of energy, which Light is a form of energy, which

helps us to perceive things, using helps us to perceive things, using our visual sense.our visual sense.

Yet, what light actually is, is a Yet, what light actually is, is a question that has concerned question that has concerned scientist, over the years.scientist, over the years.

Though it may seem perplex, yet Though it may seem perplex, yet light actually has a dual nature, light actually has a dual nature, of wave, as well as of particle!!of wave, as well as of particle!!

Seems weird ?? Well lets find Seems weird ?? Well lets find out….out….

In this In this Tutorial Tutorial you’ll learn you’ll learn about…about… What actually is light ?What actually is light ? How light propagates ?How light propagates ? How does reflection and How does reflection and

refraction occur ?refraction occur ? How does spherical mirrors How does spherical mirrors

and lenses, actually work ? and lenses, actually work ? How can light energy, be How can light energy, be

harnessed for good ?harnessed for good ?

Light - The Tutorial 4

On a whole we shall conceptualize…

1) Nature of light.2) Theories put

forward on propagation of light.

3) Reflection & refraction at plane surfaces, using wave theory of light.

Also focusing on……

4) Spherical mirrors and lenses – How do they work

5) Efficient utilization of light energy for the betterment of mankind.

Light - The Tutorial 6

Light – A Big Picture Initially many theories were put forward to the

nature of light. Newton in 1675, formulated that light was made

of small particles called corpuscles, which fly off in space in all directions.

Huygens in 1678,suggested that light consists of periodic disturbances that are transmitted through the medium in the form of waves.

The Huygens theory, though could explain the geometrical optics, but could not explain phenomenon like interference, diffraction etc.

To overcome this anomaly, Maxwell suggested the modern electromagnetic theory of light.

Maxwell’s equation forms the basis of modern optics still today, though other theories like the quantum theory has been proposed.

Lets find out a little more about Maxwell….

Light – A Big Picture

Maxwell’s Equations

Everywhere there was darkness. Then God said:

0B

0tB

c1E

tE

c1J

c4πB

4πE

And there was

light!Well, actually, it was Scottish physicist James Clerk Maxwell in 1865, and those were Maxwells

equations!!

Seems weird ?? May be !!!!

Maxwell’s Equations

Today, we call these disturbances

“electromagnetic radiation.”

According to Maxwell, light is a wave with oscillating electric and magnetic fields perpendicular to each other.

Wavelength A wave must have a unit to measure its length. The wavelength, l, is the distance from one

wavecrest to the next. The wavelength determines the color of the light.

Electromagnetic SpectrumAs wave length changes, so changes the colors and other characters of light.

Eye Sensitivity to ColorHowever

our eyes perceives the sense of each color to a varying degree, and is sensitive the most to green.

REFLECTIONREFLECTION

Reflection Reflection means the retracting back of light

rays, on hitting a surface. Reflection off a flat surface follows a simple

rule: Angle in (incidence) equals angle out Angles are measured from surface

“normal” (perpendicular).surface normal

sameangleincident ray exit ray

Reflection, continued…. Also consistent with “principle of least time” :

Light rays must follow the shortest path, so as to reach the destination point in least time. If going from point A to point B, reflecting

off a mirror, the path traveled is also the most expedient (shortest) route

A

Btoo longshortest path;equal angles

Hall Mirror Useful to think in terms of images

“image” you

“real” you

mirror onlyneeds to be half as

high as you are tall. Yourimage will be twice as far from you

as the mirror.

Plane mirrors

Normal

Angle ofincidence

Angle of reflection

i = - p

Real side Virtual side

Virtual image

Curved mirrors What if mirror isn’t flat?

still follows same rules, with local surface normal Parabolic mirrors have exact focus.

used in telescopes, backyard satellite dishes, etc. also forms virtual image

Questions What is light? What are the different theories on

nature of light? What are their success and drawbacks ? How are they different ?

How does light propagate? What is reflection and how does it

occur? How come curved mirror follow the laws

of reflection ?

REFRACTIONREFRACTION

Refraction Light also goes through some things

glass, water, eyeball, air However, light bends or deviates from its normal

path, due to change in velocity, on moving from a denser to a rarer medium or vice versa. This phenomenon is called refraction.

Light slowing factor called index of refraction glass has n = 1.52, meaning that light travels

about 1.5 times slower in glass than in vacuum water has n = 1.33 air has n = 1.00028 vacuum is n = 1.00000 (speed of light at full

capacity)

Refraction at a plane surface Light bends at interface between

refractive indices bends more the larger the difference in

refractive index can be effectively viewed as a “least

time” behavior get from A to B faster if you spend less

time in the slow medium

n2 = 1.5n1 = 1.0

A

B

Refraction continued…...

1

2

Experts only:n1sin1 = n2sin2

Refraction separates colors….As different constituent colours of white light gets

refracted to different degrees, we see a split up of white light, through a prism.

n2 = 1.5n1 = 1.0

42°

incoming ray hugs surface

Total Internal Reflection….

Reflection and Refraction

1 '1

n1 sin1 n2 sin2

Snells Law

n1

n2

n1 = 1.5 n2 = 1.0

Reflections, Refractive offset Let’s consider a thick piece of glass (n = 1.5),

and the light paths associated with it reflection fraction = [(n1 – n2)/(n1 + n2)]2

using n1 = 1.5, n2 = 1.0 (air), R = (0.5/2.5)2 = 0.04 = 4%

incoming ray(100%)

96%

92% transmitted0.16%

4%

4%

8% reflected in tworeflections (front & back)

image looks displaceddue to jog

Questions What do you think you would see from

underwater looking up at sky? Why do the sides of aquariums look like

mirrors from the front, but like ordinary glass from the sides?

If you want to spear a fish from above the water, should you aim high, right at the fish, or aim low (assume fish won’t move)?

LENSESLENSES

We know… That for mirrors the

following incident occurs….

What happens if we bend the mirror?

i = - p magnification = 1

Concave mirror.Image gets magnified.Field of view is diminished

Convex mirror.Image is reduced.Field of view increased.

Just as with mirrors, curved lenses follow same rules as flat interfaces, using local surface normal

A lens, with front and back curved surfaces, bendslight twice, each diverting incoming ray towardscenterline.

Follows laws of refraction at each surface.Parallel rays, coming, for instance from a specificdirection (like a distant bird) are focused by a convex(positive) lens to a focal point.

Placing film at this point would record an image ofthe distant bird at a very specific spot on the film.Lenses map incoming angles into positions in thefocal plane.

Lenses

Types of lenses:

• Most important simple optical device

• Lenses form images of objects

• Used in glasses, cameras, telescopes, binoculars, microscopes, …

• Converging lenses: thicker in the middle than the outside

• Diverging lenses: Thinner in the middle than the outside

Parallel rays incident on converging lens

• Light rays get refracted by lens, that is: light gets bend by a lens.

• If the rays come in parallel to the principal axis (object at infinity), they will be focused in the focal point.

• focal length f

• focal length is the same on both sides, even if lens is not symmetric. Parallel rays coming in

focus on the focal plane

Converging lens

Parallel rays incident on converging and diverging lenses

• Any lens that is thicker in the center than at the edges will make parallel rays converge to a point and is called a converging lens.

• Any lenses that are thinner in the center are called diverging lenses, because they make parallel rays diverge.

• Focal point of diverging lens: Point were diverging rays seem to be coming from.

Converging Lenses A converging lens uses refraction to bend light rays

Light rays converge after passing a converging lens Rays from a common point on an object converge to a

common point on far side of the converging lens

Real Images An image forms in space on far side of the lens

The image is a pattern of light in space that exactly resembles the object, except for size and orientation

The image is “real” – you can put your hand in it and you can capture it on a screen.

Lenses and Film

Eyes and Retina

Film records the pattern of light it’s exposed to

If you put film in a real image, it will record a pattern of light resembling the object

For a good photograph, the real image should be sharply focused on the film and have the right size

Film or retina

Focusing Light reaching the lens from an object is diverging

The nearer the object, the more its light diverges Converging lens has trouble with diverging light

Real image of nearby object forms farther from lens Real image of distant object forms closer to lens

1 1 1Object distance Image distance Focal length

Focal Length

Focal length measures the lens’ converging ability Long focal length: weak convergence, long image distance Short focal length: strong convergence, short image

distance The larger the object distance, the bigger the image

Long focal length: big images Short focal length: small images

Ray tracing for converging lens to find the image created by the lens

(a) Ray 1 leaves top point on object going parallel to the axis, then goes through focal point.

(b) Ray 2 passes through F’, therefore it is parallel to the axis beyond the lens

(c) Ray 3 passes straight through the center of the lens.

o i

f

ho

hi

fio111

The lens equation

fio111

The lens equation:

1. Draw a ray diagram

2. Solve for unknowns in the lens equation and magnification. Remember reciprocals

3. The height of the image, hi is positive if the image is upright, and negative if the image is inverted relative to the object (ho is always positive).

Magnification:oi

hhm

o

i

ExampleImage formed by a converging lens.

What is the (a) position and (b) size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal lens camera?

o = 100 cm i = ?

ho =

7.6 cm

hi

f = 5 cm

Lens Diameter

Larger lens converges more light brighter image focus becomes more critical less depth of focus

Smaller lens dimmer image focus becomes less critical more depth of focus

Aperture and f-number Aperture characterizes the diameter of the lens F-number is lens focal length (say 35 mm)

divided by lens diameter (adjusted by aperture).

Large f-number (22 or so on lens). Dim image Large depth of field/focus (focus is forgiving)

Small f-number (3.5 or so on lens). Bright image Small depth of field/focus (focus is critical)

Cameras and Projectors Cameras and projectors work the same way:

transfer an image from one plane to another projector translates “film” plane to screen plane camera translates direction into position on film pinhole camera is simplest approach, but low

throughput

Telescopes Telescopes do two things: collect a lot of light across a

big aperture (opening) and cram this light into your eye

magnify angles by ratio of the focal lengths of the main lens/mirror and eyepiece

Come in two generic varieties: refractors, dating back to

Galileo’s time (saw moons of Jupiter)

reflectors, invented by Newton! all big telescopes are reflectors

The Eye Now for our cameras… Eye forms image on retina, where light is

sensed Cornea does 80% of the work, with the lens

providing slight tweaks (accommodation, or adjusting)

Refractive indices:air: 1.0cornea: 1.376fluid: 1.336lens: 1.396

Central field of view (called fovea)densely plastered with receptors forhigh resolution & acuity. Fovea onlya few degrees across.

Questions Why are contacts and corneal surgery (e.g.,

radial keratotomy) as effective as they are without messing with innards of eye?

Why can’t we focus our eyes under water?

Why do goggles help?

Problem: Two plane mirrors make an angle of 90o. How many images are there for an object placed between them?

object

eye

1

2

3

mirror

mirror

Thin Lenses: thickness is small compared to object distance, image distance, and radius of curvature.

Converging lens

Diverging lens

Thin Lens Equation

1f

1p

1i

Lens maker Equation

1f

(n 1)(1r1

1r2

)

What is the sign convention?

Lens Equation for thin Lenses

Sign Convention

p

Virtual side - V Real side - R

i

Light

Real object - distance p is pos on V side (Incident rays are diverging)Radius of curvature is pos on R side.Real image - distance is pos on R side.Virtual object - distance is neg on R side Incident rays are converging)Radius of curvature is neg on the V side.Virtual image- distance is neg o the V side.

r2r1

Rules for drawing rays to locate images

•A ray initially parallel to the central axis will pass through the focal point.

•A ray that initially passes through the focal point will emerge from the lens parallel to the central axis.

•A ray that is directed towards the center of the lens will go straight through the lens undeflected.

SOLVEDSOLVEDEXAMPLESEXAMPLES

1. Given a lens with a focal length f = 5 cm and object distance p = +10 cm, find the following: i and m. Is the image real or virtual? Upright or inverted? Draw 3 rays.

pfi111

m y

y

ip

1i

15

1

10

110

Image is real, inverted.

. .F1 F2p

Virtual side Real side

m 1010

1

i 10 cm

2. Given a lens with the properties (lengths in cm) r1 = +30, r2 = -30, p = +10, and n = 1.5, find the following: f, i and m. Is the image real or virtual? Upright or inverted? Draw 3 rays.

21

1111rr

nf

301

301

30115.11

f

cmf 30

pfi111

151

101

3011

i

cmi 15

m y

y

ip

m 1510

1.5

Image is virtual, upright.

Virtual side Real side

r1. .F1 F2

pr2

3. A converging lens with a focal length of +20 cm is located 10 cm to the left of a diverging lens having a focal length of -15 cm. If an object is located 40 cm to the left of the converging lens, locate and describe completely the final image formed by the diverging lens. Treat each lens separately.

f1

f1

Lens 1 Lens 2

f2

f2

10

40

+20 -15

f1

f1

Lens 1 Lens 2

f2

f2

10

40

+20 -15

Ignoring the diverging lens (lens 2), the image formed by theconverging lens (lens 1) is located at a distance

1i1

1f1

1p1

1

20cm

140cm

. i1 40cm

40

This image now serves as a virtual object for lens 2, with p2 = - (40 cm - 10 cm) = - 30 cm.

30

Since m = -i1/p1= - 40/40= - 1 , the image is inverted

1i2

1f2

1p2

1

15cm

1 30cm

i2 30cm.

Thus, the image formed by lens 2 is located 30 cm to the left of lens 2. It is virtual (since i2 < 0).

f1

f1

Lens 1 Lens 2

f2

f2

10

40

+20 -15

40

30The magnification is m = (-i1/p1) x (-

i2/p2) = (-40/40)x(30/-30)

=+1, so the imagehas the same size orientation as the

object

Utilization Utilization of of

Light EnergyLight Energy

Efficient Utilization of light to solve our energy problems…. Light energy can be converted to various

useful forms to meet our daily energy requirements.

One method of doing so, is converting light energy to electrical form through the use of special converters, called solar cells.

Since each solar cell can convert only a small fraction of light energy, so an array of cells are often used.

Solar Cell As light is a renewable sources of energy, so a

wide usage of solar cell can help us to solve our problem of non renewable energy sources, and make the world a better place to live in.

Light - The TutorialLight - The Tutorial 6666

SummarySummarySo we learnt aboutSo we learnt about : : What is light, and its behavior.What is light, and its behavior. What are mirrors and how do they work.What are mirrors and how do they work. What are lenses and how do they What are lenses and how do they

work.work. How does a telescope workHow does a telescope work What are the ways of utilizing light What are the ways of utilizing light

energy for the betterment of energy for the betterment of mankind.mankind.

Application & Application & Feedback….Feedback….

From now on, I hope you can From now on, I hope you can understand yourself, how does the understand yourself, how does the optical instruments around you work.optical instruments around you work.

Make effort to utilize light energy Make effort to utilize light energy efficiently.efficiently.

How did you like this training session? How did you like this training session? Please give a feedback to your Please give a feedback to your concerned teacher.concerned teacher.

Happy learning Happy learning students……students……

Light - The TutorialLight - The Tutorial 6868

You Can Get More You Can Get More Information from…Information from… Searching Searching google.comgoogle.com on the on the

internet.internet. The Optics BookThe Optics Book - - by Sharon by Sharon

Levine, Leslie JohnstoneLevine, Leslie Johnstone The Scientific Papers of James CThe Scientific Papers of James C

lerk Maxwelllerk Maxwell - - by James Clerk Maxwellby James Clerk Maxwell

Optics and LasersOptics and Lasers - by Matt - by Matt Young Young

Consulting your science teacher.Consulting your science teacher.

BibloigraphyBibloigraphy The Optics BookThe Optics Book - - by by Sharon Sharon

Levine, Leslie JohnstoneLevine, Leslie Johnstone A complete course in ISC A complete course in ISC

PhysicsPhysics – by Dr. V.P. – by Dr. V.P. BhatnagarBhatnagar

A Text book of PhysicsA Text book of Physics, by , by Chittaranjan DasguptaChittaranjan Dasgupta

The InternetThe Internet..

Thank You

Sandeep Kar