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Reflection of Light

 Note: Both the angle of incident and angle of reflection must be measured from the

normal.

Laws of Reflection

1. 

The law of reflection state thata.  The angle of incidence is equal to the angle of reflection; the ray leaves

the surface at the same angle as it arrives.

 b.  The incident ray, the reflected ray and the normal all lie in the same

 plane; all three could be drawn on the same flat piece of paper 

Type of Mirror

Plane MirrorImages in plane mirrors

1.  Figure to the left shows how, by reflecting light, a plane mirror forms an image

of a point source of light such as a small light bulb.

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2.  The image forms in a mirror is

a.  Upright

 b.  Virtual

c.  Laterally inverted

d.  Same size as the object

Steps to draw a ray diagram for an image in a plane mirror

1.  Draw the virtual image.

2.  Draw 2 reflected rays, one from the top of the image to the top of the eye and

the other one form the top of the image from the bottom of the eye.3.  Draw the respective incident rays for the reflected rays you draw in step 2.

(Reflection of light on a plane mirror)

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Curved Mirror

1.  A curve is part of a circle. Therefore

a.  the centre of the circle will also be the centre of the curve and is calledthe centre of curvature, and

 b.  the radius of the circle will be equal to the radius of the curve, called

the curvature radius.

Important Terms

All rays parallel to the principle axis will focus at F

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Centre of curvature, C 

The geometric centre of a hollow sphere of which the concave or convex mirror is a part.

Pole of mirror, P  The centre point on the curved mirror.

Principal axis  A line which passes through the centre of curvature, C and the pole

of a curved mirror, P.

Radius of 

curvature, r 

Distance between the pole, P and the centre of curvature, C.

Principal focus, F  A point through which all rays travelling parallel to the principal

axis converge to or appear to diverge from after reflection by themirror.

Focal length, f   The distance between the principal focus, F and the pole of the

curved mirror, P.

Aperture of mirror  The portion of the surface of the mirror that reflects light.

Object distance, u  Distance of object from the pole of the mirror, P.

Image distance, v  Distance of image from the pole of the mirror,

Rules in Drawing Ray Diagram

Rule No. 1 

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 The ray of light through C will be reflected back through C.

Rule No. 2 

The ray of light parallel to the principal axis will be reflected through F.

Rule No. 3 

The ray of light through F will be reflected parallel to the principal axis.

Rules in Drawing Ray Diagram

Rule No. 1 

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A ray towards C is reflected back along its own path.

Rule No. 2 

A ray parallel to the principal axis is reflected as if it came from F.

Rule No. 3 

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A ray towards F is reflected parallel to the principal axis.

Finding the Position and Size of the Image

1.  Any two rays are sufficient to fix the position and size of the image. Look for 

the point where the rays cross after reflection from the mirror.

2.  The interception of the two rays is the focus of the ray.

Example 

Refraction of Light

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Refraction is the bending of a light ray at the boundary of two medium as the

light ray propagates from a medium to another with difference opticaldensity.

1.  Light rays are bent when they pass at an angle in or out of materials such as

glass and water. The effect is called refraction.

2.  Light passing into an optically denser medium is bent towards the normal;

light passing into an optically less dense medium is bent away from the normal.

3.  Materials such as glass, water and paraffin are said to be optically denser thanair.

The laws of refraction

1.  The incident and refracted rays are on opposite sides of the normal at the point

of incidence, and all three lie in the same plane.

2.  The value of sinisinr  is constant for light passing from one given medium into

another. This is known as Snell's law.

Snell's law states that the value of (sin i) / (sin r) is constant for light passing

from one given medium into another.

sinr sini=constant 

Refractive index

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1.  The value of is called the refractive index of the medium and it gives you an

indication of its light-bending ability.

n=sinisinrn= refractive index

2.  In SPM, when we say “refractive index”, what we mean is the absoluterefractive index of a substance. The absolute refractive index of a substance is the

refractive index where light ray travels from vacuum (or air) into the substance.

Refractive Index and the Speed of light

Refractive index = speed of light in vacuumspeed of light in medium

or n=cv 

( Note that the greater the refractive index of a medium, the lower is the speed of 

light. The more light is slowed, the more it is bent. )

Real and Apparent Depth

1.  The bending of light can give you a false impression of depth.

2.  Figure to the left shows two rays of light leaving a point on the bottom of a

swimming pool.

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3.  The rays are refracted as they leave the water. To the observer, the rays seem

to come from a higher position, and the bottom looks closer to the surface than it

really is.

4.  The real depth of the water and its apparent depth are marked on the diagram.

These are related to the refractive index of the water by the following equation:

Refractive index = real depthapparent depth

or 

n= Dd  

Summary:

Refractive index 

n=sinisinr  

n= Dd  

n=cv 

Bending of Object in a Glass

A straw in a glass with water looks bended or broken. This is due to refraction of light

Shallower Swimming Pool

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A swimming pool appears shallower than it actual is. This is because the light from

the pool is refracted away from the normal when moving from water to the air.

Atmospheric Refraction and Setting sun

The setting sun looks oval in shape because the light from the sun is refracted at

different rate when passes through the atmosphere.

Twinkling Star

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The light of stars is refracted when passes through different region in the

atmosphere. The angle of refraction varies a little from time to time. As a result,

the stars look twinkling. Total Internal Reflection and the Critical Angle

1.  In figure (a) above, the light ray is refracted away from the normal when

moving from denser medium to less dense medium.

2.  Figure (b) shows that, at a specific angle, the light ray is refracted 90o from the

normal. It is refracted so much that it is only just able to leave the water. In such

condition, the incident angle is called the critical angle.

3.  The critical angle is the angle of incident in an optically denser medium for which the angle of refraction is 90°.

4.  In figure (c), the light ray strikes the surface at an angle of incidence greater 

than c. There is no refracted ray; the surface of the water acts like a perfect mirror,

and the ray is said to have been totally internally reflected.

The Equation Relates the Critical angle (c) with the Refractive IndexThe critical angle can be calculated by using the following equation:

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Requirements for Total Internal Reflection to occur.

1.  The light ray must propagate from an optically denser medium to an optically

less dense medium.

2.  The angle of incident must exceed the critical angle.

Mirage

1.  The occurrence of mirage can be explained as follows.2.  The air on the road surface consists of many layers. On a hot day, the air near 

the ground has a low specific heat capacity, hence the temperature increase faster.

3.  The hot air becomes less dense than the cold air higher up.

4.  A ray of light originated from the sky is refracted away from the normal as the

light is travel from denser to less dense air.

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5.  As the air passes through the lower layers, the angle of incidence increases and

the refracted ray is getting further away from the normal.

6.  Finally, at a layer of air close to the road surface, the angle incidence exceeds

the critical angle. Total internal occurs and the light ray bends upward towards the

eye of the observer.

7.  The observer sees the image of the sky and the clouds on the surface of the

road as a pool of water.

Rain Bow

1.  The spectrum of a rainbow is caused by total internal reflection in the water 

droplets.2.  Different angles of total internal reflection produces different colours.

Lenses

1.  There are 2 types of lenses, namely the

a.  Convex lens

 b.  Concave lens

2.  Convex lenses are thickest through the middle, concave lenses are thickest

around the edge, but several variations on these basic shapes are possible, as shown

in figure 1.3.  Light rays passing through a convex or converging lens are bent towards the

 principal axis, whereas rays passing through a concave or diverging lens are bent

away from the principal axis.

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Figure 1: Convex Lenses

Figure 2: Concave Lenses

Important Terms

Optical centre, P   Light passing through the central block emerges in

the same direction as it arrives because the faces of 

this block are parallel. P marks the optical

centreof the lens.

Principle Axis  The principle axis of a lens is the line joining the

centres of of curvature of its surfaces.

Principle focus, F   The principle focus of a lens is the point on the priciple axis to which all rays originally parallel

and close to the axis converge, or from which they

diverge, after passing through the lens.

Focal length, f    The focal length of a lens is the distance between

the optical centre an the principle focus.

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Rays of light can pass through a lens in either direction, so every lens has two

principal foci, one on each side of the optical centre. he Power of a Lens

1.  The power of a lens is defined as the reciprocal of the focal length in unit

meter.

 P =1 f   

Important Note:  f  is in meter 

2.  The unit of power is diopter (D).

3.  The relationship of the power with the thickness and types of lens are shown in the

diagram below. 

Lens  Power of the Lens 

Converging (Convex) Positive

Diverging (Concave) Negative

Thick, with short focal length. High

Thin, with long focal length. Low

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Thinner  – Lower Power  – Longer Focal Length

Thicker  – Higher Power  – Shorter Focal Length

Example:

The power of a lens is labeled as +5D. What is the focal length of the lens (in cm)? Isthis a concave lens or a convex lens?

Answer:

 P =1 f  (+5)=1 ff  =15=0.2m = 20cm 

The power of the lens is positive. This is a convex lens.

Rules for Drawing Ray Diagram for Convex Lenses

1.  A light ray passes through the optical centre of the lens will not be refracted.

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2.  A light ray parallel to the principle axis of the lens will be refracted passes

through the principle focus.

3.  A light ray passes through principle focus will be refracted parallel to the

 principle axis.

Characteristics of the Image Formed by a Convex Lens

1.  As with a curved mirror, the position and size of an image can be found by

drawing a ray diagram.

2.  Any two of the following three rays are sufficient to fix the position and size

of the image.

3.  The characteristics, position and size of the image formed by a convex lens

depends on the object distance (u) relative to the focal length (f)

Position of Object: u > 2f 

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Characteristics of the Image: Real, inverted, diminish

Distance of image: v < 2f 

Position of Object: u = 2f 

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Characteristics of the Image: Real, inverted, same size

Distance of image: v = 2f 

Position of Object: f < u < 2f 

Characteristics of the Image: Real, inverted, magnified

Distance of image: v > 2f 

Position of Object: u = f 

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Characteristics of the Image: -

Distance of image: At infinity

Position of Object: u < 2

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Characteristics of the Image: Virtual, uprigh, magnified

Position of image: at the same side of the objectRules in Drawing Ray Diagram

for Concave Lens

1.  A light ray passes through the optical centre of the lens will not be refracted.

2.  A light ray parallel to the principle axis will be refracted away from the

 principle focus

3.  A light ray moving towards the optical centre will be refracted parallel to the

 principle axis.

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1.  The image formed by a concave lens always has the same characteristics,

namely

a.  virtual

 b.  upright

c.  diminish

2.  Figure below shows the ray diagram for the formation of image of a concave

lens.

The Lens Equation

1.  The following is the lens equation that relates the object distance (u), image

distance (v) and the focal length.

1u+1v=1 f   

2.  When using the lens equation to solve problem, it's important to note the

 positive negative sign of u, v and f.

3.  Table below give the conventional symbol and sign for u, v and f.

Positif   Negatif  

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u Real object Virtual object

v Real image Virtual image

 f   Convex lens Concave lens

Linear Magnification

The linear magnification is a quantity that indicates the ratio of the height of the

image to the height of the object.

m=vu=hiho 

m = linear magnification

u = distance of object

v = distance of image

hi = heigth of image

ho = heigth of objectagnifying Glass

1.  Magnifying glass is also known as simple microscope.

2.  A magnifying glass is a single convex lens with short focal length.

3.  The iage formed is

a.  virtual,

 b.  magnified

c.  upright

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4.  A magnifying glass enlarges the image of an object by increasing the virtual

angle at the eye when the object is viewed.

Angular magnitude and apparent size

1.  The angular magnitude of an object is the virtual angle at the eye. It is the

angle the object subtends at the eye.

2.  This angle determines the size of the image (apparent size) formed on the

retina and hence governs the apparent size of the object

Camera

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Functions

Convex lens  To focus the light of an object onto the film so that a sharp

image can be produced.

Diaphragm  To control the size of the aperture and hence control the

amount of light move into the camera.

Focusing Ring  To adjust the distance between the lens and the film so that the

image is sharply focus on the film.

Film  1.  Acts as a screen for the image to form onto it.

2.  Chemical on it will react when exposed to light and

 produce a photograph.

Shutter  Open when picture is taken to allow light move onto the film.

The shutter speed is the length of time when the shutter is

open. It control the amount of light move onto the film.

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Aperture  Open when picture is taken to allow light move onto the film.

The shutter speed is the length of time when the shutter is

open. It control the amount of light move onto the film.

Note:

1.  The film, which is normally kept in total darkness, contains a light-sensitive

chemical called silver bromide.

2.  When you press the camera button, a shutter in front of the film opens then

shuts again, exposing the film to light for a brief moment only.

3.  Different intensities and colours of light across the image cause varying

chemical changes in the film, which can later be developed, 'fixed', and used in

 printing a photograph.4.  The image formed on the film is

a.  Real

 b.  Inverted

c.  Smaller than the object.

Projector

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Function

Bulb  1.  Bulb with high brightness is used.

2.  The bulb must be placed at the centre of curvature of 

the concave mirror.

Concave mirror  1.  The function of the concave mirror is to reflect and

focus light that shines on it to the direction of the condenser.

2.  This is to increase the brightness of the image.

Condenser  1.  The condenser consists of two Plano-convex lenses.

2.  The function of the condenser is to focus all the light

that brightens the whole slide.

3.  It also acts as a heat insulator to stop heat from the bulb

so it does not spoil the slide.

Slide  1.  The slide acts as the object.

2.  It is located at a distance between f and 2f from the

 projector lens so that the image produced is real and

magnified.

3.  It is purposely placed upside down so that the image

forms on the screen looks upright.

Projector Lens  1.  The projector lens projects the image on the screen thatis placed a few meters away.

2.  It can be adjusted to focus a sharp image.

Image  The image produced is

1.  real (it form on a screen)

2.  magnified

3.  inverted (Since the slide is placed upside down, hence

the image looks upright)

Astronomical Telescope

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Astronomical Telescope 

Objective lens  Lower power 

Eye lens  Higher power 

Position of the

object 

At infinity

Nature of the

image, I1 

Real, inverted and magnified

Position of the

image, I1. 

At the principle focus of object lens, fo.

Nature of the

image, I2 

Virtual, inverted and smaller in size.

Distance in

between the two

lens 

1.  The distance between the object lens and the eye lens in a

compound microscope is equal to the sum of the focal length

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(f o + f e).

2.  If the distance between both lenses are bigger than (f o + f e),

no image can be seen.

Magnification of the compound

microscope. 

m=Focal length of the object lens,  f  oFocal length of the eye lens,  f  m 

Compound Microscope

Compound Microscope Object lens  Higher power 

Eye lens  Lower power 

Position of 

the object 

The object is placed at a position between fo and 2fo.

Nature of  Real, inverted and magnified

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the image,

I1 

Position of 

the image,

I1. 

The first image, I1 must be placed between the optical center of the eye

lens with the eye lens principle focus point, fe.

Nature of 

the image,

I2 

Virtual, inverted and magnified

Distance in

between the

two lens 

The distance between the object lens and the eye lens in a compound

microscope is bigger than the sum of the focal length (f o + f e).

If the distance between both lenses are adjusted to less than (fo + fe), no

image can be seen.

Magnification of the

compound

microscope. 

m=m1×m2 =Height of first image ,  I 1Height of object×Height of secondimage, I 2Height of first image ,  I 1 =Height of second image,  I 2Height o

f object

m1 = Linear magnification of the object lens

m2 = Linear magnification of the object lens