II.B.71Optics: Refraction

Optics began with the development of lenses by the ancient Egyptians and Mesopotamians. The earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. Refractive surgery is being well publicised as the modern way to reduce your dependence on glasses or contacts. This type of surgery includes several procedures for permanently lessening or possibly even eliminating myopia. All are intended to reduce the cornea's optical power to achieve normal or near-normal focus. It’s easy to overlook your eyes. Most people agree that sight is the sense they rely on most. Despite this, taking care of our eye health is usually an afterthought, or worse, something we take for granted.

Have you ever noticed that objects seem to bend when they are put into water? This is because as they travel from medium to medium the speed of light actually changes. One side of wave front slows down, and the entire train of fronts twists.

Figure: 10.1

The change in direction of a wave as it crosses the boundary between two mediums in which waves travel at different speeds. Refraction can occur when light travels through one medium into another. Light travelling from air and going into water would be an example.

Note Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics. When considering light's particle-like properties, the light is modelled as a collection of particles called "photons". Quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields,

photography, and medicine (particularly ophthalmology and optometry). Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. The speed of the light ray changes upon changing mediums. In almost every case the direction of the light ray changes also. We will often describe the light beam as bending toward the normal or away from the normal. The following picture, much like the one directly above, shown.

Figure: 10.2

Light bending toward the normal: Again, this is the general behaviour for light going from air into water or glass. Notice that in these conditions the angle of refraction is smaller than the angle of incidence. Light bending away from the normal: This would be the general behaviour for light going from water or glass into air. Notice that in these conditions the angle of refraction is larger than the angle of incidence.

Refraction In refractions when light ray enters form one medium to

another, its frequency remains unchanged.

Snell’s law 2

1

sin

sin

i

r

1 11 2

2 2

Deviation caused by refraction i r

2 1

2 1

1,

1 3

2 31 2

Normal

Angle of incidence

Angle of

refraction

Normal Angle of

incidence

Angle of

refraction

"Bending toward the normal." "Bending away from the normal."Angle of

incidence

Nor

mal

Air

Water Angle of refraction

Optics: Refraction10

Lateral shift

Figure: 10.3

Lateral shift sin( )

cos

t i rx

r

real depth

apparent depth

t

t x

apparent shift 1

1x t

Refractive index ari

medium

c

If a beaker contains various immiscible liquids as shown then

Apparent depth of bottom 31 2

1 2 3

....dd d

1 2combination

1 2.

1 2

.....

....

AC

App

d d dd dd

(In case of two liquids if 1 2d d than 1 2

1 2

2

)

Figure: 10.4

Refraction at spherical surface: 2 1 2 1

u R

Formula for refraction through a thin lens

1 21 2

1 1 11

f R R

(Proper signs of 1R and 2R are to be

used)

Special Cases For a double convex lens,

1 2

1 2

1 1 11

f R R

For a double concave lens

1 2

1 2

1 1 11

f R R

If media on two sides of lens are different then,

3 3 22 1

1 2f R R

Formation of image by a lens 1 1 1

f u

Lateral magnification, I f

mO u u f

Axial magnification 22

2x

fm

u u f

Power of lens 1

(in meter)P

f Diopter

Equivalent focal length:

Lenses in contact 1 2

1 1 1

F f f

1 2

1 2

f fF

f f

or 1 2P P P

Lenses at separation:1 2 1 2

1 1 1 1

F f f f f

1 2

1 2

f fF

f f d

1 2 1 2P P P dPP

Special cases

If 1,a g a the nature of lens remains unchanged; but

focal length changes.

If 1,a g a the nature of lens changes.

If 1 1,a g a f and lens behaves as a plate.

The simplest kind of lens is actually a prism. A prism is a piece of glass shaped like a triangle and bends light towards its thickest part (the bottom of the “triangle”), which is called the base. The thinnest part of a lens is called the apex. Not all lenses are prisms, but any lens can be thought as two rounded prisms joined together.

Figure: 10.5

Plano-

Convex lens

Double-

Convex lens

Concavo-

Convex lens

Convexo-

Concave lens

Plano-

Convex lens

Double-

Convex lens

d1

d2

d3

1

2

3

Air

Water

Point

Real depth

Apparent depth

Image of point

Signs of R1 and R2 have been

used

Convex Lenses

Figure: 10.6

Convex Lenses used as Magnifiers

Convex Lenses used as Magnifiers

Concave Lenses

De-Magnifier: Concave Lens is Inverse of Convex Lens.

Formation of image by convex lens:

Figure: 10.7

Table: 10.1

Position of

object

Position of

image

Size of image Nature of image

At infinity At focus Point size Real and inverted

Beyond 2F Between F and

2F

Smaller in size Real and inverted

At 2F At 2F Same size Real and inverted

Between F and

2F

Beyond 2F Bigger in size Real and inverted

At F At infinity Bigger in size Real and inverted

Between

optical centre

C and F

On the same side

as is the object

Bigger in size Virtual and erect

Formation of image by concave lens:

Figure: 10.8

Table: 10.2

Position of object

Position of image Size of image Nature of image

Anywhere One the same side between optical centre C and F

Smaller in size Virtual and erect

Ray Optics or Geometrical Optics

Snell’s law of refraction: 1 1 2 2sin sinn n

Critical angle of total reflection 1c , 21sin c

n

n

Linear magnification:0

i hM

h

Image size: h

Object size: h Object inside focal length

Common Gaussian form of

lens equation: 1 1 1

0 i f

O

f

i

Object outside focal length

2F1 F1 0

F2 2F2

Object at F

Image at infinity

2F1 F1 0

F2 2F2

Object between F and 2F

Image on the same side behind object

Object between F and 2F

Image beyond 2F

2F1 F1 0

F2 2F2

2F1 F1 0

F2 2F2

2F1 F1

0 F2 2F2

2F1 F1 0

F2 2F2

Object beyond 2F

Image between F and 2F

Object at infinity

Image at F

Object at 2F

Image at 2F

O i

f f

h'

h

Object size

Imagesize

P 1/f (f in meters)

Common Gaussian form of

lens equation: 1 1 1

O i f

Linear magnification: i h

MO h

Diverging lens (concave lens) Focal point

Parallel rays from distant object

Diverging lens Converging lens

Second lens under what the first one did.

F

Diverging lens Virtual

Object

F F

Glass

Normal Normal

Incident light

Converging lens (convex Lens)

Parallel rays from distant object

Focal point

Figure: 10.9 Minimum Deviation in Prism

Figure: 10.10

1 2 1i i

2m i

sin sin

2 2

mn

Optical Instruments Angular magnification of a magnifying glass

Ff

distance of clear vision and

f focal length

Microscope:

Angular magnification 1 2

Ff f

Limit of resolution: 1.2

2 sinrs n

Figure: 10.11

n refractive index of medium in front of objective

2 aperture angle according to figure

Total Internal Reflection

Figure: 10.12

For total internal reflection ray must pass from denser to

rarer medium and the angle of incidence in denser medium must be grater than critical angle. The cirtical angle is given

by sin 1rarerd r

denser

C

A fish or diver in water at depth ‘h’ sees outside world in horizontal circle (at surface or water) or radius

2tan

1

hr h C

Area of horizontal circle, 2

22 1

hA

Refraction at Sunset

Figure: 10.13

The sun actually falls below the horizon, i.e., it "sets", a few seconds before we see it set. Flattening of the Sun at Sunset: Rays from top of sun are also refracted, but not as much because they enter the atmosphere at a less oblique angle. Thus, the top of the sun is also flattened, but not as much as the bottom. Light from the sun can reflect off the still surface of a lake to produce a mirror-like reflection. At the same time, the water can absorb light, transforming the light energy into thermal energy. The water warms during the day and cools off at night. If you are looking down into the water form shore, you might be uncertain about the location of objects on the bottom. This happens because light is refracted as it travels from water into the air.

OO

Light striking a medium with a lower index of refraction can be totally reflected

n1 High index

material Critical Angle c

Light

c

n2

Light incident at

any angle > c is totally reflected

Reflection and transmission coefficients for non-normal incidence can be calculated form the Fresnel equations.

The ray normal to the surface is not bent.

Normal reflection coefficient

Through not bent, part of the normal ray is reflected.

n

f1 f2

Fast medium (smaller

index of refraction)

Show medium

1

2

n1 n2

Slit source Fabry-perot

Etalon Prism R

GB

RedGreen Blue

Figure: 10.14

All rays reflect internally, but the top three rays reflect only a small percentage internally; most energy leaves the prism. The 4th and 5th rays are reflected 100% internally. Critical angle is 48 degrees. Any ray, which strikes the surface from inside the water at an angle greater than 48 degrees, will not escape the water.

Figure: 10.15

The View from Below the Water

Figure: 10.16

Rays A, B, and C from the bottom of the pond are totally

internally reflected. Outside the 96 cone, the fish sees only

light reflected from the bottom.

Internal Reflections in Diamond

The critical angle for diamond in air is 24.5; any ray, which

strikes the surface on the inside at an angle of greater than

24.5, will not escape the diamond.

Figure: 10.17

Refraction through a Prism:

Figure: 10.18

1 2

1 2

r r Ai i A

A Angle of prism

and deviation caused by a prism

1 2

1 2

sin sin

sin sin

i i

r r

At position of minimum deviation. the ray travelling in prism is parallel to its base and refractive

index1sin

2

sin2

mAi

A

For maximum deviation either 1 90i or 2 90i

For thin prism: ( 1)m A

Angular dispersion: 0( )r r A

Mean deviation, 1y y A

Dispersive power

angular dispersion

mean deviation

1r r

y y

The prism is total reflecting if A > 2C, C critical angle

A hollow prism causes no dispersion.

Film Projectors

Figure: 10.19

Bulb Object (upside down) Real image

Scr

een

Only a real image (light energy) can be formed on a projector screen

N1N2

H

R Q

E N

A

P

F Gr2r1

i2 or e i1

2 2i r 1 1i r

m

Angle of incidence i

Ang

le o

f de

viat

ion

Entering light Critical angle

Fish sees outside worldinside 96 degree cone.

dark dark

Prism 1

2

3

4

5

1

2

3

2 3 4 1 5

96A B C

Camera Film Image

Figure: 10.20

Aberration: aA departure from the expected or proper course. Spherical mirrors have an aberration. There is an intrinsic defect with any mirror, which takes on the shape of a sphere. This defect prohibits the mirror from focusing the entire

Figure: 10.21

incident light from the same location on an object to a precise point. The defect is most noticeable for light rays striking the outer edges of the mirror. Light rays striking the edges of the mirror fail to focus at that same point. The result is that the images of objects as seen in spherical mirrors are often blurry. Spherical aberration is most commonly corrected by use of a mirror with a different shape. Usually, a parabolic mirror is substituted for a spherical mirror. In Chromatic Aberration different colors refract by different amounts.

Human Eye and Optical Instruments

Figure: 10.22

Distance of distinct vision D 25

In myopia, the corrective lens is concave lens of focal length = far point of defective eye.

In hypermetropia, the corrective lens is convex lens, whose

focal length is u

fu

where u = – D = – 25 cm, v = near point of defective eye. In presbyopia, the corrective lens is bifocal lens. In astigmation, the corrective lens is cylindrical lens with

proper axis.

Microscope Simple microscope: It uses only one convex lens of small

focal length. Magnification / 1 /M D f for final

image at D and M D/f for relaxed eye. If eye is placed at a

distance d then, final image will be at D. Compound microscope: It uses two convex lenses;

objective is of small focal length and eyepiece of large focal length.

Magnification, 0 eM m m 0

0 e

D

u f

or 0 e

L D

f f for

relaxed eye 0

0

1e

D

u F

or

0

1e

L D

f f

for final image at D; where L tube-length of microscope.

Figure: 10.23

Objective Eyepiece

Objective

fo fe fe

Fe I1 I2 Fo Fe

Myopia/Near sightedness corrected by a negative lens (concave) to reduce

refractive power

Hyperopia/Farsightedness corrected by a positive lens (covex) to add

refractive power

Astigmatism corrected by an asymmetric lens to compensate for the

asymmetry of the eye’s lens

Spherical Aberration

F

Spherical aberration

Chromatic Aberration

Violet Red

RedViolet

Object

Film

Real image (inverted)

Figure: 10.24

Astronomical Telescope Astronomical Telescope uses two convex lenses, objective is of large focal length and eye-piece of small focal length.

Magnification, 0

e

fM

f for relaxed eye 0 1 e

e

f f

f D

for

final image at D.

Length of telescope 0 eL f f for relaxed eye 0 ef u for

final image at D.

Terrestrial telescope: If the telescope is in near point

adjustment, magnifying power 0 01e

f fm

f D

Length of the telescope, 0 4 .eL f f u Where, f is the focal

length of the erecting lens.

If the telescope is in far point adjustment, magnifying power

0

e

fM

f

Length of he telescope, 0 4 eL f f f 0 ..ef f f

The final image is virtual, erect and appears to be magnified.

Figure: 10.25

Objective

fo

Fo

2f 2f

Fe Fe

Objective Inverting lens Eyepiece

Erect virtual image at

fe fe

Interpupillary Adjustment

Eyepieces

Eyepiece

Trinocular Head

Arm

Stage Stop

Adjustment

Slide Holder

Coaxial Course &

Fine Focus

Nosepiece Turret

Objectives

Mechanical Stage

Condenser

Filter Holder

Iris Diaphragm

X-Y Coaxial Stage control

Illumination system

Base Illumination Intensity Knob

Telescope

Figure: 10.26 Astronomical Telescope

Optical Fibres

Figure: 10.27

On total internal reflection principle optical fibres works.

Optical fibres are used in communication systems and micro-

surgeries. Since total internal reflection takes place within the

fibres, no incident energy is ever lost due to the transmission of

light across the boundary.

The intensity of the signal remains constant. Using fibre optics,

physicians are able to look inside the body with very little

invasive effect. The fiber the doctors insert is surrounded by

additional fibres that carry light down to the end.

Optical fiber

Dew shield

Main tube

Cradle

Finderscope

Eyepiece

Eyepiece holder

Star diagonal

Focusing knob

Tripod

Counterweight

Azimuth fine adjustment

Altitude fine adjustment

Right ascension setting scale

Altitude clamp

Azimuth clamp

Declination setting scale

Tripod accessories shelf

Optical Fibres in Medicine

Figure: 10.28

Water Mirage

Figure: 10.29

Internal Reflections in Prisms

Figure: 10.30

Prisms in Binoculars

Figure: 10.31

Arthroscopic Surgery Bronchoscope Colonoscope Eclipses Eclipses have long been a source of mystery and spectacle. These events were viewed with fear and dread in the past. Eclipses occur when the Sun, the Earth and the Moon line up.

One consequence of the Moon's orbit about the Earth is that the Moon can shadow the Sun's light as viewed from the Earth, or the Moon can pass through the shadow cast by the Earth. The former is called a solar eclipse and the later is called a lunar eclipse.

Solar Eclipse The shadow cast by the Moon can be divided by geometry into the completely/full shadowed umbra and the partially shadowed penumbra.

Figure: 10.32

Lunar Eclipse The Earth casts a shadow that the Moon can pass through. When this happens we say that a lunar eclipse occurs. Just as for solar eclipses, lunar eclipses can be partial or total, depending on whether the light of the Sun is partially or completely blocked from reaching the Moon; the Moon lying in the umbra of the Earth's shadow. Earth's two shadows are the penumbra and the umbra.

Figure: 10.33

Example 1. Why do stars twinkle but not the planets? Solution: The density of the atmosphere is not uniform as it goes on decreasing with the distance from the earth. The rays coming from the distant stars have to pass through the various mediums in which the light gets refracted due to the variation of densities. Also the atmosphere in the earth is not stationary due to which the position of the star changes much faster from the earth. Hence, the change in the position of the star creates the twinkling of the star. But the distance betweens the planet and the earth is much more less than the distance between the earth and the star. So, there is negligible change in the position of the planet from the earth due to which it does not appear to be twinkling at the sky.

Sun

Lunar ecllpse Moon

Partial shadow

Full shadow

Earth

Sun

Moon Solar eclipse

Moon

Moon Moon

90 degrees 180 degrees

Observer Cool air

Warm air

Bent rays travelling through cool and warm air

Virtual image seen by eye

Example 2. Why does a crack in glass plane appear shining

when viewed from a suitable direction?

Solution: In a crack glass, the air replaces the cracked

volume. When it is observed from the suitable direction, the

light of it has to pass from two medium from the glass to the

air i.e. from the denser to the rarer medium. During their

journey they make incidence angle greater than the critical

angle due to which the total internal reflection process occurs.

Hence these rays appeared to be shining when viewed from

suitable directions. So, crack appears to shine.

Example 3. If you see a fish in clear water, how should you

aim to shoot it? Explain.

Solution: As the light rays coming from a fish passes through

two medium i.e. from denser to rarer medium. As the light

passes from denser to rarer medium, according to the law of

refraction, it goes away from the normal. Due to this the fish

appear to be nearer to the surface i.e. it appears in its apparent

position. In order to shoot it we should aim at a position below

than the apparent position which is the actual position of the

fish.

Example 4. Why does a diamond sparkle with a great

brilliancy?

Solution: The refractive index of the diamond is very high and

the faces of the diamond are cut in such a way that when a

light enters into it, the angle of incident is always greater than

the critical angle, which results in the multiple total internal

reflection. So, due to this the diamond sparkles with great

brilliancy.

Example 5. Why does a clear pool of water appear to be

shallower than it actually is?

Solution: Due to the refraction of light, the light rays coming

from the bottom of the pool bends away from the normal.

Hence the light rays actually coming from the depth of the

pool appears as coming from the lower depth than actual

depth. So, the depth of the pond appears slightly raised due to

which a clear pool of water appear to be shallower than it

actually is.

Example 6. How does the refraction affect the length of the

day?

Solution: If there is no atmosphere on the earth surface, the

length of the day decreases by 4 minutes i.e. 2 minutes in

morning and 2 minutes in evening. Hence, Due to refraction of

light through the atmosphere, the length of the day increases

by 4 minutes.

Example 7. A coin placed at the bottom of a beaker containing

water seems to be raised. Explain why?

Solution: When light rays of a coin from the bottom of water

is observed by the observer in the air then the presence of the

two media results in the refraction of the light. When light rays

travel from the water (denser medium) to air (rarer medium),

bends away from the normal. So, the refracted rays coming

from a coin is observed at its apparent position rather than its

real position. Hence, a coin placed at the bottom of a beaker

containing water seems to be raised.

Example 8. Why does the sun look a little oval when it is at

the horizon?

Solution: The refraction of the light due to the variation in the

density of the air in the atmosphere is the main cause for the

oval shape of the sun when it is at the horizon. The magnitude

of refraction increases with decreasing the altitude. As a result

of which the lower portion of the sun are raised much than the

upper position. So, the vertical diameter is shortened more than

its horizontal diameter. Hence the sun acquires the oval shape

at the horizon.

Example 9. Swimming pools are always deeper than they

look. Why?

Solution: When the swimming pool is observed, the light rays

of the foot of the pool have to pass through the two medium

from water to air i.e. from denser to rarer medium. As they

passes from denser to rarer medium, it goes away from the

normal. Hence the original or real depth of the pool is

observed at its apparent position where it is raised. So,

swimming pools are always deeper than they look.

Example 10. The sun is visible a even before the actual

sunrise and after actual sunset. Explain.

Solution: The density of air decreases as the distant is

increased from the earth in the atmosphere. The magnitude of

refraction increases with decrease in the height. Due to this,

the lower portion of the sun at the time of sunset and sunrise

are raised more than the upper portion. So, the vertical

diameter of the sun is shortened more than the horizontal

diameter. As a result, the sun is visible a even before the actual

sunrise and after actual sunset.

Multiple Choice Questions

1. To an observer on the earth the stars appear to twinkle. This can be ascribed to

a. The fact that stars do not emit light continuously b. Frequent absorption of star light by their own

atmosphere c. Frequent absorption of star light by the earth's

atmosphere d. The refractive index fluctuations in the earth's

atmosphere

2. The ratio of the refractive index of red light to blue light in air is:

a. Less than unity b. Equal to unity c. Greater than unity d. Less as well as greater than unity depending upon the

experimental arrangement

3. The refractive index of a piece of transparent quartz is the greatest for

a. Red light b. Violet light c. Green light d. Yellow light

4. The refractive index of a certain glass is 1.5 for light whose wavelength in vacuum is 6000 Å. The wavelength of this light when it passes through glass is:

a. 4000 Å b. 6000 Å c. 9000 Å d. 15000 Å

5. When light travels from one medium to the other of which the refractive index is different, then which of the following will change?

a. Frequency, wavelength and velocity b. Frequency and wavelength c. Frequency and velocity d. Wavelength and velocity

6. A rectangular tank of depth 8 metre is full of water

( 4 /3), the bottom is seen at the depth

a. 6 m b. 8/3 m c. 8 cm d. 10 cm

7. A vessel of depth 2d cm is half filled with a liquid of

refractive index 1 and the upper half with a liquid of

refractive index 1. The apparent depth of the vessel

seen perpendicularly is:

a. 1 2

1 2

d

b. 1 2

1 1d

c. 1 2

1 12d

d. 1 2

12d

8 A beam of light is converging towards a point I on a screen. A plane glass plate whose thickness in the

direction of the beam ,t refractive index , is

introduced in the path of the beam. The convergence point is shifted by

a. 11t

away b.

11t

away

c. 1

1t

nearer d.

11t

nearer

9. Light travels through a glass plate of thickness t and having refractive index n. If c is the velocity of light in vacuum, the time taken by the light to travel this thickness of glass is:

a. t

nc b. tnc c. nt

c d. tc

n

10. When a light wave goes from air into water, the quality that remains unchanged is its

a. Speed b. Amplitude c. Frequency d. Wavelength

11. Light takes 8 min 20 sec to reach from sun on the earth. If the whole atmosphere is filled with water, the light will

take the time ( 4 /3).a w

a. 8 min 20 sec b. 8 min c. 6 min 11 sec d. 11 min 6 sec

12. If the speed of light in vacuum is / sec,C m then the

velocity of light in a medium of refractive index 1.5

a. is 1 .5 C b. is C

c. is1.5

C d. can have any velocity

13. On a glass plate a light wave is incident at an angle of 60°. If the reflected and the refracted waves are mutually perpendicular, the refractive index of material is:

a. 3

2 b. 3 c. 3

2 d.

1

3

14. Refractive index of glass is 3

2 and refractive index of

water is 4.

3 If the speed of light in glass is 82 .0 0 1 0

m/s, the speed in water will be

a. 82.67 10 /m s b. 82.25 10 /m s

c. 81.78 10 /m s d. 81.50 10 /m s

15. A mark at the bottom of a liquid appears to rise by 0.1 m. The depth of the liquid is 1 m. The refractive index of the liquid is:

a. 1.33 b. 9

10 c. 10

9 b. 1.5

16. A man standing in a swimming pool looks at a stone lying at the bottom. The depth of the swimming pool is h. At what distance from the surface of water is the image of the stone formed (Line of vision is normal; Refractive index of water is n)

a. h

n b. n

h c. h d. hn

17. On heating a liquid, the refractive index generally a. Decreases b. Increases or decreases depending on the rate of heating c. Does not change d. Increases

18. A ray of light passes through four transparent media with

refractive indices 1 2 3, , and 4 as shown in the

figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have

a. 1 2 b. 2 3 c. 3 4 d. 4 1

19. Which of the following statement is true? a. Velocity of light is constant in all media b. Velocity of light in vacuum is maximum c. Velocity of light is same in all reference frames d. Laws of nature have identical form in all reference

frames

20. A ray of light is incident on a transparent glass slab of refractive index 1.62. The reflected and the refracted rays are mutually perpendicular. The angle of incidence is :

a. 58 .3 b. 5 0 c. 5 3 d. 3 0

21. The mean distance of sun from the earth is 81.5 10 Km

(nearly). The time taken by the light to reach earth from the sun is:

a. 0.12 min b. 8.33 min c. 12.5 min d. 6.25 min

22. Speed of light is maximum in a. Water b. Air c. Glass d. Diamond

23. Finger prints on a piece of paper may be detected by sprinkling fluorescent powder on the paper and then looking it into

a. Mercury light b. Sunlight c. Infrared light d. Ultraviolet light

24. Critical angle of light passing from glass to air is minimum for

a. Red b. Green c. Yellow d. Violet

25. A fish is a little away below the surface of a lake. If the

critical angle is 4 9 , then the fish could see things

above the water surface within an angular range of °

where

a. 49 b. 90 c. 98 d. 124

2

26. A cut diamond sparkles because of its a. Hardness b. High refractive index c. Emission of light by the diamond d. Absorption of light by the diamond

27. A diver in a swimming pool wants to signal his distress to a person lying on the edge of the pool by flashing his water proof flash light

a. He must direct the beam vertically upwards b. He has to direct the beam horizontally c. He has to direct the beam at an angle to the vertical

which is slightly less than the critical angle of incidence for total internal reflection

d. He has to direct the beam at an angle to the vertical which is slightly more than the critical angle of incidence for the total internal reflection

28. The phenomenon utilised in an optical fibre is : a. Refraction b. Interference c. Polarisation d. Total internal reflection 29. The refractive index of water is 4 / 3 and that of glass is

5/3. What will be the critical angle for the ray of light entering water from the glass

a. 1 4sin

5 b. 1 5

sin4

c. 1 1sin

2 d. 1 2

sin1

30 Total internal reflection is possible when light rays travel a. Air to water b. Air to glass c. Glass to water d.Water to glass

Air

Water

A

B C

1 2 3 4

D

31. A lens of power +2 diopters is placed in contact with a lens of power –1 diopter. The combination will behave like

a. A convergent lens of focal length 50 cm b. A divergent lens of focal length 100 cm c. A convergent lens of focal length 100 cm d. A convergent lens of focal length 200 cm

32. A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination is:

a. – 1.5 D b. – 6.5 D c. + 6.5 D d. + 6.67 D

33. A converging lens is used to form an image on a screen. When upper half of the lens is covered by an opaque screen

a. Half the image will disappear b. Complete image will be formed of same intensity c. Half image will be formed of same intensity d. Complete image will be formed of decreased intensity

34. A thin convex lens of focal length 10 cm is placed in contact with a concave lens of same material and of same focal length. The focal length of combination will be:

a. Zero b. Infinity c. 10 cm d. 20 cm

35. A convex lens of crown glass (n=1.525) will behave as a divergent lens if immersed in

a. water (n =1.33) b. a medium of n = 1.525 c. carbon disulphide n =1.66 d. it cannot act as a divergent lens

36. A divergent lens will produce a. Always a virtual image b. Always real image c. Sometimes real and sometimes virtual d. None of the above

37. The minimum distance between an object and its real image formed by a convex lens is:

a.1.5 f b. 2 f c. 2.5 f d. 4 f

38. An object is placed at a distance of 20 cm from a convex lens of focal length 10 cm. The image is formed on the other side of the lens at a distance of:

a. 20 cm b. 10 cm c. 40 cm d. 30 cm

39. A lens behaves as a converging lens in air and a diverging lens in water. The refractive index of the material is:

a. Equal to unity b. Equal to 1.33 c. Between unity and 1.33 d. Greater than 1.33

40. The focal length of convex lens is 30 cm and the size of image is quarter of the object, then the object distance is:

a. 150 cm b. 60 cm c. 30 cm d. 40 cm

41. Two thin lenses of focal lengths 1f and 2f are in contact.

The focal length of this combination is:

a. 1 2

1 2

f f

f f b. 1 2

1 2

f f

f f c. 1 2

1 2

2 f f

f f d. 1 2

1 2

2 f f

f f

42. At what distance from a convex lens of focal length 30 cm, an object should be placed so that the size of the image be 1/2 of the object

a. 30 cm b. 60 cm c. 15 cm d. 90 cm

43. When light rays from the sun fall on a convex lens along a direction parallel to its axis?

a. Focal length for all colours is the same b. Focal length for violet colour is the shortest c. Focal length for yellow colour is the longest d. Focal length for red colour is the shortest

44. A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is 2/3. Their equivalent focal length is 30 cm. What are their individual focal lengths

a. – 75, 50 b. – 10, 15 c. 75, 50 d. – 15, 10

45. The refractive index of a material of a prism of angles 45°– 45° – 90° is 1.5. The path of the ray of light incident normally on the hypotenuse side is shown in:

a. b.

c. d.

46. A far sighted man who has lost his spectacles, reads a book by looking through a small hole (3–4 mm) in a sheet of paper. The reason will be

a. Because the hole produces an image of the letters at a longer distance

b. Because in doing so, the focal length of the eye lens is effectively increased

c. Because in doing so, the focal length of the eye lens is effectively decreased

d. None of these

47. For a normal eye, the least distance of distinct vision is: a. 0.25 m b. 0.50 m c. 25 m d. Infinite

B C

A

45° 45°

90°

B C

A

45° 45°

90°

B C

A

45° 45°

90°

B C

A

45° 45°

90°

48. For the myopic eye, the defect is cured by;

a. Convex lens b. Concave lens

c. Cylindrical lens d. Toric lens

49. Lens used to remove long sightedness (hypermetropia) is:

or

A person suffering from hypermetropia requires which

type of spectacle lenses

a. Concave lens b. Plano-concave lens

c. Convexo-concave lens d. Convex lens

50. Image is formed for the short sighted person at

a. Retina

b. Before retina

c. Behind the retina

d. Image is not formed at all

51. A presbyopic patient has near point as 30 cm and far point

as 40 cm. The dioptric power for the corrective lens for

seeing distant objects is:

a. 40 D b. 4 D

c. – 2.5 D d. 0.25 D

52. An imaginary line joining the optical centre of the eye

lens and the yellow point is called as

a. Principal axis b. Vision axis

c. Neutral axis d. Optical axis

53. The light when enters the human eye experiences most of

the refraction while passing through

a. Cornea b. Aqueous humour

c. Vitrous humour d. Crystalline lens

54 The impact of an image on the retina remains for

a. 0.1 sec b. 0.5 sec c. 10 sec d. 15 sec

55. A person is suffering from myopic defect. He is able to

see clear objects placed at 15 cm. What type and of what

focal length of lens he should use to see clearly the object

placed 60 cm away

a. Concave lens of 20 cm focal length

b. Convex lens of 20 cm focal length

c. Concave lens of 12 cm focal length

d. Convex lens of 12 cm focal length

56. The sensation of vision in the retina is carried to the brain

by:

a. Ciliary muscles b. Blind spot

c. Cylindrical lens d. Optic nerve

57. When the power of eye lens increases, the defect of vision

is produced. The defect is known as

a. Shortsightedness b. Longsightedness

c. Colourblindness d. None of these

58. A man is suffering from colour blindness for green

colour. To remove this defect, he should use goggles of

a. Green colour glasses b. Red colour glasses

c. Smoky colour glasses d. None of these

59. In human eye the focussing is done by

a. To and fro movement of eye lens

b. To and fro movement of the retina

c. Change in the convexity of the lens surface

d. Change in the refractive index of the eye fluids

60. The human eye has a lens which has a

a. Soft portion at its centre

b. Hard surface

c. Varying refractive index

d. Constant refractive index

ANSWERS

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

d a b a d a b a c c

11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

d c b b c a a d b a

21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

b b d d c b c d a c

31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

c a d b c a d a c a

41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

b d b d a c a b d b

51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

c b a a a d a d c c

SOLUTIONS

2. (a) blue redµ µ>

3. (b) 1

,r v

µ λ λλ

∝ >

4. (a) airmedium

60004000

1.5Å

λλ

µ= = =

5. (d) Velocity and wavelength change but frequency

remains same.

6. (a) 8

64 / 3

hh m

hµ ′= ⇒ = =

′

7. (b) 1 2

1 2 1 2

1 1d dh d

8. (a) Normal shift 1

1x t

and shift takes place in

direction of ray.

9. (c) distance

time speed /

t nt

c x c

10. (c) Let and represents frequency and wavelength of

light in medium respectively.

So, /

/

v c c

11. (d) a w

w a

c t

c t

25 4 111 11

3 9 9wt min 6 sec

12. (c) 1.5m

m

C CC

C

13. (b) From figure 60 , 30o oi r

So, sin60

3sin30

14. (b) 1

v

g w

w g

v

v

8

3 / 2

4 / 3 2 10wv

82.25 10 /wv m s

15. (c) Real depth 1m

Apparent depth 1 0 .1 0 .9 m

Refractive index Real depth

Apparent depth

1 10

0.9 9

16. (a) ''

h hh

h n

17. (a) Refractive index

1

Termperature

18. (d) For successive refraction through different media

sin constant.

Here as is same in the two extreme media, 1 4.

19. (b) Velocity of light is maximum in vacuum.

20. (a) tan i

1 1tan tan 1.62 58.3i

21. (b) 8 3

8

1.5 10 10500sec 8.33min.

3 10

st

22. (b) 1

,v

is smaller for air than water, glass and

diamond.

24. (d) 1

sina g C

1sin

a g

C

As for violet colour is maximum, so sin C is minimum

and hence critical angle C is minimum for voilet colour.

25. (c) From figure given in question 2 9 8 .c

26. (b) Due to high refractive index its critical angle is very

small so that most of the light incident on the diamond is

total internally reflected repeatedly and diamond sparkles.

27. (c) When incident angle is greater than critical angle, then

total internal reflection takes place and will come back in

same medium.

29. (a) 1

sinw g C

5/3 1

4 /3 sing

w C

14 4sin sin

5 5C C

30. (c) Total internal reflection occurs when light ray travels

from denser medium to rarer medium.

31. (c) 1 2

1 2

1 1 1 1

100 100 100

P P

f f f

100f cm

A convergent lens of focal length 100 cm.

32. (a) Focal length of the combination can be calculated as

1 2

1 1 1

F f f

1 1 1

( 40) ( 25)F

200

3F cm

100 100

1.5200/3

P DF

t

I ' I

x

33. (d) Because to form the complete image only two rays are

to be passed through the lens and moreover, since the

total amount of light released by the object is not passing

through the lens, therefore image is faint (intensity is

decreased).

34. (b) 1 2

1 2

10( 10) 100

10 ( 10) 10 10

f ff

f f

35. (c) A lens shows opposite behaviour if medium lens 36. (a) A concave lens always forms virtual image for real

objects.

38. (a) 1 1 1

f v u

(Given 2 0u cm, 10f cm, ?v )

1 1 1

2010 ( 20)

v cmv

39. (c) air lens water i.e., 1 1.33lens

40. (a) f

mf u

1 30

4 30 u

150u cm

42. (d) 1

2m

f

mu f

1 30

2 30u

90u cm

43. (b) Focal length for voilet colour is minimum.

44. (d) 1

2

2

3

f

f . . . (i)

1 2

1 1 1

30f f . . . (ii)

Solving equation (i) and (ii), we get

2 15f cm (Concave)

1 10f cm (Convex)

45. (a) According to given conditions TIR must take place at

both the surfaces AB and AC. Hence, only option (a) is

correct.

46. (c) Man is suffering from hypermetropia. The hole works

like a convex lens.

48. (b) In myopia, ,u

v d distance of far point

By 2 . .

. . . .1.22

N AR P N A

we get f d

Since f is negative, hence the lens used is concave.

49. (d) Hypermetropia is removed by convex lens.

50. (b) In short sightedness, the focal length of eye lens

decreases, so image is formed before retina.

51. (c) In this case, for seeing distant objects the far point is

40 cm. Hence, the required focal length is

f d (distance of far point) 4 0 c m

Power 100 100

2.540

P cm Df

55. (a) For viewing far objects, concave lenses are used and

for concave lens

u = wants to see 60 ;cm

v = can see 15cm

So, from 1 1 1

f v u 20 .f cm

57. (a) In short sightedness, the focal length of eye lens

decreases and so the power of eye lens increases.

58. (d) Colour blindness is a genetic disease and still cannot

be cured.

59. (c) Convexity to lens changes by the pressure applied by

ciliary muscles.

Retina

Convex lens

INear point

O

2f

I

2f

4f