Refraction at plane surface and Prisms

Dr. M K RaghavendraBASE, Bangalore

Type 1 – Snell’s law and RISnell’s law: 1 2

sin( )sin( )

inr

1

1 22

vnv

Relative R I in terms of speed of light

21 2

1

nnn

Relative R I in terms of absolute R I

cnv

Absolute R I in terms of speed of light

Modified Snell’s law

1 1 2 2sin sinn i n i1

1 22

n

Relative R I in terms of wavelength of lightV Y R

V Y Rn n n

Frequency remains constant

1) A ray of light is incident on the interface of two media at an angle of 450 and is refracted in to the other medium at an angle of 300. If the speed of light in the first medium is 3X108ms-1 ,what is the speed of light in the second medium?

(1) 1.96X108ms-1

(2) 2.12X108ms-1

(3) 3.18X108ms-1

(4) 3.33X108ms-1

Snell’s law: sin( )sin( )

inr

cnv

Thus sin( )sin( )

i cr v

8

8

88 1

sin45 3 10sin30

1/ 2 3 101/ 2

3 10 2.12 102

Xv

Xv

Xv X ms

1 1

2 2

generalsinsin

Ini vi v

2)A ray of light is travelling from medium A to medium B. The angle of incidence is i and that of refraction is r. Graph between sin(i) and sin(r) is as shown in Figure below. We can conclude the following (i) Speed of light in medium B is three-fourth of that in medium A.(ii) Total internal reflection cannot take place.(iii) Refractive index of medium B is greater than that of medium A.

Correct conclusions are(1) Only (i) and (ii) (2) Only (ii) and (iii) (3) (i), (ii) and (iii) (4) Only (i) and (iii)

sin (r)

sin (i)

O370

The slope of the straight line: sin tansinri

0sin tan37sinsin 3 sin 4

ri

rori

Medium B is denser than medium Asin 3 sin 434

B

A

B A

vri v

v v

Since nb > na TIR cannot take place

sin (r)

sin (i)

O370 sin (i)

sin (r

)

3) Given refractive index of glass with respect to air is ang = 3/2 and that of water with respect to air is anw = 4/3, the refractive index of glass with respect to water is (1) 8/9

(2) 9/8

(3) 2

(4) 1/2

11 2

2

nnn

and g wa g a w

a a

n nn nn n

/ 3/ 2 9/ 4/ 3 8

g g aw g

w w a

n n nn

n n n

Type 2: Normal Shift and Lateral Shift

Lateral shiftsin( )cosL

t i rSr

V Y RS S S

Normal shift a) Object in denser

b) Object in rarer

1(1 )Nr d

S tn

( 1)NS t n

Re depthApparent depthr d

aln

depthReal depthr d

Apparentn

V Y RS S S

4) A vessel of height h is filled with a liquid of refractive index n1 to a height h/2 and the upper half of the vessel is filled with a liquid of refractive index n2. The apparent depth of the vessel as seen along the normal is

1) 2)

3) 4)

1 2

1 2

n nh

n n

21

21

2 nnnnh

21

21

nnnn

2h

21

21

nnnn

h2

In case of one liquid the apparent depth is given by

real depthrefractive index

In case of many layers of liquid . i

i

tA Dn

1 2

2 1

1 2

/ 2 / 2.

=2

h hA Dn n

n nhn n

5) A ray of light passes through four transparent media with refractive indices 123 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 (1) 1 = 2

(2) 2 = 3

(3) 3 = 4

(4) 4 =1

1 2 3

4

A

BC

D

sin sina a b bi i

Apply to medium 1 and medium 4 1 1 4 4sin sini i

Since ray AB and CD are parallel, i1 and i4 are equal

Implies 1 = 4

In genral sin sin sin ...............a a b b c ci i i

6) An ink dot on a paper placed on a table top is viewed from a distance of 30 cm above it with the help of a telescope. A 16 cm thick glass slab is placed on the ink dot. By what distance the telescope should be raised to refocus the ink dot ? The refractive index of glass is 1.6.

(1) 3 cm(2) 4 cm(3) 5 cm(4) 6 cm

The telescope should be moved up by a distance (y) equal to normal shift produced by the slab

11nS tn

116 1 61.6ny S cm

7) Consider the situation shown in the figure. The bottom of the vessel is a plane mirror, S is a small fish located at a height of H/2 from the plane of the mirror, T is a human eye located at a height of H from the surface of water. The distances at which the fish sees the images of the eye (with respect to its position) are

1)

2)

3)

4)

belownHandabovenH 232

212

below 231 and above

211

nH

nH

below 23 and above

21

nHnH

below 232 and above

222

nH

nH

S

T

H (H/2)

H

S

T

H (H/2)

H

Image 1

nH + H/2

Image 2

nH + H

nH + H+H/2

Image 1: H (n+1/2)

Image 2: H (n+3/2)

A.P = nH

Type 3: Critical angle and Total Internal Reflection

1sinr d

Cn

sin r

d

nCn

V Y R

V Y R

n n nC C C

sin d

r

vCv

8) A, B and C are three optical media of respective critical angles C1, C2 and C3. Total internal reflection of light can occur from A to B and also from B to C but not from C to A. Then the correct relation between critical angles is

(1)C1>C2>C3

(2) C1= C2= C3

(3)C3> C1> C2

(4)C1<C2<C3

T I R can occur when light travels from medium A to medium B

A Bn n

T I R can occur when light travels from medium B to medium C

B Cn n

Therefore A B Cn n n

1 2 3C C C

9) What is the critical angle, C for calcite (=1.5) immersed in oil (=1.1)?

(1)

(2)

(3)

(4)

5.11.1tan 1C

5.11.1cos 1C

1.15.1sin 1C

5.11.1sin 1C

1sin O

O C C

nCn n

1.1sin 1.5C

Type 4: Prism, angle of deviation, minimum deviation

sin 2sin 2

A D

n A

1 2

1 2

d i i AA r r

10) The minimum angle of deviation for a prism of refractive index 1.732 is equal to its refracting angle. What is the angle of prism?

(1) 400

(2) 450

(3) 600

(4) 300

In this case A = D

sin( )2sin( )2

A D

n A

sin( ) sin21.732

sin( ) sin2 2

A AA

A A

2sin cossin 2 23 2cos 2sin sin2 23 cos2 2

A AA AA A

A

A/2 =300

Or A=60o

11) A ray of light is incident on one refracting face of a prism of angle 750. It passes through the prism and is incident on the other face at critical angle. If the refractive index of the material of the prism is √2, then the angle of incidence on the first face is(1) 300

(2) 450

(3) 600

(4) 75 0

1 1sin 2Cn

C = 450

r1 C

750

We know that r1 + C =750

r1 =300

0

sin sinsin2 sin30

ibut nr

i

0

1 1sin 2 2 245

i X

i

Type 5: Small angled prism , angular dispersion and dispersive power

( 1)d A n Deviation

( )V RA n n Angular dispersion

Dispersive powerangular dispersion

mean deviation 12

V R

v R

n nn n

2F C

mean Dn nn n

In case of C D F line

12) The dispersive power of the material of the prism for which refractive index for violet and red colours are nv = 1.524, nr = 1.514 respectively is

(1) 0.025(2) 0.034(3) 0.019(4) 0.015

Dispersive power is given byangular dispersion

net deviation

( )12

V R

V R

n nn n

(1.524 1.514) 0.01 0.0191.524 1.514 0.51912

Type 6: Combination of Prisms

Dispersion with out deviation ( 1) ( 1)D DA n A n

( 1)(1 )dA n

Deviation with out dispersion ( ) ( )F C F CA n n A n n

( 1) ( 1)D Dd A n A n

13) A crown glass prism of 60 is cemented with a flint glass prism to form a pair which produces dispersion without deviation. If the refractive index of the crown glass prism is 1.52 and that of flint glass 1.66, then the angle of flint glass pair should be (1) 4.730

(2) 5.730

(3) 6.730

(4) 7.730

Condition for dispersion with out deviation is

11 2( 1) ( 1)y yA n A n

2

2

6(1.52 1) (1.66 1)

6 0.52 4.720.66

A

XA

Conceptual questions

14) Light appears to travel in straight line because

(1)The frequency of light is very small

(2) Light consists of very small particles

(3) The wavelength of light is very small

(4) The velocity of light is different for different colours.

15) When light is refracted through a prism, maximum deviation occurs when the following conditions are satisfied(i) the ray is incident grazing the first face (ii) the ray emerges out grazing its second face Options (1) Only in case (i) (2) Only in case (ii)(3) In both the cases (4) Not under these cases

16) A man is swimming underwater with undisturbed surface. Looking up at a bright sky through the water, he will see

(1)a bright patch directly above whose angular size is independent of the depth of the swimmer(2)a shining surface of the water(3) just darkness(4) a bright patch directly above whose angular size depends upon the depth of the swimmer

CC

All the bestThank You