##### Refraction

What is Refraction ? Does refraction happen for mechanical waves too ? And why does Refraction happen. i.e why does light bend at the interface of two mediums. Answer lies in the wave nature of light and speed of light in different mediums

##### Refractive Index

What is Refractive index ? Is refractive index relative or absolute

##### Q1

A monochromatic beam of light of wavelength 6000 A in Vacuum enters a medium of refractive index 1.5. In the medium speed is ... it\'s wavelength is ..... and it\'s frequency is .....
A light wave of frequency 5 ? 1014 Hz enters a medium of refractive index 1.5. In the medium the velocity of the light wave is .... and its wavelength is....

##### Snells Law

What is Snell?s Law ? Why does Snell?s Law relate the sine of angles and Refractive indices ?

##### Q2

1) Find the speed of light in medium a if speed of light in medium b is c/3, where c = speed of light in vacuum and light refract from medium a to medium b making 45o and 60o, respectively, with the normal.

2) A beam of light propagates from medium 1, at an angle $$\alpha _{1}$$ into medium 2 at an angle $$\alpha _{2}$$ as shown. Wavelength of light in medium 1 is $$\lambda_{1}$$ . What is the wavelength of light in medium 2 ?

##### Q3

The figure shows two transparent media, medium - 1 and medium - 2. The lines ab and cd represent wavefronts of a light wave travelling in medium - 1 and the lines ef and gf represent wavefronts of the light wave in medium - 2 after refraction. Mark correct options in the following.

1) Light travels as a
a) parallel beam in each medium
b) convergent beam in each medium
c) divergent beam in each medium
d) divergent beam in one medium and convergent beam in the other medium

2) The phases of the light wave at c, d, e and f are fc , fd , fe and ff respectively. It is given that fc ? ff
a) fc cannot be equal to fd
b) fd can be equal to fe
c) ( fd - ff ) is equal to ( fc - fe )
d) ( fd - fc ) is not equal to ( ff - fe )

3) Speed of light is
a) the same in medium - 1 and medium - 2
b) larger in medium - 1 than in medium - 2
c) larger in medium - 2 than in medium - 1
d) different at b and d

##### Q4

A beam of light passes through 3 slabs of different mediums as shown in figure. Find the relation between the indices of refraction m1 , m2 , and m3 ?
A fourth slab is now introduced after the third slab such that the ray in the fourth slab is parallel to the ray in the first slab. What can be said about the refractive index of the fourth slab ?

##### Q5

1) An observer is viewing along the line shown in fig. when there is no water filled in the tank, he can see only wall AB and no other part of the base of tank. Then water is filled in till height h and he is just able to see the point C as shown in fig. Find the angle of refraction into air ( r ) and angle of incidence from water
( i ) Also find the depth h to which water has been filled.

2) A person looking into a vessel can just see the point A on the rim of the bottom of a cylindrical vessel when it is empty. When the vessel is completely filled with a liquid refractive index 1.5, he observe a mark B at the center of the vessel. What is the height of the vessel if the diameter of its cross section is 2

##### Refraction - Vector form

Understanding Refraction and Snell?s Law in Vector form and in 3-D

##### Q6

1. x-y plane separates two media, z $$\geq$$ 0 contains a medium of refractive index = 1 and z $$\leq$$ 0 contains a medium of refractive index .

2. A ray of light is incident from first medium along a vector $$\hat{i}+\hat{j}-\hat{k}$$. Find the unit vector along the refracted ray.

##### Total Internal Reflection

Why is called ?Total? Internal Reflection ? What is the criteria for Total Internal Reflection to happen ?

##### Q7

Light rays travel from liquid (refractive index = 2 ) to air.
a) What is the maximum angle of deviation ?
b) What is the maximum angle of deviation wrt the refracted ray ?
c) what is the angle of incidence corresponding to this maximum angle(s)
of deviation ?
d) at what angle(s) of incidence, can the angle of deviation be 30o ?

##### Q8

1) A ray of light passes through a rectangular glass block placed in a homogeneous medium. It is refracted and totally reflected. Which diagram shows a possible path of this ray?
2) Critical angle of glass is $$\theta_{\mathrm{g}}$$ and that of water is $$\theta_{\mathrm{w}}$$. The critical angle for water and glass surface would be $$\left(\mu_{g}=3 / 2, \mu_{w}=4 / 4\right)$$
a) less than $$\theta_{\mathrm{w}}$$
b) between $$\theta_{\mathrm{g}}$$ and $$\theta_{\mathrm{w}}$$
c) greater than $$\theta_{\mathrm{w}}$$
d) less than $$\theta_{\mathrm{g}}$$

##### Q9

A laser beam and a sound wave from directional sources both enter a liquid at an angle of 60o from the horizontal surface of the liquid. The speed of sound in the liquid is 5 times than that of the speed of the sound in air. For light, the refractive index of the liquid is 1.8
Find the angle made with the surface of liquid by the refracted/reflected light and sound.

##### Q10

1) A ray of light is incident at the glass-liquid interface at an angle i. It emerges parallel to the surface of liquid as shown in figure.
a) Find the refractive index of glass interms of angle i.
b) At what angle to the normal must a ray be incident on the top surface of liquid (air-liquid interface) so that it is reflected from the bottom surface of glass (glass-air interface) ?
2) A rectangular glass plate of thickness 10 cm and refractive index 1.5 is placed over a small coin. A beaker filled with water of refractive index 4/3 to a height of 10 cm is placed over the glass plate. If the eye is slowly moved away from the normal, beyond a certain position the coin is found to disappear due to total internal reflection . At which surface does this happens and why ?

##### Q11

A right angled prism of refractive index m1 is placed in a rectangular block of refractive index m2, which is surrounded by a medium of refractive index m3 , as shown in the figure, A ray of light e enters the rectangular block at normal incidence. Depending upon the relationships between m1 , m2 and m3 , it takes one of the four possible paths ef, eg, eh or ei.
Match the paths in Column I with conditions of refractive indices in Column II

##### Q12

1) Find the angle of refraction in a medium ( m = 2 ) if light is incident in vacuum, with the angle of incidence equal to twice the critical angle for that interface.
2) A ray of light travelling in a transparent medium fall on a surface separating the medium from air at an angle of incidence 450. The ray undergoes total internal reflection. If m is the refractive index of the medium with respect to air, select the possible value (s) of m from the following
a) 1.3
b) 1.4
c) 1.5
d) 1.6

##### App Depth & Normal Shift

Why does the object appear to be at different distance (or shifted ) when viewed through a slab of another medium ? How can we calculate the Apparent Depth and Normal Shift ?

##### Q13

Light from a point source undergoes refraction at an interface.

1) If the object is Real, then its image after refraction
a) will be real
b) will be virtual
c) may be real or virtual

2) If the object is Virtual, then its image after refraction
a) will be real
b) will be virtual
c) may be real or virtual

##### Q14

Consider the situation in figure. An observer is watching a fish in a fish tank whose bottom is a partially reflecting plane mirror. Refractive index of water is m.
a) At what distance does the observer perceive the fish from itself ?
b) At what distance does the observer perceive the image of fish in the mirror from itself ?
c) At what distance does the fish perceive the observer from itself ?
d) At what distance does the fish perceive the image of observer in the mirror from itself ?

##### Q15

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at it. At an instant, when the ball is 12.8 m above the water surface, find the

a) speed of ball as seen by fish
b) acceleration of ball as seen by fish

take g = 10 m/s2

##### Q16

A fish rising vertically up toward the surface of water with speed 3 m/s observes a bird
a) diving vertically down towards it with speed 9 m/s
b) diving vertically down towards it with speed 1 m/s
c) rising vertically upwards away from it with speed 3 m/s

Find
a) the actual velocity of bird
b) velocity of fish as perceived by the bird

##### Q17

A fish is floating inside a tank filled with water. The tank is now being drained so that the surface of water moves down with a velocity of 1 cm/s. A bird is viewing the fish from above.
a) find the apparent velocity of fish as seen by the bird
b) find the apparent velocity of bird as seen by the fish

##### Q18

Find the apparent length of rod in each of the 3 cases shown below. Actual length of rod is l

##### Slabs

Apparent Depth and Normal Shift caused by a slab of transparent material.

##### Q19

Find the apparent depth of the object in the cases shown below.
Repeat the question if refractive index of medium of observer = 1.8

##### Q20

Identify the True and False statements.
(i) A glass slab cannot deviate light
(ii) A glass slab can produce lateral displacement
(iii) The shift produced by slab depends on the converging and
diverging nature of beam
(iv) Apparent shift in case of a slab always occurs in the direction of
incident light ray
(v) The shift produced by a slab can never exceed its thickness

##### Q21

A convergent beam is incident on two slabs placed in contact as shown in Figure. Where will the rays finally converge?

##### Q22

An object is lying as shown in figure. Find the ratio d1/d2 and the condition on refractive indices m, m1 and m2 so that the image coincides with the object.

##### Q23

A vessel contains a slab of glass 8 cm thick and of refractive index 1.6. Over the slab, the vessel is filled by oil of refractive index m2 upto height 4.5 cm and then by water of refractive index 4/3 and height 6 cm as shown in figure. An observer looking down from above observes that a mark at the bottom of glass slab appears to be raised up to a position 6 cm from bottom of the slab.
a) Find refractive index of oil (m2).
b) Find the effective refractive index of all the layers.

##### Q24

A ray of light is incident from a medium of refractive index mi on a parallel sided glass slab of refractive index mr and thickness \'t\' as shown in fig. Find the lateral displacement x of the ray as it passes through the slab.

##### Prism - 1

Deviation of light by a Prism. How is the Angle of deviation by a prism related to the refractive index and angle of prism ? Explains the Graph of Angle of deviation wrt the Angle of incidence and Graph of Angle of deviation wrt the Refractive index of prism.

##### Prism - 2

Explains the conditions for Minimum and Maximum Deviation through a prism. And the cases for Grazing Incidence and Grazing Emergence though a prism.

##### Q25

1) A system of two identical prisms are placed and a ray of light is incident on the first prism as shown in figure. By what angle the second identical prism must be rotated, so that the final ray suffers net minimum deviation.

2) A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and of the same material as P are now added as shown in figure. The ray will suffer
(a) greater deviation
(b) no deviation
(c) same deviation as before
(d) total internal reflection

##### Q26

An isosceles prism of angle 120o has refractive index 1.44. Two parallel rays of monochromatic light enter the prism parallel to each other in air as shown. The rays emerging from the opposite face
a) are parallel to each other
b) are diverging
c) make an angle 2 [ sin-1 ( 0.72 ) - 30o ] with each other
d) make an angle 2 sin-1 ( 0.72 ) with each other

##### Q27

A prism is placed with air on both sides. For no ray to pass through the prism irrespective of the angle of incidence,
1) find the condition on angle of prism A, if the critical angle between the prism-air interface is f

2) find the condition on refractive index of prism, if the angle of prism is fixed to be = A

3) Show that a ray incident at an angle q can pass through the prism when

##### Q28

Figure shows a triangular prism of refracting angle 90o. A ray of light incident at face AB at an angle q1 refracts at point Q with an angle of refraction 90o.
a) What is the refractive index of the prism in terms of q1 ?
b) What is the maximum value that the refractive index can have ? What happens to the light at Q if the incident angle at Q is
c) increased slightly, and d) decreased slightly ?
For a prism, A = 60o , n = 7/3. Find the minimum possible angle of incidence, so that the light ray is reflected from the second surface. Also, find dmax

##### Q29

A right angled prism ( 45o - 90o - 45o ) of refractive index n has a plane of refractive index n1 ( n1 < n ) cemented to its diagonal face. The assembly is in air. The ray is incident on AB
a) calculate the angle of incidence at AB for which the ray strikes the diagonal face at the critical angle.
b) assuming n = 1.352, calculate the angle of incidence at AB for which the refracted ray passes through the diagonal face undeviated.

##### Thin Prism

Angle of Deviation for a Thin Prism. Why is the angle of deviation though a thin prism same for all incident rays ? Or is it same for all incident rays ?

##### Q30

A thin bi-prism (see figure A) of obtuse angle a = 178o is placed at a distance l = 20 cm from a point source.
How many images are formed and what is the separation between them? Refractive index of the material m = 1.5.
Repeat the above the question if the prism is rotated by an of 45o as shown in figure B or if the shape of prism is different but the top and bottom angles of prism are the same as that of prism in figure A

##### Chromatic Dispersion

Why do we see colors when light passes though a prism ?

##### Q31

1) Red and violet colors are made to pass separately through a prism (angle of the prism is 60o). In the position of minimum deviation, the angle of refraction will be a) 30o for both the colors b) equal but not 30o for both the colors c) greater for the violet color d) greater for the red color
2) A beam of light consisting of red, green and blue colors is incident on an isosceles right-angled prism. Refractive indices for red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. Which colors will be separated by the prism ?
3) A beam of white light enters the curved surface of a semicircular glass along the normal. The incident beam is moved clockwise, such that the beam always enters along the normal to the curved side. Just before the refracted beam disappears, it becomes predominantly red.
True / False ?

##### Q32

1) A prism made of glass is placed inside a surrounding medium. Both prism and medium have a higher refractive index for violet light than red light. Which diagram is correct, if refractive index of prism
a) is more than the refractive index of surrounding medium
b) is less than the refractive index of surrounding medium

2) A beam of white light passing through a hollow prism give no spectrum T / F ?

##### Q33

Find the dispersive power of a thin prism of 15o having refractive index for red light = 1.56 and for violet light = 1.64

##### Q34

White light falls on one face of crown glass prism of refracting angle 50o. The angle of incidence is 30o ( mV = 1.538, mR = 1.52 )
Find the
a) mean deviation produced by the prism and
b) the angle of dispersion

##### Deviation & Dispersion

Discussion on the cases of Deviation without Dispersion and Dispersion without Deviation for prisms. Can we have a case where both Deviation and Dispersion are zero ?

##### Q35

Two thin prisms are combined to form an achromatic combination. For prism I, A = 4o , m = 1.46, m = 1.40, m = 1.36. For prism II, m = 1.9, m = 1.80 and m = 1.7. Find the prism angle of prism II and the net mean deviation.

##### Q36

i) A thin prism P1 with angle 4o and made from glass of refractive index 1.54 is combined with another thin prism P2 made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is
a) 5o
b) 4o
c) 3o
d) 2o

ii) The refractive indices of the crown glass for violet and red light are 1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle 6o is made of crown glass. A beam of white light is incident at a small angle on the prism. The other flint glass isosceles prism is combined with the crown glass prism such that there is no deviation of the incident light.
a) Determine the angle of the flint glass prism
b) Calculate the net dispersion of the combined system

##### 1

A light ray is incident on a glass sphere of refractive index m = 3/2 at an angle of incidence 60o as shown in figure.
a) Find the angle r, r\', e and the total deviation after two refractions.
b) If the ray emerges from the sphere horizontally. Find the refractive index of the sphere.

##### 2

Monochromatic light is incident on a plane interface AB between two media of refractive indices n1 and n2 ( n2 > n1 ) at an angle of incidence i as shown in the figure. The angle i is infinitesimally greater than the critical angle for the two media so that total internal reflection takes place. Now if a transparent slab DEFG of uniform thickness and of refractive index n3 is introduced on the interface ( as shown in the figure), show that for any value of n3 all light will ultimately be reflected back again into medium II. Consider separately the cases
a) n3 < n1 and b) n3 > n1

##### 3

1) Light from a denser medium 1 passes to a rarer medium 2. When the angle of incidence is q, the partially reflected and refracted rays are mutually perpendicular. Critical angle for the interface will be a) sin-1 ( cot q ) b) sin-1 ( tan q ) c) sin-1 ( cos q ) d) sin-1 ( sec q ) 2) A ray of light passes from glass, having a refractive index of 1.6 to air. The angle of incidence for which the angle of refraction is twice the angle of incidence is

##### 4

A glass cube of size 24 cm has a small air bubble trapped inside it. When viewed from the left side, the bubble appears to be at a distance of 10 cm from the face, and when viewed from the right side, bubble appears to be at a distance of 6 cm from it. Find the position of bubble and refractive index of glass.

##### 5

An observer can see a point at height \'h\' through a pin-hole as shown in fig. The vessel height is \'3h\' and its radius is \'h\'. When the vessel is filled with a liquid up-to a height 2h, he can see the bottom corner of vessel. Find the refractive index of liquid.

##### 6

A pole is standing in clear water. Pole stands 1 m above the water surface. The pond is 2m deep. What is the length of shadow of pole on bottom of the pond if the sun is 30o over the horizon ?

##### 7

A rectangular slab of refractive index m is placed over another slab of refractive index 3. Both slabs have identical dimensions. If a small coin is placed below the lower slab, for what value of m will the coin appear to be at the interface between the two slabs, when viewed from the top ?

##### 8

An observer watches a fish through a 3 cm thick glass wall of a fish tank, as shown in figure
a) how far does the fish appear to the observer ?
b) how far does the observer appear to the fish ?

Repeat the above question if thickness of glass wall is negligible

##### 9

1) Light is incident at an angle a on a planer end of a transparent cylindrical rod of refractive index n. Determine the least value of n so that the light entering the rod does not emerges from the curved surface of the rod irrespective of the value a
2) A rectangular block of glass is placed on a printed page lying on a horizontal surface. Find the minimum value of refractive index of glass for which the letters on the page are not visible from any of the vertical faces of the block.

##### 10

1) A rectangular glass slab (n1) is immersed in water (n2) as shown ( n1 > n2 ). The maximum value of angle of incidence amax, such that the ray comes out only from the opposite vertical surface, is given by

2) For the incident ray as shown in figure, find the minimum angle of incidence i so that the ray is totally reflected by both the slabs.

##### 11

A ray of light travels from a liquid of refractive index m into air. If the incident beam is rotating at a rate w, Find the angular speed of the refracted/reflected beam as a function of the angle of incidence, for the full rotation of the incident ray.

##### 12

An object is placed in front of a slab ( m = 1.5 ) of thickness 6 cm at a disyance 28 cm from it. Other face of the slab is silvered. Find the position of final image.

##### 13

A 20 cm thick glass slab of refractive index 1.5 is kept in front of a plane mirror. Find the position of the image (relative to mirror) as seen by an observer through the glass slab when a point object is kept in air at a distance of 40 cm from the mirror.

##### 14

An object is placed at 8 cm in front of a glass slab, whose one face is silvered as shown in figure. The thickness of the slab is 6 cm. If the image formed 10 cm behind the silvered face, find the refractive index of glass.

##### 15

An object is placed at a distance of 32 cm from a concave mirror of focal length 10 cm. A glass slab of refractive index m = 3/2 and thickness 6 cm is inserted between the object and mirror, as shown in figure.
Find the final position of image after reflection and passing through the slab, if
a) x = 5 cm b) x = 20 cm

##### 16

The image of an object kept at a distance of 30 cm in front of a concave mirror is found to coincide with itself. If a glass slab ( m = 1.5 ) of thickness 3 cm is introduced between the mirror and the object, then by what distance and in which direction should the mirror be moved so that the final image coincides with the object again.

##### 17

A concave mirror of focal length 20 cm is placed inside water with its shining surface upwards and principal axis vertical as shown in figure. Rays are incident parallel to the principal axis of concave mirror. Find the position of image as seen by the observer if
a) x = 30 cm b) x = 10 cm

##### 18

A concave mirror of focal length f lies on a horizontal table and water is filled in it up to a height of h ( h < f ). A point object lies on the water surface at a point vertically above the point of contact of the mirror with the table. Locate the image of particle as seen from a point directly above it. The refractive index of water is f/h.
Also find the distance where the object should be placed so that its image is formed on itself ?

##### 19

a) An equilateral prism is made of glass of refractive index 1.5. Calculate the angles of minimum and maximum deviations. Given

b) A ray of light undergo deviation of 30o when incident on an equilateral prism of refractive index

2. Find the angle made by the ray inside the prism with the base of the prism.

##### 20

A ray of light is incident normally on one of the faces of a prism of apex angle 30o and refractive index under root 2 . The angle of deviation of the ray is ..... degrees.
A ray of light is incident at an angle of 60o on one face of a prism which has an angle 30o. The ray emerging out of the prism makes an angle of 30o with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of the lens.

##### 21

1) A prism is made of glass of refractive index 1.6. If the angle of minimum deviation is equal to the refracting angle of the prism, calculate the angle of the prism.

2) A ray of light suffers minimum deviation through a prism of refractive index 2 . What is the angle of prism if the angle of incidence is double the angle of refraction within the prism?

##### 22

1) In an isosceles prism of angle 45o, it is found that when the angle of incidence is the same as the prism angle, the emergent ray grazes the emergent surface.
a) Find the refractive index of the material of the prism
b) Find the angle of incidence for minimum deviation
2) For a prism, it is found that for an angle of incidence 60o , the angle of refraction ?A? , angle of deviation ?d?, and angle of emergence ?e? become equal.
a) Find the angle of minimum deviation
b) Find the refractive index of the material of the prism

##### 23

1) One of the refracting surfaces of a prism of angle 30o is silvered. A ray of light incident on the other surface at angle of 60o retraces its path. Find the refractive index of the material of prism.

2) An isosceles prism has one of the refracting surfaces silvered. A ray of light is incident normally on the other surface. After two reflections, the ray emerges from the base of prism perpendicular to it. Find the angle of prism.

##### 24

A ray of monochromatic light is incident on the face AC of prism ABCD near vertex B at an incident angle of 60o (see figure). If the refractive index of the material of the prism is 3, which of the following is (are) correct ?
a) the ray gets totally internally reflected at face CD
b) the ray comes out through face AD
c) the angle between the incident ray and the emergent ray is 90o
d) the angle between the incident ray and the emergent ray is 120o

##### 25

ACB is right angled prism with other angles as 60o and 30o. Refractive index of the prism is 1.5. AB has thin layer of liquid on it as shown. Light falls normally on the face AC.
a) For total internal reflection, find the maximum refractive index of the liquid.
b) For what range of angle of incidence (at the face AC) will the ray always undergo total internal reflection at the prism-liquid interface ?

##### 26

1) A ray of light is incident normally on the face AB of the glass prism ABC ( mg = 5/3 ) as shown. Find the largest value of angle a so that the ray is totally reflected at the face AC,
a) if surrounding medium is air
b) if the prism is immersed in water (surrounding medium is water with mw = 4/3 )

2) A ray of light incident normally on one of the faces of a right angled isosceles prism is found to be totally reflected. What is the minimum value of the refractive index of the material of the prism ? If the prism is immersed in water, trace the path of the emergent rays for the same incident ray, indicating values of all the angles.

##### 27

For a prism with refracting angle equal to p/2 , prove that

##### 28

1) A right-angled prism of apex angle 4o and refractive index 1.5 is located in front of a vertical plane mirror as shown in figure. A horizontal ray of light is falling on the prism. a) Find the total deviation produced in the light ray as it emerges 2nd time from the prism. b) Find the angle by which the mirror should be rotated, so that the light ray will retrace its path as it emerges 2nd time from the prism.
2) A ray of light strikes a plane mirror at an angle of incidence 45o as shown in figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4o. Through what angle must the mirror be rotated if the total deviation of the ray is to be 90o ?

##### 29

O is a point object kept on the principal axis of a concave mirror M of radius of curvature 20 cm. P is a prism of angle 1.8o. Light falling on the prism ( at small angle of incidence ) gets refracted through the prism and then falls on the mirror. Refractive index of the prism is 3/2. Find the distance between the images formed by the concave mirror due to this light.

##### 30

A glass prism is immersed in a hypothetical liquid. The graph shows the refractive index n of glass and liquid as a function of wavelength l of incident light.
When a ray of white light is incident on the prism parallel to the base, which of the following is/are true ?
a) yellow ray travels without deviation
b) blue ray is deviated towards the vertex
c) red ray is deviated towards the base
d) there is no dispersion

##### 31

The dispersive powers of crown and flint glasses are 0.03 and 0.05, respectively. The refractive index for yellow light for these glasses are 1.518 and 1.62, respectively. If we want to make an achromatic combination of these prisms that produces a mean deviation of 1o what are the angles of the two prisms needed?

##### 32

A prism of refractive index n1 and another prism of refractive index n2 are stuck together as shown in the figure. n1 and n2 depend on the wavelength of light (l) according to :
where l is in nm
a) Calculate the wavelength l0 for which rays incident at any angle on the interface BC pass through without bending at that interface.
b) For light of wavelength l0, find the angle of incidence i on the face AC such that the deviation produced by the combination of prisms is minimum.

##### 33

The x-y plane is the boundary between two transparent media. Medium -1 with z 0 has a refractive index 2 and medium - 2 with z ? 0 has a refractive index 3. A ray of light in medium - 1 given by vector A = 6 3 i + 8 3 j - 10 k is incident on the plane of separation. Find the unit vector in the direction of the refracted ray in medium - 2.

##### 34

A ray of light enters a sphere of refractive index m as shown in the figure.
1) Select the correct statement :
a) Incident rays are partially reflected at point A
b) Incident rays are totally reflected at point A
c) Incident rays are totally transmitted through A
d) None of these

2) An expression of the angle between incident ray and emergent ray
( angle of deviation ) will be
a) 0o b) f c) a - f d) p - 4a + 2f.

3) Find the expression for angle f for which deviation is minimum

##### 35

A right angled prism is to be made with angles A and B ( B < A ) as shown in fig. It is desired that a ray of light incident on the face AB emerges parallel to the incident ray after two internal reflections
i) What should be the minimum refractive index n for this to be possible ?
ii) For n = 5/3, is it possible to achieve this with the angle B equal to 30o ?

##### 36

A point source of light is placed at a depth of h below the surface of a large deep lake. Show that the fraction f of the light energy that comes out of the water surface is independent of h and is given by

##### 37

1) A glass slab [ m = 5/3 ] of thickness 8 cm is placed over a point source of light on a plane surface. Light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ?
2) A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in figure. Light emerging from the block into the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. Find the refractive index of the liquid.
3) A point source of light is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc of radius 1 cm floating on the surface. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. What is the maximum height of liquid for which the source cannot be seen from above ?

##### 38

There is a point source of light lying at a depth h inside a water body. An observer standing outside the water body observes the point source. If the line of vision of observer makes an angle q with the normal, then find the apparent depth and lateral shift of the point as seen by the observer. Take refractive index of water to be m and that of air to be 1

##### 39

A ray of light travelling in air is incident at grazing angle ( incidence angle = 90o ) on a long rectangular slab of a transparent medium of thickness t = 1 m. The point of incidence is the origin O( 0, 0 ). The medium has a variable index of refraction n( y ) given by
n ( y ) = [ ky3/2 + 1 ]1/2 where k = 1 m-3/2
The refractive index of air is 1.
a) Obtain a relation between the slope of the trajectory of the ray at a point ( x, y ) in the medium and the incident angle at that point.
b) Obtain an equation for the trajectory y( x ) of the ray in the medium.
c) Determine the coordinates ( x1, y1 ) of the point P, where the ray intersects the upper surface of the slab - air boundary.
d) Indicate the path of the ray subsequently.

##### 40

Due to a vertical temperature gradient in the atmosphere, the index of refraction of air varies vertically. Suppose index of refraction varies as n = no 1 + ay , where no is index of refraction at the surface and a = 2 ? 10-6 m-1. A person of height h = 2 m stands on a level surface. Beyond what distance will he not see the runway?

##### 41

A ray of light travelling in air is incident at angle of 30o on the surface of a slab in which refractive index varies with y. The light travels along the curve y = 4x2 in the slab ( y and x are in meter ).
Find the refractive index of the slab as a function of y.
And find the refractive index of slab at y = 0 and y = 1 m.

##### 42

A point source is placed below a slab of height 1 m whose refractive index varies with y as
Find the apparent depth of point as seen from above.