Ray Optics and Optical Instruments

At the interface between two materials having refractive indices n1 and n2, the critical angle for reflection of an em wave is 1C. The n2 material is replaced by another material having refractive index n3 such that the critical angle at the interface between n1 and n3 materials is 2C. If n3 > n2 > n1; n2n3 = 25 and 2C - 1C = 12, then 1C is :

1. -1 ( 16n1 )
2. -1 ( 13n1 )
3. -1 ( 56n1 )
4. -1 ( 23n1 )

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

1. 96 cm
2. 72 cm
3. 24 cm
4. 48 cm

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is : [figure]

1. 0.124R
2. 0.114R
3. 0.411R
4. 0.214R

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L1, L2 by AB plane and L3, L4 by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L1 and L3 is [figure]

1. 1:2
2. 1:1
3. 2:1
4. 1:4

A thin prism P1 with angle 4 made of glass having refractive index 1.54, is combined with another thin prism P2 made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism P2 in degrees is

1. 1.5
2. 16/3
3. 3
4. 4

A hemispherical vessel is completely filled with a liquid of refractive index . A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is . [figure]

1. 32
2. 32
3. 3
4. 2

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is -3, then the magnitude of the radius of curvature of the mirror is :

1. 3.75 cm
2. 15 cm
3. 7.5 cm
4. 30 cm

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A. If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of -2, then the radius of curvature of meniscus is :

1. 23 cm
2. 43 cm
3. 13 cm
4. 1 cm

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5 D ? ['D' stands for dioptre]

1. 0.04
2. 0.1
3. 0.40
4. 0.01

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is

1. 0.15 m
2. 0.10 m
3. 0.25 m
4. 0.20 m