Ray Optics and Optical Instruments · Question 2

Consider two isosceles prisms 1 and 2 with prism angles A1 and A2 and refractive indices n1 and n2, respectively, as shown in the figure. The faces a1b1 and a2b2 are parallel to each other and perpendicular to the mirror M. If a ray of light is incident on the face a1c1 and emerges from the face a2c2, then the correct statement(s) is/are: [figure]

1. If both the prisms are at minimum deviation condition, then n2n1= ( A12 )/ ( A22 ).
2. If prism 2 is at minimum deviation condition, then i1=n2 ( A22 ) is always true.
3. If both the prisms 1 and 2 are thin and are at minimum deviation condition with angles of deviation m1 and m2, respectively, then = m12(n1-1)+ m22(n2-1).
4. If prism 1 is at minimum deviation condition, then i2=n1 ( A12 ) is always true.

Two identical concave mirrors each of focal length f are facing each other as shown in the schematic diagram. The focal length f is much larger than the size of the mirrors. A glass slab of thickness t and refractive index n0 is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source S is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on S itself, which of the following distances between the two mirrors is/are correct: [figure]

1. 4f+ (1- 1n0 )t
2. 2f+ (1- 1n0 )t
3. 4f+(n0-1)t
4. 2f+(n0-1)t

A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence 0. The ray partially refracts into the sphere with angle of refraction 0 and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is . Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

1. P → 5; Q → 2; R → 1; S → 4
2. P → 5; Q → 1; R → 2; S → 4
3. P → 3; Q → 2; R → 1; S → 4
4. P → 3; Q → 1; R → 2; S → 5

A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index n up to the level QPR. If the image of a point object O at a height of h (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct? [figure]

1. For n=1.42, h=50 cm.
2. For n=1.35, h=36 cm.
3. For n=1.45, h=65 cm.
4. For n=1.48, h=85 cm.

Two equilateral-triangular prisms P1 and P2 are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism P1 at an angle of incidence such that the outgoing ray undergoes minimum deviation in prism P2. If the respective refractive indices of P1 and P2 are 32 and 3, then = -1 [ 32 ( ) ], where the value of is . [figure]