Ray Optics and Optical Instruments

A beam of polychromatic light passes through a thin prism of prism angle 6 . The refractive index of the material of the prism varies with wavelength ( ) as n( )= + 2, where =3 m-1 and =0.096 m2. If is the wavelength at which the angle of minimum deviation Dm is smallest, then the correct value of Dm at is

1. 6.4
2. 4.8
3. 3.2
4. 2.4

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 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]