A uniform, horizontal parallel beam of light is incident upon a prism as shown. The prism is in the shape of a quarter cylinder, of radius 5cm, and has refractive index 5/3. The width of the regionat which the incident rays after normal incidence on plane surface and subsequent refraction at curved surface intersect on x axis is (Neglect the ray which travels along x-axis)

Options

A. `4cm`
B. `5//4cm`
C. `9//4cm`
D. `25//4cm`

Answer

D

Explanation

The ray first above x-axis shale after refraction at cured surface intersect x-axis at A at a distance `x_(1)` from where
`(1)/(24) = (mu-1)/(R)` or `x_(1) = (R)/(mu-1) =(15)/(2)cm`

critical angle for air glass
`theta = sin^(-13//5) = 37^(@)`
`(3)/(1+x_(2)) = tan 53^(@) rArr x = (5)/(4)`
`:.` Range width `= x_(1) - x_(2) (15)/(2)-(5)/(4) = (25)/(4)cm`