A prism of refractive angle `60^(@)` and refractive index 1.5 is kept in water of refractive index 1.33 . What is the angle of minimum deviation for a monochromatic ray of light in water ?
(Given `sin 34^(@) = 0.56`)

Options

A. `4^(@)`
B. `8^(@)`
C. `16^(@)`
D. `120^(@)`

Answer

B

Explanation

When the ray travels from water to glass in the prism , `""_(w) n_(g) = (""_(a) n_(g))/(""_(a) n_(w)) = (3//2) /(4//3) = (9)/(8)`
and for the prism A = `60^(@)`
`therefore (9)/(8) = (sin ((60^(@) + delta m)/(2)))/(sin ((60^(@))/(2)))`
`therefore (9)/(8) xx (1)/(2) = sin ((60 + delta m)/(2))`
`therefore sin ((60 + delta m)/(2)) = (9)/(16) = 0.56 = sin 34^(@)`
`therefore (60 + delta m)/(2) = 34^(@) therefore delta m = 68^(@) - 60^(@) = 8^(@)`