A monochromatic ray of light strikes one face of a prism at an angle of `60^(@)` and the angle of refraction is `30^(@)` . The refracting angle of the prism is `60^(@)` . What is the angle of emergence ?

Options

A. `30^(@)`
B. `45^(@)`
C. `50^(@)`
D. `60^(@)`

Answer

D

Explanation

`n = (sin i)/(sin r) = (sin 60^(@))/(sin 30^(@)) = (sqrt3)/(2) xx (2)/(1) = sqrt3`
`therefore n = (sin ((A + delta_(m))/(2)))/(sin ((A)/(2)))`
`therefore sqrt3 = (sin ((60^(@) + delta_(m))/(2)))/(sin 30^(@)) `
`therefore sin ((60^(@) + delta_(m))/(2)) = sqrt3 xx (1)/(2) = (sqrt3)/(2) = sin 60^(@)`
`therefore (60^(@) + delta_(m))/(2) = 60^(@)`
`therefore delta_(m) = 120^(@) - 60^(@) = 60^(@)`
For a prism `A + delta_(m) = i+ e`
`therefore 60^(@) + 60^(@) = 60 + e therefore e = 60^(@)`