A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in the figure and emerges from the other refracting face AC as RS such that AQ = AR. If the angle of prism `A = 60^(@)` and the refractive index of the material of prism is 3^1/2, then the angle of deviation of the ray is

Options

A. `60^(@)`
B. `45^(@)`
C. `30^(@)`
D. None of the above

Answer

A

Explanation

(a) For a given prism, the angle of deviation depends upon the angle of incidence of the light rays falling on the prism. Taking tringle FQR, we have
`delta=angleFQR+angleFRQ`
Since, `DeltaAQR` is an equilateral triangle,therefore,
`angleFQR=(60^(@))/2=30^(@)=angleFRQ`
`therefore delta=30^(@)+30^(@)=60^(@)`
Hence, angle of deviation of the ray is `60^(@)`.