A glass prism has refractive index `sqrt(2)` and refracting angle `30^(@)` . One of the refracting surface of the prism is silvered. A beam of monchromatic light will retrace it path it its angle of incidence on the unsilvered refracting surface of the prism is

Options

A. `45^(@)`
B. `60^(@)`
C. `0^(@)`
D. `30^(@)`

Answer

A

Explanation

According to the given condition, the beam of light will retrace its path after reflection from `BC`. So
`/_CPQ=90^(@)`
Thus, angle of refraction at suface `AC`
`/_PQN=-r=90^(@)-60^(@)=30^(@)`
By Snell's law
`mu=(sini)/(sin r)`
`impliessqrt(2)=(sini)/(sin 30^(@))`
`:. sqrt(2)xxsin 30^(@)=sin i`
`implies sqrt(2)xx(1)/(2)=sini`
`impliessin i(1)/(sqrt(2))=sin 45^(@)`
`:. t=45^(@)`
Aliter: `A=r+0 ` if `r=30^(@)`
From Snell's law at surface `AB`
`mu=(sin i)/(sin r)`
`impliessqrt(2)=(sin i)/(sin 30^(@))impliesi=45^(@)`