A ray is incident on a sphere of refractive index `sqrt(2)` as shown in figure. Angle of refraction of the ray inside sphere is `30^(@)` if total deviation suffered by the ray is `30x^(0)`, then find x.

Answer

5

Explanation

`(sini)/(sinr)=sqrt(2)impliesi=45^(@)`
total deviation
`=(45^(@)-30^(@))+180^(@)-2(30^(@))+(45^(@)-30^(@))`
`=30^(@)+120^(@)`
`=150^(@)=30x`
`x=5`