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

`(sin(i))/(sinr)=sqrt(2)impliesi=45^(@)`
Total deviation
`=(45.^(@)-30.^(@))+180.^(@)-2(30.^@)+(45^(@)-30^(@))`
`(30^(@)+120^(@)`
`=150^(@)=30x`
`x=5`.