A ray is incident on a glass sphere as shown.The opposite surface of the sphere is partially silvered .If the net deviation of the ray transmitted at the partially silvered surface is `1//3^(rd)`of the net deviation suffered by the ray reflected at the partially silvered surface(after emerging out of the sphere).Find the refractive index of the sphere.

Answer

`sqrt(3)`

Explanation

As given in question

`(60-r) + (60 -r) = (1)/(3) (60-r) + (180 - 2r) + (60-r)`
`implies 120 -2r = 100 - (4r)/(3) implies (2r)/(3) = 20 implies r = 30^(@)`
`therefore` 1 sin 60 = `mu xx "sin"30^(@) implies u = sqrt(3)`