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

for refracted rays
`delta_(1)=60^(@)-theta`(Clock Wise)
`delta_(3)=60^(@)-theta`(Clock Wise)
for reflated ray
`delta_(2)=180^(@)-2theta`(Clock Wise)
`delta_("net")=delta_(1)+delta_(2)+delta_(3)`
`delta_("net")=(60^(@)-theta)+(180^(@)-2theta)+(60^(@)-theta)`
`delta_("net")=300^(@)-4theta`
For transmitted ray
`delta_("net")=delta_(1)+delta_(2)`
`=2(60^(@)-theta)`
Given that`delta_("net")=(1)/(3)delta_("net")`
`2(60^(@)-theta)=(1)/(3)(300^(@)-4theta)`
`360^(@)-6theta=300^(@)-4theta`
`2theta=60^(@)`
`theta=30^(@)`
Applying Snell's law at first surface
`1xxsin60^(@)=musin30^(@)`
`mu=sqrt(3)`