One face of a prism with a refrective angle of `30^@` is coated with silver. A ray of light incident on another face at an angle of `45^@` is refracted and reflected from the silver coated face and retraces its path. What is the refractive index of the prism?

Explanation

Given, `A=30^(@),i_(1)=45^(@)and r_(2)=0`
Since, `r_(1)+r_(2)=A`
`therefore r_(1)=A=30^(@)`
Now, refractive index of the prism,
`mu=(sini_(1))/(sinr_(1))=(sin45^(@))/(sin30^(@))=(1//sqrt2)/(1//2)=sqrt2`