Rays of light fall on the plane surface of a half cylinder at an angle `45^@` in the plane perpendicular to the axis (see figure). Refractive index of glass is `sqrt2.` Discuss the condition that the rays do not suffer total internal reflection.

Answer

A, B, C, D

Explanation

`sqrt2=(sin 45^@)/sinr`

`r=30^@`
`theta_C=sin^-1(1/mu)=45^@`
Applying sine law in `Delta`CPM,
`(CP)/(sin theta_C)=(CM)/(sin(90^@+r))`
`:. (CP)/((1//sqrt2))=R/cosr [R=radius]`
`:. CP=sqrt(2/3) R`
As we move away from C, angle PMC will
increse. Therefore, CP ? `sqrt(2/3) R.` Same is the case
on left side of C.