Light is incident normally on face AB of a prism as shown in Figure. A liquid of refractive index `mu` is placed on face AC of the prism. The prism is made of glass of refractive indices `3//2` . Find the limits of `mu` for which total internal reflection takes place on the face AC.

Options

A. `mugt(3)/(4)`
B. `mult(3sqrt(3))/(4)`
C. `mugtsqrt(3)`
D. `mult(sqrt(3))/(2)`

Answer

C

Explanation

Critical angle between glass and liquid face is
`sintheta_(c)=(3//2)/(mu)=(3)/(2mu)` ....(1)
Angle of incidence at `AC` is `60^(@)`
i.e., `i=60^(@)`
For total internal refelction to take place
or `sin i gt sin theta_(c)`
or `sin60^(@)gt(3)/(2mu)`
or `(sqrt(3))/(2)gt(3)/(2mu)`
or `mgtsqrt(3)`