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 indes `3//2` . Find the limits of `mu` for which total internal reflection takes place on the face AC.

Options

A. `mu gt (sqrt3)/(2)`
B. `mu lt (3sqrt3)/(4)`
C. `mu gt sqrt3`
D. `mu lt (sqrt3)/(2)`

Answer

B

Explanation

Critical angle between glass and liquid face is `sin theta_(C ) = (mu)/(3//2)`
`:. Sin theta_(c ) = (2 mu)/(3)`
Angle of incidence at face AC is `60^(@)`
For TIR to take plane `l gt theta_(c )`
or `sin 60^(@) gt (2 mu)/(3)` or `mu lt (3 sqrt3)/(4)`