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

Explanation

Critical angle between glass and liquid face is
`sin theta_C = (mu )/(3/2) = ( 2mu )/(3) `
Angle of incidence at face AC is `60^@`.

For the TIR to takes place at the face AC, the angle of incidence at the face AC, `i gt theta_C`,
`60^@ gt theta_C or sin 60 ^@ gt ( 2mu )/(3 ) or mu lt (3 sqrt(3))/(4)`