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)`

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)` (i)
Angle of incident at face AC is `60^(@)`
i.e., `i=60^(@)`
For total internal reflectino to take place,
`i gt theta_(c)`
or `sini gt sintheta_(c)`
or `sin60^(@) gt (3)/(2mu)`
or `(sqrt(3))/(2) gt (3r)/(2mu)`
or `mu gt sqrt(3)`