ACB is right-angled prism with other angles as `60^(@)` and `30^(@)` . Refractive index of the prism is 1.5. AB has thin layer of liquid on it as shown. Light falls normally on the face Ac. For total internal reflection, maximum refractive index of the liquid is

Options

A. 1.4
B. 1.3
C. 1.2
D. 1.6

Answer

b.

Explanation

Clearly, `i_(c)le60^(@)`
So, maximum possible value of `i_(c)` is `60^(@)`.
Now, `._1mu_(g)=(1)/(sini_(c))`
`(mu_(g))/(mu_(1))=(1)/(sini_(c))`
or `mu_(1)=mu_(g)sini_(c)=1.5sin60^(@)=1.5xx(sqrt(3))/(2)`
`=1.5xx0.866=1.299=1.3`