A ray of light is incident on the left vertical face of glass cube of refractive index `n_2,` as shown in figure. The plane of incidence is the plane of the page, and the cube is surrounded by liquid (refractive index`=n_1`). What is the largest angle of incidence `theta_1` for which total internal reflection occurs at the top surfaces?

Answer

A, B

Explanation

`n_1` should be less than `n_2` for TIR at M.
`sin theta_C=n_1/n_2`
At N, `n_1sin theta_1=n_2sin(90^@-theta_C)=n_2 cos theta_C`
`:. sin theta_1=n_2/n_1 cos theta_C`
`sin theta_1=n_2/n_1 sqrt(1-sin^2 theta_C)`
`=sqrt(n_2^2-n_1^2)/n_1`