Question bank/JEE Main/Physics

In the shown figure a ray of light enters the face XY of a right
angered prism at grazing incident. It emerges from the adjacent face. YZ
at an angle$\ \theta$. If x is the critical angle of the prism held in
water of refractive index $\frac{4}{3}$, then the angle$\ \theta$ with
normal is

A$\theta = \sin^{- 1}\lbrack tanx\rbrack$B$\theta = \sin^{- 1}\lbrack\frac{4}{3}tanx\rbrack$C$\theta = \sin^{- 1}\lbrack\frac{3}{4}cotx\rbrack$D$\theta = \sin^{- 1}\lbrack cotx\rbrack$

Show answer and solution▾

[IMAGE] As at XY
$\frac{4}{3}sin90 = \mu sinx$
At YZ
$\mu cosx = \frac{4}{3}sin\theta$
On solving
$\theta = \sin^{- 1}(cotx)$

Source: Grass-G / P-17 Physics paper 26 Nov Second.docx