Question

Let PQR is a right angled prism with other angles as ${60}^o$ and ${30}^o$. PQ has a thin layer of liquid and light falls normally on the face PR as shown in figure. If the refractive index of prism is 1.5, then for total internal reflection, maximum refractive index of liquid will be

• A. 1.2
• B. 1.3
• C. 1.4
• D. 1.5

Answer 1

The correct option is B 1.3

For total internal reflection, at PQ
$\theta <C$
From geometry of figure,
$\theta =60$ i.e., 60 > C
$=\sin 60>\sin C$
$=\frac{\sqrt{3}}{2}>\frac{{\mu }_{liquid}}{{\mu }_{prism}}={\mu }_{liquid}<\frac{\sqrt{3}}{2}\times {\mu }_{prism}$
$={\mu }_{liquid}<\frac{\sqrt{3}}{2}\times 1.5={\mu }_{liquid}<1.3$