Question

What is the minimum value of the refractive index for a ${90}^{\circ }–{45}^{\circ }–{45}^{\circ }$ prism
which is used to deviate a beam through ${90}^{\circ }$ by total internal reflection ?

• A. $\frac{3}{2}$
• B. $\sqrt{3}$
• C. $\sqrt{2}$
• D. $\frac{5}{3}$

Answer 1

The correct option is C $\sqrt{2}$

At face AB, the ray of light suffers no deviation. At face AC :


$\mu =\frac{1}{sin\left({\theta }_C\right)}=\frac{1}{sin\left({45}^{\circ }\right)}$
$\therefore {\mu }_{min}=\sqrt{2}$