Question

At what angle should a ray of light be incident on one of the face of an equilateral prism, so that the emergent ray may graze the surface of the prism having refractive index $(\mu =2)$ ?

• A. ${30}^{\circ }$
• B. ${90}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${90}^{\circ }$

As the emergent ray graze the surface of the prism, thus, emergent angle,
$e={90}^{\circ }$
So, the angle of incidence $\left(r_2\right)$ at the surface should have critical value.
From formula,
$r_2={\sin }^{-1}\left(\frac{{\mu }_r}{{\mu }_d}\right)$
$\Rightarrow r_2={\sin }^{-1}\left(\frac{1}{2}\right)$
$\Rightarrow r_2={30}^{\circ }$
Also, $r_1+r_2=A$
So, $r_1+{30}^{\circ }={60}^{\circ }$
$\Rightarrow r_1={30}^{\circ }$


Now, applying Snell's law at the incidence surface,
${\mu }_r\sin i={\mu }_d\sin r_1$
$\Rightarrow 1\times \sin i=2\times \sin {30}^{\circ }$
$\Rightarrow \sin i=1$
$\Rightarrow i={90}^{\circ }$

Why this question? Tips: Apply Snell's law at incidence surface and focus on the geometry of ray diagram.