Question

A ray of light strikes a transparent rectangular slab of refractive index $\sqrt{2}$ at an angle of incidence of ${45}^o$. The angle between the reflected and refracted rays is:

• A. ${75}^o$
• B. ${90}^o$
• C. ${105}^o$
• D. ${120}^o$

Answer 1

Answer: (C)

Applying Snell's law at air-glass surface,we get
I sine i= $\sqrt{2}$ sin r'
sin r' = $\frac{1}{\sqrt{2}}$ sin i
= $\frac{1}{\sqrt{2}}$ sin ${45}^{\circ }(\therefore i={45}^{\circ })$
$\Rightarrow$ sin r'= $\frac{1}{2}$ or r' = $si{n}^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$
From figure,
$i+\theta +{30}^{\circ }={180}^{\circ }$ ($\therefore$ i = r = ${45}^{\circ }$)
${45}^{\circ }+\theta +{30}^{\circ }={180}^{\circ }or\theta ={180}^{\circ }-{75}^{\circ }={105}^{\circ }$
Hence the angle between reflected and refracted rays is ${105}^{\circ }$