Question

As shown in above figure, a beam of light in air is incident upon the smooth surface of glass ${30}^o$ with glass surface. Calculate the refractive index of the glass if the reflected beam and refracted beam are perpendicular to each other.

• A. $\frac{1}{2}$
• B. $\frac{1}{2}\sqrt{3}$
• C. $\sqrt{3}$
• D. $2\sqrt{3}$
• E. $3\sqrt{3}$

Answer 1

Answer: (C)

$\sqrt{3}$

From figure, $i={90}^o-{30}^o={60}^o$

And, from law of reflection , angle of reflection=$r=i={60}^o$

Since, reflected and refracted ray are normal,

hence,

$r+R+{90}^o={180}^o$ where $R$= angle of refraction

$⟹R={90}^o-r={90}^o-{60}^o={30}^o$

From Snell's Law:-

$\mu =\frac{\sin i}{\sin R}=\frac{\sin {60}^o}{\sin {30}^o}$

$⟹\mu =\sqrt{3}$

Answer-(C)