Question

A ray of light passes through an equilateral glass prism, such that the angle of incidence is equal to the angle of emergence. If the angle of emergence is 3/4 times the angle of prism, calculate the refractive index of the glass prism.

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

Answer 1

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

Angle of prism for equilateral prism
A = 60°
Angle of incidence = Angle of emergence $=\frac{3}{4}$ × Angle of the prism
⇒ $i=e=\frac{3}{4}A$
⇒ $i=\frac{3}{4}\times {60}^o={45}^o$
Also, angle of refraction $r=\frac{A}{2}=\frac{{60}^o}{2}={30}^o$ [ As i = e]
According to Snell’s law, $\mu =\frac{\sin i}{\sin r}$
$\Rightarrow \mu =\frac{\sin {45}^{\circ }}{\sin {30}^{\circ }}=\frac{\left(\frac{1}{\sqrt{2}}\right)}{\left(\frac{1}{2}\right)}=\sqrt{2}$
Hence, the correct answer is option (c).