Question

A light ray from air is incident (as shown in figure) at one end of a glass fiber (refractive index, $\mu=1.5$ ) making an incidence angle of $60^{\circ}$ on the lateral surface, so that it undergoes a total internal reflection. How much time would it take to traverse the straight fiber of length $1\, km$ ?

• A. $3.33\, \mu s$
• B. $6.67\, \mu s$
• C. $5.77\, \mu s$
• D. $3.854\, \mu s$

Answer 1

Answer: (D)

Velocity of light in fiber $v=\frac{c}{\mu}=\frac{3 \times 10^{8}}{1.5}=2 \times 10^{8} m / s$
Straight length is $1\, km$,
Distance covered by light,
$s=\frac{1 km }{\sin 60^{\circ}}=\frac{1000}{\sqrt{3} / 2}=\frac{2000}{\sqrt{3}}$
So, time taken $=\frac{s}{v}=\frac{2000 / \sqrt{3}}{2 \times 10^{8}}=3.85 \mu s$