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 $1km$ ?

• 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 $1km$,
Distance covered by light,
$s=\frac{1km}{\sin 60^{\circ }}=\frac{1000}{\sqrt{3}/2}=\frac{2000}{\sqrt{3}}$
So, time taken $=\frac{s}{v}=\frac{2000/\sqrt{3}}{2\times 10^8}=3.85\mu s$