Question

A light ray going from air is incident (as shown in figure) at one end of a glass fibre (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 fibre of length 1 km?

• A. $3.3\, \mu s$
• B. $6.6\, \mu s$
• C. $5.7\, \mu s$
• D. $3.85\, \mu s$

Answer 1

Answer: (D)

$3.85\, \mu s$

Answer 2

When total internal reflection just takes place form lateral surface i = C,ie, $60^\circ = C$
$\Rightarrow sin\, 60^\circ = sin\, C = \frac{1}{\mu}$
$\Rightarrow \mu = \frac{2}{\sqrt 3}$
Time taken by light to traverse some distance in a medium
$t=\frac{\mu x}{c}=\frac{\frac{2}{\sqrt 3} \times 10^3}{3 \times 10^8}$
$= 3.85 \mu s$