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)

When total internal reflection just takes place form lateral surface i = C,ie, $60^{\circ }=C$
$\Rightarrow sin60^{\circ }=sinC=\frac{1}{\mu }$
$\Rightarrow \mu =\frac{2}{\sqrt{3}}$
Time taken by light to traverse some distance in a medium
$t=\frac{\mu x}{c}=\frac{\frac{2}{\sqrt{3}}\times 10^3}{3\times 10^8}$
$=3.85\mu s$