Question

A light ray from the air is incident (as shown in the 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

Time taken by light to traverse some distance in a medium $t=\frac{\mu x}{c}$

• A. 3.33 μ sec
• B. 6.67 μ sec
• C. 5.77 μ sec
• D. 3.85 μ sec

Answer 1

The correct option is D 3.85 μ sec

When total internal reflection just takes place from lateral surface i = C i.e. ${60}^{\circ }=C$
$\Rightarrow sin{60}^{\circ }=sinC=\frac{1}{\mu }\Rightarrow \mu =\frac{2}{\sqrt{3}}$

Time taken by light to traverse some distance in a medium $t=\frac{\mu x}{c}=\frac{\frac{2}{\sqrt{3}}\times {10}^3}{3\times {10}^3}=3.85\mu sec.$