Question

A light ray from air is incident (as shown in figure) at one end of a glass fiber (refractive index m = 1.5) making an incidence angle of 60^o 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
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• A. $3.33\mu sec$
• B. $6.67\mu sec$
• C. $5.77\mu sec$
• D. $3.85\mu sec$

Answer 1

The correct option is D $3.85\mu sec$

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 $t=\frac{\mu x}{c}=\frac{\frac{2}{\sqrt{3}}\times {10}^3}{3\times {10}^8}=3.85\mu sec$.