A light ray from air is incident (as shown in figure) at one end of a glass fiber (refractive index $μ =$ 1.5) making an incidence angle of 60° 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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3.33 µ sec

6.67 µ sec

3.85 µ sec

5.77 µ sec

answer is C.

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Detailed Solution

When total internal reflection just takes place from lateral surf'ace i = Critical angle = $60^{0}$

Time taken by light to traverse length x in the medium = $\frac{x}{v} = \frac{x}{\frac{c}{μ}} = \frac{μ x}{c}$

If L be the length of the fibre then x = $\frac{L}{S i n 60^{0}} = \frac{2 L}{\sqrt{3}}$

Therefore time t = $\frac{2 μ L}{\sqrt{3} c} = \frac{2 \times 1.5 \times 1000}{\sqrt{3} \times 3 \times 10^{8}} s e c o n d = 5.77 μ s$

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