Q157 / 170 · Manipal (MET) 2019 · Physics
A light ray from air is incident (as shown in 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 ?
- A$3.33 \mu \mathrm{~s}$
- B$6.67 \mu \mathrm{~s}$
- C$5.77 \mu \mathrm{~s}$
- Correct answerD$3.85 \mu \mathrm{~s}$
Solution
Velocity of light in fiber
$v=\frac{c}{\mu}=\frac{3 \times 10^8}{1.5}=2 \times 10^8 \mathrm{~m} / \mathrm{s}$
Straight length is 1 km , Distance covered by light, $s=\frac{1 \mathrm{~km}}{\sin 60^{\circ}}=\frac{1000}{\sqrt{3} / 2}=\frac{2000}{\sqrt{3}}$
So, time taken $=\frac{s}{v}=\frac{2000 / \sqrt{3}}{2 \times 10^8}=3.85 \mu \mathrm{~s}$
Straight length is 1 km , Distance covered by light, $s=\frac{1 \mathrm{~km}}{\sin 60^{\circ}}=\frac{1000}{\sqrt{3} / 2}=\frac{2000}{\sqrt{3}}$
So, time taken $=\frac{s}{v}=\frac{2000 / \sqrt{3}}{2 \times 10^8}=3.85 \mu \mathrm{~s}$
Hence, the correct answer is option: 'D'.