Question

In the figure, the optical fibre is l = 2 m long and has a diameter of d = 20 µm. If a ray of light is incident on one end of the fiber at angle θ₁ = 40°, the number of reflections it makes before emerging from the other end is close to ______.

(Refractive index of fiber is 1.31 and sin40° = 0.64)

पर्याय

• 55000

• 66000

• 45000

• 57000

Answer 1

In the figure, the optical fibre is l = 2 m long and has a diameter of d = 20 µm. If a ray of light is incident on one end of the fiber at angle θ₁ = 40°, the number of reflections it makes before emerging from the other end is close to 57000.

Explanation:

Given: Optical fibre length, l = 2 m, the diameter of the fibre, d = 20 µm, Angle of incidence at the fiber's entrance θ₁ = 40°, the refractive index of fibre, μ₂ = 1.31.

To find:

The total number of reflections inside the fibre.

Snell's law:

`mu_1/mu_2 = (sintheta_2)/(sin40^circ)`, (The refractive index of air is µ₁.)

`sintheta_2 = 1/1.31 sin40^circ`,

θ₂ = 29.39

θ = 90 - θ₂ = 90 - 29.39 = 60.6 (θ as shown in the diagram)

`tantheta = tan60.6 = x/d` (x is labelled in the diagram.)

`x = (20 xx 10^-6)`tan60.6 = 35.5µm

Number of total reflections;

`n = 1/x = (2m)/(35.5mum) = 56338.`