Question

In figure, the optical fiber is l = 2m long and has a diameter of d = 20 μ m. If a ray of light is incident on one end of the fiber at angle
θ₁ = 40º , the number of reflection it makes before emerging from the other end is close to:
(A) 57000 (B) 45000
(C) 66000 (D) 55000

Answer 1

The number of reflection it makes before emerging from the other end is close to:

(A) 57000

This can be calculated as follows:

• Given, l = 2m and θ₁ = 40º

• Thus, As per the question,

        l sin  40º = 1.31 sin θ

               sin θ = 0.64 / 1.31

                        ≈ 1/2

• ∴ θ = 30º

• Now, a = D / ( 1 / √3 )

                    = 20√3 x 10⁻⁶ m

• Thus, number of reflections = 20 / (20√3 x 10⁻⁶)

                                                       ≈ 57000