In figure, the optical fiber is $l=2 \mathrm{~m}$ long and has a diameter of $d=20 \mu \mathrm{~m}$. If a ray of light is incident on one end of the fiber at angle $\theta_{1}=40^{\circ}$, the number of reflection it makes before emerging from the other end is close to:

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Geometrical Optics

In figure, the optical fiber is

l = 2 m

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

θ_{1} = 4 0^{\circ}

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

Answer: (D)

Light entering the end face at

4 0^{\circ}

refracts to an internal angle

θ_{2}

given by

sin 4 0^{\circ} = 1.31 sin θ_{2}

, so

sin θ_{2} \approx \frac{0.643}{1.31} \approx 0.49

and

θ_{2} \approx 2 9^{\circ}

. Between successive reflections the ray advances

x = \frac{d}{tan θ _{2}}

along the fibre, with diameter

d = 20 μ

m, so over the length

l = 2

m the number of reflections is

N = \frac{l}{x} = \frac{l tan θ _{2}}{d} \approx \frac{2 \times 0.56}{20 \times 1 0 ^{- 6}} \approx 5.5 \times 1 0^{4}

, close to

55000

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Single correct option