Question

In the figure, the optical fiber is $2m$ long and has a diameter $d=20\mu m$. If a ray of light is incident on one end of the fiber at angle ${\theta }_1={40}^{\circ }$, the number of reflections it makes before emerging from the other end is close to (refractive index of fiber is $1.31$ and $sin{40}^{\circ }=0.64$)

• A. 66000
• B. 55000
• C. 45000
• D. 57000

Answer 1

The correct option is D 57000

$1.\sin \left(40\right)=1.31\sin \left(\theta \right)\Rightarrow \sin \left(\theta \right)=\frac{0.64}{1.31}\approx 0.49\Rightarrow \theta =30°\tan 30°=\frac{d}{x}=\frac{1}{\sqrt{3}}\Rightarrow x=\sqrt{3}d$
No. of reflections $=\frac{l}{x}=\frac{l}{\sqrt{3}d}=\frac{2}{20\sqrt{3}\times {10}^{-6}}=57735\approx 57000$