In figure, the optical fiber 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 sin 40°=0.64)

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Accepted Answer

(3) 57000. At entry: sin θ₂=(0.64)/(1.31)≈0.489⇒θ₂≈29.2°, tan θ₂≈0.560. Axial distance between successive reflections: d/(tan θ₂)=(20×10⁻⁶)/(0.560)≈3.57×10⁻⁵ m. N=(l tan θ₂)/d=(2×0.560)/(20×10⁻⁶)≈5.6×10⁴. With sin 40°=0.64 this is 55990, almost midway between the options; with the exact sin 40°=0.643, tan θ₂≈0.563 and N≈56300, nearest 57000.

In figure, the optical fiber 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 sin 40°=0.64)

Step-by-step solution

Why the other options are wrong