An optical fiber consists of a non-graded glass core (index of refraction $n_{1}$ ) surrounded by a cladding (index of refraction $n_{2}$ ) $n_{2} < n_{1}$ . Suppose if a beam of light enters the fiber from air at an angle ‘ $θ$ ’ with the fiber axis as shown. Then (c is speed of light in vacuums)

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The time difference between ray that travels ‘L’ distance along fiber axis and that is reflecting at critical angle is $Δ t = \frac{L n_{2}}{c n_{1}} (n_{1} - n_{2})$

The greatest possible value of ‘ $θ$ ’ for which ray can be propagated through fiber is $θ = \cos^{- 1} \sqrt{n_{1}^{2} - n_{2}^{2}}$

The time difference between ray that travels ‘L’ distance along fiber axis and that is reflecting at critical angle is $Δ t = \frac{L n_{1}}{c n_{2}} (n_{1} - n_{2})$

The greatest possible value of ‘ $θ$ ’ for which ray can be propagated through fiber is $θ = \sin^{- 1} \sqrt{n_{1}^{2} - n_{2}^{2}}$

answer is A, D.

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Detailed Solution

$\sin θ = μ \sin r, u s e r + c + 90 = 180, t_{1} = \frac{L}{c} t_{2} = \frac{2 A B n_{1}}{c} = \frac{L {n^{2}}_{1}}{c n_{2}} t_{2} - t_{1} = \frac{L n_{1}}{c} [\frac{n_{1}}{n_{2}} - 1] Δ t = \frac{L n_{1}}{c n_{2}} [n_{1} - n_{2}]$