A ray of light entering from air into a denser medium of refractive index \frac{4}{3}, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ should be equal to:

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Physics

Straight Line Motion

Question

A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$ , as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ should be equal to:

$\sin^{- 1} \frac{\sqrt{7}}{4}$

$\sin^{- 1} \frac{\sqrt{5}}{3}$

$\sin^{- 1} \frac{\sqrt{5}}{4}$

$\sin^{- 1} \frac{\sqrt{7}}{3}$

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$1 \times sinθ = \frac{4}{3} \sin (90 - C)$

$sinθ = \frac{4}{3} cosC$

but $sinC = \frac{1}{μ} = \frac{5}{4}$

$cosC = \frac{\sqrt{7}}{4}$

$sinθ = \frac{4}{3} \times \frac{\sqrt{7}}{4} = \frac{\sqrt{7}}{3}$

For T.I.R. $sinθ \leq \frac{\sqrt{7}}{3}; θ = \sin^{- 1} \frac{\sqrt{7}}{3}$

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