A light beam is travelling from Region IV (figure). The refractive index in regionals I, II, III and IV are n0,n02,n06 and n08 respectively. The angle of incidence θ for which the beam just misses entering region IV is -

For refraction at parallel interfacesn0sin⁡θ=n02sin⁡α=n06sin⁡β=n08sin⁡90∘∴sin⁡θ=18

A light beam is travelling from Region IV (figure). The refractive index in regionals I, II, III and IV are n0,n02,n06 and n08 respectively. The angle of incidence θ for which the beam just misses entering region IV is -

For refraction at parallel interfacesn0sin⁡θ=n02sin⁡α=n06sin⁡β=n08sin⁡90∘∴sin⁡θ=18

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A light beam is travelling from Region IV (figure). The refractive index in regionals I, II, III and IV are $n_{0}, \frac{n_{0}}{2}, \frac{n_{0}}{6}$ and $\frac{n_{0}}{8}$ respectively. The angle of incidence $θ$ for which the beam just misses entering region IV is -

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$\sin^{- 1} (1 / 4)$

$\sin^{- 1} (1 / 3)$

$\begin{aligned} \sin^{- 1} (1 / 8) \end{aligned}$

$\begin{aligned} \sin^{- 1} (3 / 4) \end{aligned}$

answer is B.

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Detailed Solution

For refraction at parallel interfaces

$n_{0} \sin θ = \frac{n_{0}}{2} \sin α = \frac{n_{0}}{6} \sin β = \frac{n_{0}}{8} \sin 90^{\circ}$

$∴ \sin θ = \frac{1}{8}$

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A light beam is travelling from Region IV (figure). The refractive index in regionals I, II, III and IV are n0,n02,n06 and n08 respectively. The angle of incidence θ for which the beam just misses entering region IV is -

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A light beam is travelling from Region IV (figure). The refractive index in regionals I, II, III and IV are $n_{0}, \frac{n_{0}}{2}, \frac{n_{0}}{6}$ and $\frac{n_{0}}{8}$ respectively. The angle of incidence $θ$ for which the beam just misses entering region IV is -