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(D) According to Snell's law, for a series of parallel layers, the product of the refractive index and the sine of the angle of incidence remains cons

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(D) According to Snell's law, for a series of parallel layers, the product of the refractive index and the sine of the angle of incidence remains constant at every interface.Let $\mu_0$ be the refractive index of the $0^{	ext{th}}$ layer and $i_0$ be the angle of incidence at the first interface.$\mu_0 \sin i_0 = \mu_m \sin r_m$Given:$\mu_0 = \mu = 1.5$$i_0 = 30^{\circ}$$\mu_m = \mu - m \Delta \mu = 1.5 - m(0.015)$Since the ray emerges parallel to the interface after the $m^{	ext{th}}$ refraction, the angle of refraction $r_m = 90^{\circ}$.Substituting the values:$1.5 \sin 30^{\circ} = (1.5 - m 	imes 0.015) \sin 90^{\circ}$$1.5 	imes 0.5 = (1.5 - 0.015m) 	imes 1$$0.75 = 1.5 - 0.015m$$0.015m = 1.5 - 0.75$$0.015m = 0.75$$m = \frac{0.75}{0.015} = \frac{750}{15} = 50$Thus, the value of $m$ is $50$.

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