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(B) According to Snell's law,for a stack of parallel layers,the product of the refractive index and the sine of the angle of incidence remains constan

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) According to Snell's law,for a stack of parallel layers,the product of the refractive index and the sine of the angle of incidence remains constant at every interface.Let the refractive index of the initial medium be $n = 1.6$ and the angle of incidence be $	heta = 30^{\circ}$.The refractive index of the $m^{	ext{th}}$ slab is given by $n_m = n - m \Delta n$,where $\Delta n = 0.1$.The ray emerges parallel to the interface between the $(m-1)^{	ext{th}}$ and $m^{	ext{th}}$ slabs,which means the angle of refraction in the $m^{	ext{th}}$ slab is $90^{\circ}$.Applying Snell's law between the initial medium and the $m^{	ext{th}}$ slab:$n \sin 	heta = n_m \sin 90^{\circ}$Substituting the given values:$1.6 	imes \sin 30^{\circ} = (1.6 - m 	imes 0.1) 	imes 1$$1.6 	imes 0.5 = 1.6 - 0.1m$$0.8 = 1.6 - 0.1m$$0.1m = 1.6 - 0.8$$0.1m = 0.8$$m = 8$Thus,the value of $m$ is $8$.

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