Question 165: Ray Optics

Question

Time taken by light to travel in two different materials $$A$$ and $$B$$ of refractive indices $$\mu_{A}$$ and $$\mu_{B}$$ of same thickness is $$t_{1}$$ and $$t_{2}$$ respectively. If $$t_{2}-t_{1}=5 	imes 10^{-10}$$ s and the ratio of $$\mu_{A}$$ to $$\mu_{B}$$ is $$1: 2$$. Then, the thickness of material, in meter is: (Given $$v_{\mathrm{A}}$$ and $$v_{\mathrm{B}}$$ are velocities of light in $$A$$ and $$B$$ materials respectively.)

Accepted Answer

$${t_2} - {t_1} = 5 	imes {10^{ - 10}}$$
$$ \Rightarrow {d \over {{v_B}}} - {d \over {{v_A}}} = 5 	imes {10^{ - 10}}$$
and, $${{{v_B}} \over {{v_A}}} = {{{\mu _A}} \over {{\mu _B}}} = {1 \over 2}$$
$$ \Rightarrow d\left( {1 - {{{v_B}} \over {{v_A}}}} ight) = 5 	imes {10^{ - 10}} 	imes {v_B}$$
$$ \Rightarrow d\left( {1 - {1 \over 2}} ight) = 5 	imes {10^{ - 10}} 	imes {v_B}$$
$$ \Rightarrow d = 10 	imes {10^{ - 10}} 	imes {v_B}\,m$$
$$ \Rightarrow d = 5 	imes {10^{ - 10}} 	imes {v_A}\,m$$

Answer

$$5 	imes 10^{-10} \,v_{\mathrm{A}}\, \mathrm{m}$$

Answer

$$5 	imes 10^{-10} \mathrm{~m}$$

Answer

$$1.5 	imes 10^{-10} \mathrm{~m}$$

Answer

$$5 	imes 10^{-10} \,v_{\mathrm{B}} \,\mathrm{m}$$

Ray Optics

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