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

Option: 1
$5 \times 10^{-10} v_{\mathrm{A}} \mathrm{m}$

Option: 2
$5 \times 10^{-10} \mathrm{~m}$

Option: 3
$1.5 \times 10^{-10} \mathrm{~m}$

Option: 4
$5 \times 10^{-10} v_{\mathrm{B}} \mathrm{m}$

Answers (1)

best_answer

Let the thickness of material be d

From Snell's law,

$\mathrm{\frac{\mu_A}{\mu_B}=\frac{V_B}{V_A}=\frac{1}{2} }$

$\mathrm{\frac{V_B}{V_A}=\frac{d / t_2}{d / t_1}=\frac{1}{2} }$

$\mathrm{\frac{t_1}{t_2}=\frac{1}{2} }$

$\mathrm{\frac{t_2}{t_1}=\frac{2}{1}}$

$\mathrm{\frac{t_2-t_1}{t_1}=1 }$

$\mathrm{t_1=5 \times 10^{-10} \mathrm{~s} }$

$\mathrm{V_A=\frac{d}{t_1} }$

$\mathrm{d=V_A t_1=(5 \times10^{-10})V{_{A}}}$

Hence (1) is correct option

Posted by

manish painkra

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