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  • The  - plane separates two media <img alt="\mathrm{A}" src="https://entrancecorner.oncodecogs.c

The \mathrm{xz} - plane separates two media \mathrm{A} and \mathrm{B} with refractive indices \mathrm{\mu _{1}} and \mathrm{\mu _{2}} , respectively. A ray of light travels from \mathrm{A} and \mathrm{B}. Its directions in the two media are given by the unit vectors \mathrm{r_{A}=a\hat{i}+b\hat{j}} and \mathrm{r_{B}=\alpha \hat{i}+\beta \hat{j}} respectively, where \mathrm{ \hat{i}} and \mathrm{ \hat{j}} are unit vectors in the \mathrm{ x} and \mathrm{y} - directions. Then;

Option: 1

\mu_1 \mathrm{a}=\mu_2 \alpha


Option: 2

\mu_1 \alpha=\mu_2^a


Option: 3

\mu_1 b=\mu_2 \beta


Option: 4

None of these 


Answers (1)

best_answer

From the Snell’s law, \mu_1 \sin i_1=\mu_2 \sin i_2

\begin{aligned} & \therefore \quad \frac{\mu_1 \mathrm{a}}{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}=\frac{\mu_2 \alpha}{\sqrt{\alpha^2+\beta^2}} \quad\left(\because \sin \theta=\frac{\text { Height }}{\text { Hypotenuse }}\right)\left(\begin{array}{l} \because \mathrm{r}_{\mathrm{A}}=\mathrm{a} \hat{\mathrm{i}}+\mathrm{b} \hat{\mathrm{j}} \text { and } \\ \mathrm{r}_{\mathrm{B}}=\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}} \text { are unit vectors } \end{array}\right) \\ & \quad \sqrt{\mathrm{a}^2+\mathrm{b}^2}=\sqrt{\alpha^2+\beta^2}=1 \\ & \therefore \quad \mu_1 \mathrm{a}=\mu_2 \alpha \end{aligned}
 

Posted by

Irshad Anwar

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