The x-z plane separates two media A and B of refractive indices $μ_{1} = 1.5$ and $μ_{2} = 2$ . A ray of light travels from A to B. Its directions in the two media are given by unit vectors ${\vec{u}}_{1} = a \hat{i} + b \hat{j}$ and ${\vec{u}}_{2} = c \hat{i} + d \hat{j}$ . Then

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$\frac{a}{c} = \frac{4}{3}$

$\frac{b}{d} = \frac{3}{4}$

$\frac{a}{c} = \frac{3}{4}$

$\frac{b}{d} = \frac{4}{3}$

answer is A.

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Detailed Solution

Applying Snell’s law $μ_{1} \sin i = μ_{2} \sin r (\frac{3}{2}) (\frac{a}{\sqrt{a^{2} + b^{2}}}) = 2 (\frac{c}{\sqrt{c^{2} + d^{2}}})$ Here $\sqrt{a^{2} + b^{2}} = \sqrt{c^{2} + d^{2}} = 1$ $∴$ $\frac{a}{c} = \frac{4}{3}$

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