The velocity of light in diamond is left(frac | vedclass

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(A) Given that the velocity of light in diamond is $v_d = \frac{5}{12}c$ and in water is $v_w = \frac{3}{4}c$,where $c$ is the speed of light in air.R

Vedclass · Accepted Answer

$\sin^{-1}(9/10)$

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(A) Given that the velocity of light in diamond is $v_d = \frac{5}{12}c$ and in water is $v_w = \frac{3}{4}c$,where $c$ is the speed of light in air.Refractive index of diamond with respect to water is given by ${}_w n_d = \frac{n_d}{n_w} = \frac{c/v_d}{c/v_w} = \frac{v_w}{v_d}$.Substituting the values: ${}_w n_d = \frac{3/4 c}{5/12 c} = \frac{3}{4} 	imes \frac{12}{5} = \frac{9}{5}$.Using Snell's Law: ${}_w n_d = \frac{\sin i}{\sin r}$.Therefore,$\sin i = {}_w n_d 	imes \sin r = \frac{9}{5} 	imes \sin 30^{\circ}$.Since $\sin 30^{\circ} = \frac{1}{2}$,we get $\sin i = \frac{9}{5} 	imes \frac{1}{2} = \frac{9}{10}$.Thus,$i = \sin^{-1}\left(\frac{9}{10}ight)$.

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