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Question

(C) The refractive index $(n)$ of a medium is defined as the ratio of the speed of light in a vacuum $(c)$ to the speed of light in that medium $(v)$,

Vedclass · Accepted Answer

$\frac{9}{8}$

Vedclass · Answer

(C) The refractive index $(n)$ of a medium is defined as the ratio of the speed of light in a vacuum $(c)$ to the speed of light in that medium $(v)$,given by $n = \frac{c}{v}$.From this,the velocity of light in a medium is $v = \frac{c}{n}$.Let $n_w = \frac{4}{3}$ be the refractive index of water and $n_g = \frac{3}{2}$ be the refractive index of glass.The velocity of light in water is $v_w = \frac{c}{n_w}$ and in glass is $v_g = \frac{c}{n_g}$.The ratio of the velocity of light in water to that in glass is $\frac{v_w}{v_g} = \frac{c/n_w}{c/n_g} = \frac{n_g}{n_w}$.Substituting the given values: $\frac{v_w}{v_g} = \frac{3/2}{4/3} = \frac{3}{2} 	imes \frac{3}{4} = \frac{9}{8}$.Therefore,the ratio is $\frac{9}{8}$.

If the absolute refractive indices of water and glass are $\frac{4}{3}$ and $\frac{3}{2}$ respectively,then what will be the ratio of the velocity of light in water to that of glass?

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