The velocity of light in glass whose refractive index with respect to air is $1.5$ is $2 \times 10^{8} m s^{- 1}$ and in certain liquid, the velocity of light is found to be $2.50 \times 10^{8} m s^{- 1}$ . Find the refractive index of that liquid with respect to air.

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1.2

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1.5

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1.6

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Solution

The correct option is B
1.2

Refractive index ( $μ$ ) is inversely proportional to velocity ( $ν$ ).
${Let μ}_{l}$ = Refractive index of liquid wrt air
$μ_{g}$ =Refractive index of glass wrt air =1.5
$ν_{l}$ = velocity of light in liquid = $2.5 \times 10^{8}$
$ν_{g}$ =velocity of light in glass = $2 \times 10^{8}$

$μ α \frac{1}{v}$
$\Rightarrow \frac{μ_{l}}{μ_{g}} = \frac{v_{g}}{v_{l}}$
$\Rightarrow \frac{μ_{l}}{1.5} = \frac{2 \times 10^{8}}{2.5 \times 10^{8}}$
$\Rightarrow μ_{l} = 1.2$

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The velocity of light in glass whose refractive index with respect to air is 1.5 is 2×108 ms−1and in certain liquid, the velocity of light is found to be 2.50×108 ms−1. Find the refractive index of that liquid with respect to air.

The velocity of light in glass whose refractive index with respect to air is $1.5$ is $2 \times 10^{8} m s^{- 1}$ and in certain liquid, the velocity of light is found to be $2.50 \times 10^{8} m s^{- 1}$ . Find the refractive index of that liquid with respect to air.