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The refractive index of glass with respect to air is $\frac {3}{2}$ and the refractive index of water with respect to air is $\frac {4}{3}$. The refractive index of glass with respect to water will be:(a) 1.525 (b) 1.225 (c) 1.425 (d) 1.125
(d) 1.125
Explanation
Given:
Refractive index of glass with respect to air, $_{a}\ {n}_{g}$ = $\frac {3}{2}$ Refractive index of water with respect to air, $_{a}\ {n}_{w}$ = $\frac {4}{3}$.
To find: Refractive index of glass with respect to water $(_{w}\ {n}_{g})$.
Solution:
From the formula for refractive index, we know that-
$Refractive\ index\ of\ a\ medium=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ medium}$
Here,
$Refractive\ index\ of\ glass\ with\ respect\ to \ water,\ (_{w}\ {n}_{g})=\frac {Refractive\ index\ of\ glass\ with\ respect\ to \ air}{Refractive\ index\ of\ water\ with\ respect\ to \ air}$
$_{w}\ {n}_{g}=\frac {\frac {3}{2}}{\frac {4}{3}}$
$_{w}\ {n}_{g}={\frac {3}{2}}\times {\frac {3}{4}}$
$_{w}\ {n}_{g}={\frac {9}{8}}$
$_{w}\ {n}_{g}=1.125$
Thus, the refractive index of glass with respect to water is 1.125.
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