Question

# If the absolute refractive index of Glass is 1.5 and that of water is 4/3 find the refractive index of water with respect to glass

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Solution

## Dear Student, $\mathrm{If}{\mathrm{v}}_{1}\mathrm{is}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}\phantom{\rule{0ex}{0ex}}{\mathrm{v}}_{2}\mathrm{is}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{glass}\phantom{\rule{0ex}{0ex}}{\mathrm{v}}_{3}\mathrm{is}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{water}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{glass}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{vacuum},{\mathrm{n}}_{\mathrm{g}}=\frac{{\mathrm{v}}_{1}}{{\mathrm{v}}_{2}}=\frac{3}{2}\phantom{\rule{0ex}{0ex}}\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{water}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{vacuum},{\mathrm{n}}_{\mathrm{w}}=\frac{{\mathrm{v}}_{1}}{{\mathrm{v}}_{3}}=\frac{4}{3}\phantom{\rule{0ex}{0ex}}\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{water}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{glass},{}_{\mathrm{g}}\mathrm{n}_{\mathrm{w}}=\frac{{\mathrm{v}}_{2}}{{\mathrm{v}}_{3}}\phantom{\rule{0ex}{0ex}}{}_{\mathrm{g}}\mathrm{n}_{\mathrm{w}}=\frac{{\mathrm{v}}_{2}}{{\mathrm{v}}_{1}}×\frac{{\mathrm{v}}_{1}}{{\mathrm{v}}_{3}}\phantom{\rule{0ex}{0ex}}{}_{\mathrm{g}}\mathrm{n}_{\mathrm{w}}=\frac{2}{3}×\frac{4}{3}=\frac{8}{9}$

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