Question

The refractive index of water with respect to air is ${}_a{u}_w$ and of glass with respect to air is ${}_a{u}_g$. Express the refractive index of glass with respect to water

• A. $\frac{{}_a{u}_g}{{}_a{u}_w}$
• B. $\frac{{}_g{u}_a}{{}_a{u}_w}$
• C. $\frac{{}_a{u}_w}{{}_a{u}_g}$
• D. $\frac{{}_a{u}_a}{{}_g{u}_g}$

Answer 1

The correct option is A $\frac{{}_a{u}_g}{{}_a{u}_w}$

Refractive index of water w.r.t air
${}_a{\mu }_w=\frac{{\mu }_w}{{\mu }_a}$
Refractive index of glass w.r.t air
${}_a{\mu }_g=\frac{{\mu }_g}{{\mu }_a}$
Hence refractive index of glass w.r.t water
${}_w{\mu }_g=\frac{{\mu }_g}{{\mu }_w}=\frac{{}_a{\mu }_g}{{}_a{\mu }_w}$