Refractive index of glass relative to water is 9: 8. What is the refractive index of water relative to glass?

Refractive index of glass relative to water is = $\frac{8}{9}$

To find : the refractive index of water relative to glass

Solution:

We know, that the refractive index of a medium 1 with respect to medium 2 is reciprocal to the refractive index of medium 2 with respect to medium 1.

Therefore,

Refractive index of glass relative to water,  $^{w}\mu_{g}$ $ =\frac{{\mu }_{g}}{{\mu}_{w}}=\frac{9}{8}$     (given)

Refractive index of water relative to glass, $^{g}\mu_{w}$ $=\frac{{\mu }_{w}}{{\mu }_{g}}=\frac{1}{^{w}\mu_{g}}=\frac{1}{\frac{{\mu }_{g}}{{\mu }_{w}}}=\frac{1}{\frac{9}{8}}=\frac{8}{9}$

Hence, the refractive index of water relative to glass is $ \frac{8}{9}$