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