Question

Refractive index of glass relative to water is $\dfrac{9}{8}$. What is the refractive index of water relative to glass?

Answer 1

Hint: Refractive index of a medium is defined as the measure of the speed of light in that medium with respect to the speed of light in vacuum. Refractive index of any medium is a dimensionless quantity. It is related to the refraction of light.

Complete step by step answer:
The measure of the speed of light varies in different objects. As the light bends when refracted from an object, its speed gets affected. The quantity which measures the speed of light in that medium with respect to the speed of light in vacuum is known as refractive index. It is expressed as $\mu $.

In the given question, the refractive index of glass with respect to water is given as $\dfrac{9}{8}$.Let the refractive index of water be ${\mu _w}$. And the refractive index of glass is ${\mu _g}$.According to question, the refractive index of glass with respect to water can be represented as,
$\dfrac{{{\mu _g}}}{{{\mu _w}}} = \dfrac{9}{8} - - - - - \left( 1 \right)$.

Now, we have to find the refractive index of water with respect to glass, which can be expressed as $\dfrac{{{\mu _w}}}{{{\mu _g}}}$.By inverting the equation $\left( 1 \right)$ we can find the desired result.
$\therefore \dfrac{{{\mu _w}}}{{{\mu _g}}} = \dfrac{8}{9}$.

So, the refractive index of water relative to glass is $\dfrac{8}{9}$.

Note: It must be noted that the refractive index of anything with respect to others is represented in fraction where the denominator is the part to which the refractive index is compared. In other words, we can say that (with respect to) part should be the denominator.Refractive index is a dimensionless quantity as it is the ratio of the same quantity.