Question

With respect to air, the refractive indices of water and benzene are $1.33$ and $1.50$ respectively. Calculate the refractive index of benzene with respect to water.

Answer 1

Step 1 - Given data and assumptions made

Refractive index of water with respect to air is, ${\mu }_w=1.33$

Refractive index of benzene with respect to air is, ${\mu }_b=1.50$

Assume the relative refractive index of benzene with respect to water as, ${}_w{\mu }_b$.

Step 2 - Finding the relative refractive index.

Now, the formula to calculate the relative refractive index is given by, ${}_w{\mu }_b=\frac{{\mu }_b}{{\mu }_w}$. Substitute the values into the formula.

$$\begin{gathered} {}_w{\mu }_b=\frac{1.50}{1.33} \\ \approx 1.13 \end{gathered}$$

Thus, the refractive index of benzene with respect to water is $1.13$.