The Refractive index of water with respect to air is 1. 33 and that of the diamond is 2. 42. What is the refractive index of water with respect to diamond?

Let the speed of light in water be 𝑣_w and in diamond be v_d.

The Refractive index of water w.r.t diamond is say $\left(\mathrm{n}\right)=\frac{\text{ Speed of light in diamond }}{\text{ Speed of light in water }}$

$\mathrm{n}=\frac{{\mathrm{v}}_{\mathrm{d}}}{{\mathrm{v}}_{\mathrm{w}}}$

Dividing both the numerator and denominator by the speed of light (𝑐) we get:

$\mathrm{n}=\left(\frac{{\mathrm{v}}_{\mathrm{d}}}{\mathrm{c}}\right)÷\left(\frac{{\mathrm{v}}_{\mathrm{w}}}{\mathrm{c}}\right)$

$\Rightarrow \text{ Inverse Ratio of the refractive index of diamond and water. }$

Refractive index of water = 1. 33 (Given)

Refractive index of diamond = 2. 42 (Given)

$\mathrm{n}=\frac{{\mathrm{v}}_{\mathrm{w}}}{{\mathrm{v}}_{\mathrm{d}}}$

$\Rightarrow \mathrm{n}=\frac{1.33}{2.42}$

$\Rightarrow \mathrm{n}=0.55\text{ (approx.) }$

The refractive index of diamond with respect to water is 1.82.