# prism dispersive power in water

What is dispersive power of a prism? What happens to the dispersive power of a prism immersed in water?

P.S:The answer may be on the net but I'm getting contradictive answers so decided to ask here.

A prism uses the fact that a plane wave of light traversing the boundary of two media with different indices of refraction, changes direction according to the Snell's law: $$n_1 \sin \theta_1 = n_2 \sin \theta_2\to \sin \theta_2 = \frac{n_2}{n_1}\sin \theta_1$$
From the relation above it is evident that the more the difference between the refraction indices of the two media, the more the angle $\theta_2$ differs from $\theta_1$. We can show this very easily assuming the difference in the refractive indices is small (which is usually the case):
$$\theta_2 = \theta_1 + \Delta \theta \to \sin (\theta_1+\Delta \theta) = \frac{n_2}{n_1}\sin \theta_1$$ $$\sin \theta_1 \cos \Delta \theta + \sin \Delta \theta \cos \theta_1=\frac{n_2}{n_1}\sin \theta_1$$ $$\cos \Delta\approx 1\quad , \quad \sin \Delta \theta \approx \Delta \theta \to$$ $$\Delta \theta = \frac{n_2 - n_1}{n_1}\sin \theta_1$$
By immersing the prism in water, you effectively reduce the difference in $n$ s of the two media, $($because $n_{glass}>n_{water}>n_{air})$ which results in a smaller $\Delta \theta$ (or smaller refraction).