The angular dispersion caused by a prism

The angular dispersion produced by a thin prism is given by $\theta = (\mu_v - \mu_r)A$, where $\mu_v$ and $\mu_r$ are the refractive indices for violet and red light respectively, and $A$ is the angle of the prism.

The dispersive power of the material of the prism is defined as $\omega = \dfrac{\mu_v - \mu_r}{\mu - 1}$, where $\mu$ is the average refractive index (usually for yellow light).

Rearranging this, we get $\mu_v - \mu_r = \omega(\mu - 1)$.

Substituting this into the expression for angular dispersion, we obtain:

$\theta = \omega(\mu - 1)A$

From this relation, it is evident that for a given angle of prism $A$ and dispersive power $\omega$, the angular dispersion $\theta$ is directly proportional to $(\mu - 1)$.

Therefore, the angular dispersion increases when the average refractive index increases.