9.3 Refraction through a Prism

9.3 Refraction through a Prism

For a prism with angle $A$, the angle of deviation $\delta$ is:

$$\delta = (i_1 + i_2) - A$$

At minimum deviation ($\delta = \delta_m$), the ray passes symmetrically: $i_1 = i_2 = i$ and $r_1 = r_2 = r$.

$$r = \frac{A}{2}, \quad i = \frac{A + \delta_m}{2}$$

The refractive index of the prism:

$$n = \frac{\sin\left(\dfrac{A + \delta_m}{2}\right)}{\sin\left(\dfrac{A}{2}\right)}$$

Dispersion

White light splits into its component colours when passing through a prism because the refractive index depends on wavelength:

$$n_{\text{violet}} > n_{\text{red}}$$ $$\therefore \; \delta_{\text{violet}} > \delta_{\text{red}}$$