Refraction and Dispersion of Light through a Prism

A prism is a transparent optical block bounded by two plane refracting surfaces inclined to each other at an angle $A$, called the refracting (or apex) angle of the prism. A ray of monochromatic light entering one face of the prism is refracted twice -- once on entering, bending towards the normal at the first face since it enters a denser medium, and once on leaving, bending away from the normal at the second face since it leaves back into air -- and the overall effect of these two refractions is to bend the ray away from its original direction by a net angle $\delta$, called the angle of deviation, and also to displace it towards the prism's base. As the angle of incidence at the first face is varied continuously, the angle of deviation $\delta$ first decreases, reaches one single minimum value $D_m$ (the angle of minimum deviation), and then increases again; at exactly this minimum-deviation condition the ray inside the prism travels symmetrically, parallel to the base, and the angle of incidence at the first face equals the angle of emergence at the second face. At minimum deviation, the refracting angle, the angle of minimum deviation and the refractive index $n$ of the prism material are related by the compact prism formula $n=\frac{\sin\left(\dfrac{A+D_m}{2}\right)}{\sin\left(\dfrac{A}{2}\right)},$ which is exactly the standard laboratory method for measuring a transparent material's refractive index precisely, by measuring $A$ and $D_m$ on a spectrometer. Because the refractive index of every real transparent material varies slightly with the wavelength (colour) of light -- being very slightly greater for violet light than for red light -- a prism, unlike a plane parallel-sided slab, deviates different colours of light by slightly different angles, so that when a narrow beam of white light (a mixture of all visible colours) enters a prism, it emerges spread out into its full visible spectrum, from violet (deviated most) through to red (deviated least); this splitting of white light into its constituent colours is called dispersion, and the angle bet …