Part 4/6:
The deviation can be expressed as:
[ D(\alpha) = \alpha + \pi - 4\beta ]
where (\alpha) is the initial angle and (\beta) is derived from the light's travel through the medium. To determine the most pronounced deviation angle — and thus where the brightest rainbow colors appear — one needs to find the derivative of the deviation with respect to the angle of incidence and set it to zero.
This calculus yields several equations involving sine and cosine functions, which ultimately allow one to calculate the specific angles needed for different wavelengths of light.