 Minimum deviation

For a homogeneous optical prism in air, let its apex angle be $\varphi$ and refractive index $n>1$. A transmitted ray through both refracting faces exists only iffor a nongrazing symmetric path. At minimum deviation, both internal angles are $\varphi /2$ and both external angles are $({\delta }_{\min }+\varphi )/2$. Snell's law gives

To see the feasibility condition, the internal angles sum to $\varphi$ and each must be below the escape critical angle $\arcsin (1/n)$. The symmetric path satisfies both restrictions exactly when the displayed inequality holds. Under the ordinary transmitted-ray geometry, symmetry also minimizes the sum of the two external angles.

Measuring ${\delta }_{\min }$ therefore determines $n$ at the chosen wavelength. For $\varphi =60^{\circ }$ and $n=1.5$, the deviation is approximately $37.18^{\circ }$. The formula does not describe an emerging ray when the required refraction is forbidden.

Minimum deviation is a concept that can refer to different things depending on the context. Here are a few interpretations: 1. **Statistics and Data Analysis**: In statistics, minimum deviation often refers to the smallest difference between observed values and a central value (like the mean or median). It's used in various statistical calculations and optimization problems to minimize the spread of data points.