# Angle of incidence (optics)

In geometric optics, the **angle of incidence** is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal. The ray can be formed by any wave: optical, acoustic, microwave, X-ray and so on. In the figure below, the line representing a ray makes an angle θ with the normal (dotted line). The angle of incidence at which light is first totally internally reflected is known as the critical angle. The angle of reflection and angle of refraction are other angles related to beams.

Determining the angle of reflection with respect to a planar surface is trivial, but the computation for almost any other surface is significantly more difficult. The exact solution for a sphere (which has important applications in astronomy and computer graphics) was an open problem for nearly 50 years until a closed-form result was derived by mathematicians Allen R Miller and Emanuel Vegh in 1991.^{[1]}

## Glancing angle

When dealing with a beam that is nearly parallel to a surface, it is sometimes more useful to refer to the angle between the beam and the surface, rather than that between the beam and the surface normal, in other words 90° minus the angle of incidence. This small angle is called a **glancing angle** or **grazing angle**. Incidence at grazing angles is called "grazing incidence".

Grazing incidence diffraction is used in X-ray spectroscopy and atom optics, where significant reflection can be achieved only at small values of the grazing angle. Ridged mirrors are designed for reflection of atoms coming at small grazing angle. This angle is usually measured in milliradians. In optics, there is Lloyd's mirror.

## See also

## Notes

- ↑ Allen R Miller and Emanuel Vegh (1993). "Exact Result for the Grazing Angle of Specular Reflection from a Sphere".
*SIAM Review*.**35**: 472–480. doi:10.1137/1035091.