Angle of incidence (optics)

The angle of incidence, in geometric optics, is the angle between a ray incident on a surface and the line perpendicular (at 90 degree angle) to the surface at the point of incidence, called the normal. The ray can be formed by any waves, such as optical, acoustic, microwave, and X-ray. 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.

In computer graphics and geography, the angle of incidence is also known as the illumination angle of a surface with a light source, such as the Earth's surface and the Sun.^[1] It can also be equivalently described as the angle between the tangent plane of the surface and another plane at right angles to the light rays.^[2] This means that the illumination angle of a certain point on Earth's surface is 0° if the Sun is precisely overhead and that it is 90° at sunset or sunrise.

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.

Refraction of light at the interface between two media

Grazing angle or glancing angle

Focusing X-rays with glancing reflection

Grazing angle, often called the glancing angle, is the angle between an incident ray and the surface it is approaching and is calculated as 90° minus incidence angle (the incidence ray and normal to the surface). Its conception is especially significant as it approaches near-parallelism with a surface so that it will become extremely small and find extensive application in areas of study. ^[3]

For instance, in X-ray optics, grazing incidence finds application in reflecting X-rays in telescopes by making mirrors at shallow grazing angles to focus high-energy rays that can no longer be changed by conventional lenses; it is essential in studying phenomena such as black holes in astronomy.

In spectroscopy, especially in infrared spectrometry, it enhances sensitivity while studying films that are extremely thin, while in diffraction methods, grazing incidence diffraction with X-rays or neutrons allows precise studies of surface structure through a technique that is extensively used in materials research.

In atom optics, it allows atomic beam reflection to aid experiments such as interferometry, thus showing applicability to a wide range of study subjects. ^[3]

See also

• Effect of Sun angle on climate
• Illumination angle
• Phase angle (astronomy)
• Plane of incidence
• Reflection (physics)
• Refraction
• Scattering vector
• Total internal reflection