Angle of Incidence Calculator

Calculate the angle of incidence when light hits a surface, given the angle of refraction and refractive indices of both media.

ANGLE OF INCIDENCE
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Angle of Incidence
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Critical Angle
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Reflectance (s-pol)
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Brewster Angle
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Angle of Incidence Explained

The angle of incidence is the angle between an incoming ray of light and the normal (perpendicular line) to the surface at the point of contact. It is a fundamental concept in optics that determines how light reflects and refracts when passing between different media such as air, water, glass, and crystals.

Understanding the angle of incidence is essential for designing lenses, fiber optics, solar panels, anti-reflective coatings, and optical instruments. It also explains everyday phenomena like why pools look shallower than they are and why diamonds sparkle with fire and brilliance.

Snell Law

n1 sin(θi) = n2 sin(θr)
θi = arcsin(n2 sin(θr) / n1)

Where n1 and n2 are the refractive indices of the two media, theta_i is the angle of incidence, and theta_r is the angle of refraction.

Refractive Indices of Common Materials

MaterialRefractive Index
Vacuum1.000
Air1.0003
Water1.333
Crown Glass1.52
Flint Glass1.62
Diamond2.42

FAQ

What is total internal reflection?

When light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle, all light is reflected back. This is the principle behind fiber optics and prism-based retroreflectors used in road signs.

What is the Brewster angle?

The Brewster angle is the angle of incidence at which reflected light is completely polarized. At this angle, the reflected and refracted rays are perpendicular. Polarizing sunglasses exploit this to reduce glare from horizontal surfaces.

Why does light bend when entering glass?

Light travels slower in denser media. When a wavefront enters glass at an angle, one side slows down before the other, causing the wave to change direction. This is analogous to how a car veers when one wheel hits mud while the other is still on pavement.