Prism Calculator

The angle of deviation (δ) is the angle between the original direction of the incident ray and the final direction of the emergent ray after passing through the prism. It depends on the prism angle, refractive index, and the angle of incidence.

The angle of deviation is calculated using δ = i + e − A, where i is the angle of incidence, e is the angle of emergence, and A is the prism angle. Snell's law (n₁ sin i = n₂ sin r) is applied at each surface to find the refraction angles.

The minimum angle of deviation (δₘ) occurs when the ray passes symmetrically through the prism, meaning the angle of incidence equals the angle of emergence. It is given by δₘ = 2i − A at this condition, or derived from n = sin((A + δₘ)/2) / sin(A/2).

Crown glass has a refractive index of about 1.52, flint glass about 1.62, and diamond about 2.42. Water is approximately 1.33. The higher the refractive index, the more the light bends and the greater the deviation.

If the angle of incidence is too small, the refracted ray inside the prism may hit the second surface at an angle greater than the critical angle, causing total internal reflection. In that case, no light emerges from the second face.

A larger prism angle (A) generally increases the angle of deviation. It also affects the minimum deviation, as δₘ = 2iₘ − A where iₘ is the angle of incidence at minimum deviation. Wider prisms spread light more.

The two internal refraction angles r₁ and r₂ always add up to the prism angle A, i.e., r₁ + r₂ = A. This geometric constraint comes from the triangular cross-section of the prism and is used alongside Snell's law to solve for the emergence angle.

Yes. For a dispersive prism, you can enter the refractive index for a specific wavelength of light (e.g., red, green, or violet). Different wavelengths have slightly different refractive indices, which is why a prism splits white light into a spectrum.