Prism Deviation Calculator

How it is calculated

The tool uses the minimum-deviation formula δ = 2 · asin( n · sin(A / 2) ) − A. A is the prism's apex angle in degrees, n is the refractive index of the glass relative to the surrounding air (taken as 1), and δ is the smallest angle by which the ray is turned, shown in degrees with two decimals.

Inputs outside physical limits give no result: the apex angle must be above 0° and below 180°, and the index must be at least 1. If n · sin(A / 2) is greater than 1 the ray is totally internally reflected inside the prism and cannot emerge symmetrically, so the tool again returns nothing; with A = 60°, for example, an index of 2.1 fails. The formula holds for light of a single colour, because n depends on wavelength.

Common mistakes

• Entering the angle of incidence or the base angle in the apex field; A is the angle between the two faces the light passes through.
• Typing the apex angle in radians, so 1.047 is read as about one degree instead of 60.
• Using the index for the wrong colour: blue light has a higher n than red, so dispersive glass gives a different deviation for each wavelength.
• Applying the result to any incident angle; the formula is only the minimum deviation, and other angles of incidence deviate the ray more.
• Entering an index below 1 or a prism in water or oil without adjusting n; the tool assumes the prism sits in air, so use the relative index n(glass) / n(medium) when it does not.