a thin prism, which is generally a prism with an apical angle of less than 15°. For simplicity, we will assume that the initial object ray is striking the first surface normally (or perpendicularly). Since the ray is normal—or at a 90° angle—to the first surface, no refraction occurs. However, once the ray strikes the second surface, it reaches the surface at an angle i and is therefore refracted (or bent) in the direction of the base.

For thin prisms, which include most prisms in ophthalmic optics, the refraction at the second surface depends primarily on the apical angle (a) of the prism and the refractive index (n) of the material. In practice, the angle of incidence at the first surface will affect the extent to which light is deviated by the prism. The amount of deviation, in degrees, is given by the angle (d), while d = i' - i.

Moreover, the angles of incidence (i) and refraction (i') are related by the refractive index (n) of the prism material according to Snell's law. For a thin prism, with a relatively small apical angle (a), it can be shown that the approximate deviation (d), in degrees, is given by:

d = (n - 1) × a

For small amounts of deviation, 1 degree of deviation is roughly equal to 1.75 prism diopters. For prisms made from hard resin, the refractive index (n) is 1.500. This simplifies our formula even further, since 1.500 - 1 = 1/2. Consequently, for prisms made from hard resin, the deviation in degrees is roughly equal to half the apical angle.

For example, consider a ray of light from an object point passing through a hard resin prism (n = 1.500) with an apical angle of 10°. The deviation (d) of this ray is equal to (n - 1) × a = (1.500 - 1) × 10 = 5°. This is approximately 8.75 prism diopters.