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where θ 1 is the angle of reflection (or incidence) and θ 2 is the angle of refraction. Using Snell's law, = , one can calculate the incident angle θ 1 = θ B at which no light is reflected:
Refraction of light at the interface between two media of different refractive indices, with n 2 > n 1. Since the velocity is lower in the second medium (v 2 < v 1), the angle of refraction θ 2 is less than the angle of incidence θ 1; that is, the ray in the higher-index medium is closer to the normal.
This phenomenon, known as total internal reflection, occurs at incidence angles for which Snell's law predicts that the sine of the angle of refraction would exceed unity (whereas in fact sin θ ≤ 1 for all real θ). For glass with n = 1.5 surrounded by air, the critical angle is approximately 42°.
The reflection angle is equal to the incidence angle, and the amount of light that is reflected is determined by the reflectivity of the surface. The reflectivity can be calculated from the refractive index and the incidence angle with the Fresnel equations, which for normal incidence reduces to [42]: 44
Fig. 5: Behavior of a ray incident from a medium of higher refractive index n 1 to a medium of lower refractive index n 2, at increasing angles of incidence [Note 2] Fig. 6: The angle of refraction for grazing incidence from air to water is the critical angle for incidence from water to air. Obviously the angle of refraction cannot exceed 90°.
For a given, sufficiently high refractive index, there are two angles meeting this criterion; for example, an index of 1.5 requires an angle of 50.2° or 53.3°. Conversely, if the angle of incidence and reflection is fixed, the phase difference introduced by the rhomb depends only on its refractive index, which typically varies only slightly ...
where n is the index of refraction of the medium in which the lens is working (1.00 for air, 1.33 for pure water, and typically 1.52 for immersion oil; [1] see also list of refractive indices), and θ is the half-angle of the maximum cone of light that can enter or exit the lens. In general, this is the angle of the real marginal ray in the
Below is described how the transfer matrix is applied to electromagnetic waves (for example light) of a given frequency propagating through a stack of layers at normal incidence. It can be generalized to deal with incidence at an angle, absorbing media , and media with magnetic properties .