Image 1 Caption: A diagram illustrating the dispersion of monochromatic light rays by a prism of made from 5 of the 6 conventional spectral color terms (orange is omitted). The black line segments are normals (i.e., the perpendiculars) to the glass medium interface.
Prisms disperse light using refraction which is governed by Snell's law (AKA the law of refraction). In many scientific applications, greater and better dispersion is obtained using a diffraction grating (which relies on diffraction rather than refraction) rather than a prism. A compact disc is incidentally acts as a crude diffraction grating. That is NOT its function, but it disperses light rather prettily. By the by, nowadays the compact disc is a retro technology (Wikipedia: Compact disc: Current_status). For more on compact discs, see Optics file: diffraction_compact_disk.html.
Note monochromatic light is an ideal limit that CANNOT be reached in practice. By monochromatic light, one means polychromatic light with a very narrow wavelength band.
Features:
Actually, the prism disperses light beyond the visible band (fiducial range 0.4--0.7 μm) (i.e., into the ultraviolet band (fiducial range 0.01--0.4 μm) and infrared band (fiducial range 0.7 μm -- 0.1 cm)), but the human eye does NOT notice that. For example, a prism made of fused quartz (AKA quartz glass, silica glass) disperses light beyond the visible band (fiducial range 0.4--0.7 μm). Note for fused quartz (AKA quartz glass, the best transmittance range is 0.18--2.7 μm (Wikipedia: Fused quartz: List of physical properties).
n_1*sin(θ_1) = n_2*sin(θ_2) ,where the n_i are the refractive indexes n_i = c/v_i (n_i ≥ 1 always), vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns, v_i is the light speed in optical medium i (v_i ≤ c always), and the θ_i are the angles (i.e., incidence angle and refraction angle) of the light ray from the normal (i.e., the perpendicular) to the medium interface.
Note
sin(θ_2) = (n_1/n_2)*sin(θ_1) ,and so θ_2 subceeds/exceeds θ_1 if n_2 is greater/lesser than n_1.
In particular, note that a light ray bends toward a normal going from medium 1 to 2 if n_2 is greater than n_1.
Most common transparent solids and liquids have n_i greater than air's n_air, and so light rays bend toward/away the normal when entering/leaving these common materials when they are embedded in air.
Note incidence angles and refraction angles greater than 90° do NOT happen definitionally and have NO meaning in Snell's law. But what happens for case of incidence angles greater than those that give refraction angles of 90°? Total internal reflection which is illustrated by Image 5 below and which we discuss below Image 5.
For prisms (which are made from some kind of optical glass), the refractive index decreases with increasing wavelength. Thus, in Image 1 and Image 2, violet light refracts more than the red light.
Image 1 and Image 2 actually tell all. But we can supplement the images with some description:
Exiting the prism at short range there is a strong remixing the of the colored light rays, and so the overall emergent light beam will be polychromatic though with a complexly different mixture than the incident light beam.
However, at long range from the prism, the dispersed colored light beams will spread out because they emerge at different angles. So again there will be dispersed spectrum.
By the by,
an common example of such an
optical medium
object
is plate glass.
Note:
Exiting the slab, the colored light rays would be remixed and the exiting light beam would be polychromatic.
A derivation of total internal reflection is beyond our scope, but a derivation of the formula for the critical angle θ_critical is given below.
n_1*sin(θ_1) = n_2*sin(θ_2) .
Say θ_2 = 90°, then sin(θ_2) = 1, θ_critical = θ_1, and
θ_critical = arcsin(n_2/n_1) .Since arcsin(x) is undefined for x > 1, there is only a critical angle for the case of n_2/n_1 ≤ 1: i.e., for the optical medium 1 having having the higher refractive index than optical medium 2.
Total internal reflection occurs in optical medium 1 at the medium interface for θ_1 > θ_critical. Total internal reflection is, in fact, specular reflection (if the medium interface is sufficiently smooth) where reflection angle equals the incidence angle as illustrated in Image 5.