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From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted by will also vary with wavelength, causing an angular separation of the colors known as angular dispersion.
A ray trace through a prism with apex angle α. Regions 0, 1, and 2 have indices of refraction, , and , and primed angles ′ indicate the ray's angle after refraction.. Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface.
The second prism should have an index of refraction higher than that of the liquid, so that light only enters the prism at angles smaller than the critical angle for total reflection. This angle can then be measured either by looking through a telescope, [clarification needed] or with a digital photodetector placed in the focal plane of a lens.
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, [1] and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
In optics, Cauchy's transmission equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material. It is named for the mathematician Augustin-Louis Cauchy, who originally defined it in 1830 in his article "The refraction and reflection of light". [1]
Dispersive prisms are used to break up light into its constituent spectral colors because the refractive index depends on wavelength; the white light entering the prism is a mixture of different wavelengths, each of which gets bent slightly differently. Blue light is slowed more than red light and will therefore be bent more than red light.
Rainbows are formed by dispersion of light, in which the refraction angle depends on the light's frequency. Refraction is also responsible for rainbows and for the splitting of white light into a rainbow-spectrum as it passes through a glass prism. Glass and water have higher refractive indexes than air.
Refraction at interface. Many materials have a well-characterized refractive index, but these indices often depend strongly upon the frequency of light, causing optical dispersion. Standard refractive index measurements are taken at the "yellow doublet" sodium D line, with a wavelength (λ) of 589 nanometers.