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As the refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes the focal length of lenses to be wavelength dependent. This is a type of chromatic aberration, which often needs to be corrected for in imaging systems.
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.
Let the angle of refraction, measured in the same sense, be θ t, where the subscript t stands for transmitted (reserving r for reflected). In the absence of Doppler shifts, ω does not change on reflection or refraction. Hence, by , the magnitude of the wave vector is proportional to the refractive index.
where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres. Usually, it is sufficient to use a two-term form of the ...
For step-index multimode fiber in a given medium, the acceptance angle is determined only by the indices of refraction of the core, the cladding, and the medium: =, where n is the refractive index of the medium around the fiber, n core is the refractive index of the fiber core, and n clad is the refractive index of the cladding.
For a glass medium (n 2 ≈ 1.5) in air (n 1 ≈ 1), Brewster's angle for visible light is approximately 56°, while for an air-water interface (n 2 ≈ 1.33), it is approximately 53°. Since the refractive index for a given medium changes depending on the wavelength of light, Brewster's angle will also vary with wavelength.
where n is the local refractive index as a function of distance along the path C. An electromagnetic wave propagating along a path C has the phase shift over C as if it was propagating a path in a vacuum , length of which, is equal to the optical path length of C .
The refractive index (n) and extinction coefficient (k) are related to the interaction between a material and incident light, and are associated with refraction and absorption (respectively). They can be considered as the "fingerprint of the material".