Geometrical optics describes propagation by rays and Snell's law, neglecting diffraction on scales much larger than the wavelength.
An optical axis is the reference line through the centres of rotational symmetry of an optical system. A folded system can have successive axis segments related by reflection.
The incident ray, reflected ray and surface normal lie in one plane; incidence and reflection angles measured from the normal are equal. For a unit incident direction and unit normal , reflection gives .
In a stationary reciprocal optical medium, reversing the direction of a ray produces a ray along the same path. Snell's law is unchanged when its two media and ray directions are interchanged.
The focal length measures the focusing power of an optical lens or mirror. In a thin converging lens, parallel paraxial rays meet a distance beyond the lens.
A thin lens is modeled with negligible thickness relative to its object and image distances. For real conjugate distances , it obeys , with focal length .
For fixed object-screen separation , a converging thin lens focuses at two positions separated by . Thus . The method finds focal length without needing to locate a thin lens's optical center precisely.
For a thin optical lens in air, surface radii and refractive index give . The radii carry the usual signed curvature convention.
The five Seidel aberrations of a rotationally symmetric optical system are spherical aberration, coma, astigmatism, field curvature, and optical distortion.
Spherical aberration makes rays at different pupil radii focus at different axial positions. Its primary pupil dependence is quartic; the balanced Zernike spherical mode also contains quadratic and constant terms to remove defocus and piston.
Chromatic aberration is wavelength-dependent imaging caused by optical dispersion. Axial chromatic aberration changes focal length with wavelength; lateral chromatic aberration changes image scale.
An achromatic lens combines elements with different Abbe numbers to make two specified wavelengths share a focal length. Other wavelengths can retain secondary chromatic error.
For two thin lenses in contact, achromatism requires , where are their Abbe numbers. With total power , the component powers are and . A positive doublet using a larger- crown glass element and smaller- flint glass element therefore uses a converging crown and a diverging flint.
Optical dispersion is the dependence of refractive index or phase velocity on frequency. It gives an optical prism wavelength-dependent deviation and causes chromatic aberration.
The Abbe number compares refractive strength with visible optical dispersion. The traditional reference lines are near nm, respectively. A large means weak relative dispersion.
An Abbe diagram plots refractive index against Abbe number to show available optical glass families. Many diagrams put increasing to the left. Ordinary crown glasses have larger than ordinary flint glasses, while modern compositions occupy a broader region.
For a homogeneous optical prism in air, with apex angle and refractive index , minimum deviation occurs at the symmetric ray path. Then both internal angles are and both external angles are , so Snell's law givesMeasuring the deviation therefore determines the refractive index at the chosen wavelength.
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Geometrical optics is a branch of optics that describes light propagation in terms of rays. It simplifies the behavior of light by assuming that it travels in straight lines and can be represented as rays. This approach is particularly useful for understanding how light interacts with various optical elements, such as lenses, mirrors, and prisms, where the wavelength of light is much smaller than the dimensions of the optical components.