A calcite crystal laid upon a graph paper with blue lines showing the double refraction
Diagram of rays at a surface, where is the angle of refraction.
In this example, optic axis along the surface is shown perpendicular to plane of incidence. Incoming light in the s polarization (which means perpendicular to plane of incidence - and so in this example becomes "parallel polarisation" to optic axis, thus is called extraordinary ray) sees a greater refractive index than light in the p polarization (which becomes ordinary ray because "perpendicular polarisation" to optic axis) and so s polarization ray is undergoing greater refraction on entering and exiting the crystal.
Simple ray diagram showing typical chief and marginal rays
Doubly refracted image as seen through a calcite crystal, seen through a rotating polarizing filter illustrating the opposite polarization states of the two images.
Rays and wavefronts
Comparison of positive and negative birefringence : In positive birefringence (figure 1), the ordinary ray (p-polarisation in this case w.r.t. magenta-coloured plane of incidence), perpendicular to optic axis A is the fast ray (F) while the extraordinary ray (s-polarisation in this case and parallel to optic axis A) is the slow ray (S). In negative birefringence (figure 2), it is the reverse.
View from under the Sky Pool, London with coloured fringes due to stress birefringence of partially polarised skylight through a circular polariser
Sandwiched in between crossed polarizers, clear polystyrene cutlery exhibits wavelength-dependent birefringence
Reflective twisted-nematic liquid-crystal display. Light reflected by the surface (6) (or coming from a backlight) is horizontally polarized (5) and passes through the liquid-crystal modulator (3) sandwiched in between transparent layers (2, 4) containing electrodes. Horizontally polarized light is blocked by the vertically oriented polarizer (1), except where its polarization has been rotated by the liquid crystal (3), appearing bright to the viewer.
Color pattern of a plastic box with "frozen in" mechanical stress placed between two crossed polarizers
Birefringent rutile observed in different polarizations using a rotating polarizer (or analyzer)
Surface of the allowed k vectors for a fixed frequency for a biaxial crystal (see ).

Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths.

- Birefringence

If the material is birefringent, the refracted ray may split into ordinary and extraordinary rays, which experience different indexes of refraction when passing through the birefringent material.

- Ray (optics)
A calcite crystal laid upon a graph paper with blue lines showing the double refraction

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Optics

Branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

Branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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The Nimrud lens
Alhazen (Ibn al-Haytham), "the father of Optics"
Reproduction of a page of Ibn Sahl's manuscript showing his knowledge of the law of refraction.
The first treatise about optics by Johannes Kepler, Ad Vitellionem paralipomena quibus astronomiae pars optica traditur (1604)
Cover of the first edition of Newton's Opticks (1704)
Geometry of reflection and refraction of light rays
Diagram of specular reflection
Illustration of Snell's Law for the case n1 < n2, such as air/water interface
A ray tracing diagram for a converging lens.
Images of black letters in a thin convex lens of focal length f are shown in red. Selected rays are shown for letters E, I and K in blue, green and orange, respectively. Note that E (at 2f) has an equal-size, real and inverted image; I (at f) has its image at infinity; and K (at f/2) has a double-size, virtual and upright image.
When oil or fuel is spilled, colourful patterns are formed by thin-film interference.
Conceptual animation of light dispersion through a prism. High frequency (blue) light is deflected the most, and low frequency (red) the least.
Dispersion: two sinusoids propagating at different speeds make a moving interference pattern. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure. In effect, the individual waves (which travel with the phase velocity) escape from the wave packet (which travels with the group velocity).
Linear polarization diagram
Circular polarization diagram
Elliptical polarization diagram
A polariser changing the orientation of linearly polarised light. In this picture, θ1 – θ0 = θi.
The effects of a polarising filter on the sky in a photograph. Left picture is taken without polariser. For the right picture, filter was adjusted to eliminate certain polarizations of the scattered blue light from the sky.
Experiments such as this one with high-power lasers are part of the modern optics research.
VLT's laser guide star
Model of a human eye. Features mentioned in this article are 1. vitreous humour 3. ciliary muscle, 6. pupil, 7. anterior chamber, 8. cornea, 10. lens cortex, 22. optic nerve, 26. fovea, 30. retina
The Ponzo Illusion relies on the fact that parallel lines appear to converge as they approach infinity.
Illustrations of various optical instruments from the 1728 Cyclopaedia
Photograph taken with aperture 32
Photograph taken with aperture 5
A colourful sky is often due to scattering of light off particulates and pollution, as in this photograph of a sunset during the October 2007 California wildfires.

The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces.

Media that have different indexes of refraction for different polarization modes are called birefringent.