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Reflection and Refraction
When a light wave strikes a smooth border between two transparent media, the wave is partly reflected and partly refracted into the second medium. In geometric optics, the laws of reflection and refraction are based on a notion of rays. A ray is a narrow beam or an idealized representation of such a beam on a ray diagram, which can be used to indicate the positions of objects and images in a system of lenses or mirrors.
The law of reflection states that the incident and reflected rays, as well as the normal to the surface, all lie in the same plane. The angle of reflection θ1' is equal to the angle of incidence θ1.
The law of refraction states that incident and refracted rays as well as the normal to the surface all lie in the same plane. The ratio of the sines of the angles of incidence θ1 and refraction θ2, where both angles are measured from the normal to the surface, is equal to the constant for the two given materials:
sinθ1/sinθ2 = n.
The constant n is called the relative index of refraction of the second material with respect to the first. The index of refraction of an optical material with respect to vacuum is called the absolute index of refraction, or simply the index of refraction.
The relative index of refraction of two optical materials is equal to the ratio of their indexes of refraction
n = n1/n2.
When a ray is incident on an interface with a second material whose index of refraction is smaller than that of the material in which the ray is traveling n2 < n1 (for example, from glass to air), one can observe total internal reflection, i.e. disappearance of the refracted ray. This can be seen at angles of incidence that are greater than the critical angle θait.
For the incident ray θ1 = θait, sinθ2 = 1, sinθait = n2/n1 < 1. If the second material is air (n2 =1) , this formula assumes a more convenient form
sinθait = 1/n,
where n = n1 > 1 is the index of refraction of the first material.
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