The discovery of the law of refraction

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The law of refraction states that for a ray that is incident (i.e. acting on) on the surface between two media, the ratio of the sine of the angle of the incident ray to the sine of the angle of the refracted ray is equal to the ratio of the ray’s velocity in the first medium to the ray’s velocity in the second medium. This is given that the incident ray, the refracted ray, and the normal to the surface, all lie in the same plane[1][2].

“θ” are the respective angles, “v” are the respective velocities, and “n” the respective refractive indices. This is all equivalent to “n”, the relative refractive index.


The Persian mathematician and physicist Abu Saad Al Alaa Ibn Sahl (circa 940-1000) discovered[3] the law of refraction in 984. Ibn Sahl found that the ratio of line segments L₁ and L₂ as shown in the figure is constant. This in fact means that the two sines have a constant ratio and this is equal to the refractive index of the second medium (n₂) with the refractive index of the air (n₁) equal to 1. Ibn Sahl was not aware of the parameter “n” which was defined as the refractive index later on.