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Does the angle of refraction depend on the properties of the material if the angle of the incidence is the same for two different materials?

Say I shed light on a surface with angle $ \theta $ and shed another light with the same angle $ \theta $ on two separate surfaces, are both the refraction angle going to be the same for both?

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The refraction angle will be different for different materials provided these materials have a different index of refraction. Reversely, by measuring the angle you can determine the index of refraction of the material. You can look up Snell's law.

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