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There are multiple ways to derive the index of refraction for a medium. Although most values have already been recorded the most obvious way if studying a new medium is to find a ratio between two mediums as either sound or light passes between the two. For example if you wanted to measure the index of refraction of say, water; and you already know that the index of refraction for air is approximately 1.00 then you might shine a laser from the air into the water and measure how much the light bends toward the normal (a line perpendicular to barrier between the air and water). A ratio of the cosines of the two angles that result will give you the index of refraction for water (approximately 1.33).

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