As refractive index of diamond is much greater hence critical angle for diamond-air interface is quite small. Thus, a diamond cutter has large options to cut the diamond faces so that light suffers total internal reflection from these faces.
The refractive index of diamond is much greater than that of glass. How does a diamond cutter makes use of this fact?
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A diamond cutter uses the high refractive index of diamond to create sharp, precise cuts. The greater refractive index causes light to refract more sharply, enhancing brilliance and ensuring the diamond’s facets reflect light effectively for maximum sparkle.
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