Diamond not only has a high index of refraction, but also has a great deal of di

Question

Diamond not only has a high index of refraction, but also has a great deal of dispersion, meaning that different colors of light see different indices of refraction. Red light, for example, sees an index of refraction of 2.41, while blue light sees an index of 2.45. Different indices mean different amounts of bending, meaning that the colors get separated in the gemstone. That gives diamond its characteristic colorful sparkle.

If light containing a mixture of blue light and red light enters a diamond at an angle of 36 degrees with respect to the surface normal, the blue and red light will separate. What will be the angle D (in degrees) between the two rays in the interior of the diamond?

Explanation / Answer

We know that, snell law says
n1Sin(A) = n2Sin (B) where A and B is the incidence and refracted angle of red lightand n1 & n2 is the refractive index in the two medium
Similarly for blue light
n1Sin(A) = n2Sin(C) where C is the refracted angle
The value of the refractive indices is given in the above paragraph
for red light n = 2.41 and for blue n = 2.45 (please note if some other value is provided for these then please use same)
so for red light
n1Sin(A) = n2Sin (B)
1*Sin(36) = 2.41*Sin(B)
B = 14.1165 degree
Now for blue light
n1Sin(A) = n2Sin (C)
1*Sin36 = 2.45Sin(C)
C = 13.8814 degree
So the thetaD = B- C = 0.2351 degree

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