A jeweller wishes to determine the refractive index of an unknown gemstone. The

Question

A jeweller wishes to determine the refractive index of an unknown gemstone. The jeweller cuts and polishes the top and side of the gem then shines a narrow laser beam at an angle theta1A = 45 degree incident to the top face. The diagram is shown below. Ray diagram of laser beam entering the top surface of the gemstone then internally reflecting off the side. Calculate the refractive index that would satisfy the critical condition for total internal reflection within the gemstone with this illumination. Note that it is surrounded by air (nair = 1. 0).

Explanation / Answer

let refractive indec of diamond is n_d

1*sin45 = n_dsin2A

Now we equate 1B to critical angle

so sin1B = 1/n_d => cos2A = 1/n_d

=> 1/n_d = sqrt(2*n_d2 - 1)/sqrt(2)*n_d

=> 2 = 2*n_d2 - 1

=> n_d = sqrt(3/2) = 1.225 Answer

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