You did it. You bought that diamond but you need to convince yourself it is real

Question

You did it. You bought that diamond but you need to convince yourself it is real (or, your significant other gave you the diamond and you want to know if it is real). Calculate the critical angle for diamond surrounded by air (n = 2.419 and n = 1.000, respectively) and for the diamond surrounded by water (n = 1.333). Next, do the same calculations but instead of the n = 2.419 you used for diamond use the n = 1.923 of cubic zirconia. Describe how you might use these figures and a concentrated beam of light (like from a laser pointer) to assess whether your diamond is the real thing. 6. "There is no dark side of the moon, really. Matter of fact, it's all dark." The famous album cover depicts a light ray being dispersed by an equilateral prism (i.e., each angle of the triangular prism is 60degree). If the prism is flint glass, the index of refraction for violet light is n_upsilon = 1.66 and that for red light is n_r = 1.62. If the white light is incident with an angle of 50degree, calculate the angles for each the violet light and the red light after they have passed through the prism (so two refractions, one entering the glass and one leaving the glass). Now find the difference between these to angles, which is called the angular dispersion. 7. In The Matrix, Spoon Boy hands Neo a spoon so that Neo can attempt to bend it with his mind.^1 The scene shows Neo looking into the concave side of the spoon as he attempts to bend it, and the convex side clearly shows Spoon Boy watching. If the spoon is a section of a sphere with a radius of curvature of 10.0 cm, and if the image of Spoon Boy appears to be 4.0 cm behind the spoon, find the distance from Spoon Boy to the spoon.

Explanation / Answer

Critical angle of diamond surrounded by air

=>    2.419 * sin(theta) = 1 * sin90

=> thetacritical = 24.418 degree

Critical angle of diamond surrounded by water

=>    2.419 * sin(theta) = 1.333 * sin90

=> thetacritical = 33.439 degree

Critical angle of cubic zirconia surrounded by air

=>    1.923 * sin(theta) = 1 * sin90

=> thetacritical = 31.33 degree

Critical angle of cubic zirconia surrounded by water

=>   1.923 * sin(theta) = 1.333 * sin90

=> thetacritical = 43.88 degree

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