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Medium X Refraction Calculation #4 [Refer to diagram on the Left] Diamond Water Consider the scenario where a piece of diamond shares an interface with water on the right and one with glass at the bottom. The top surface of the diamond is in contact with medium X. The refractive indices of each media are given in the diagram. n =2.40 1 = 1.33 A beam of light is travelling within medium X and approaches the X-diamond interface at A with an incident angle of $1- After entering the diamond, the light ray approaches the water - diamond interface at B an incident angle of 03. If total internal reflection occurs at B, the beam of light will encounter the diamond-glass interface at point C 62 is the angle of incidence of the light at the diamond-glass interface at C, as well as the angle of refraction of the light at the Glass X-diamond interface at A. n = 1.60 Note that 02 + 03 = 90% at all times. Questions (there are 5 blanks to be filled): . Calculate the separate values of the critical angle for total internal reflection at point B and point C. These values should be calculated to exactly 3 significant figures. Exact values should be used at all intermediate steps (if any) up to this point. The critical angle at point B is : _ 1 degrees The critical angle at point C is : 2 degrees . Use the above critical angles at B and at C (each with exactly 3 significant figures) to calculate the minimum and the maximum value of 62 such that all light that enters the diamond at point A will reach the diamond-glass interface at C, but no light will enter the glass. . Hint: 02 + 03 = 90 at all times. The minimum value of 02 is : 3 degrees The maximum value of 02 is : 4 degrees . Will 62 have a larger range or a smaller allowed range of angles if the refractive index , of water is now larger (but still smaller than that for diamond)? For the blank below, type in a numerical value of 1 if the range is larger, and O if the range is smaller. The range of angles will be: 5 ( for Larger, 0 for Smaller). Note: While doing the calculation for each blank above, exact values should be used at all intermediate steps (if any). Every final answer below should be expressed in exactly 3 significant figures (in these cases, exactly 1 decimal place)