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Medium Refraction Calculation #4 [Refer to diagram on the Left] Consider the scenario where a piece of diamond shares an interface with water on the right and one with glass at the bottom. Diamond Water n = 1.33 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 A beam of light is travelling within medium X and approaches the X-diamond interface at A with an incident angle of 91- After entering the diamond, the light ray approaches the water - diamond interface at B an incident angle of , If total internal reflection occurs at B, the beam of light will encounter the diamond-glass interface at point C 6, 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 Bis : 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 6, 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: 92 + 0, = 90" at all times. The minimum value of 6, is : 3 degrees The maximion value of 6, is : 4 degrees Will 62 have a larger range or a smaller allowed range of angles if the refractive index n 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 0 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 a significant figures (in these cases, exactly a decimal place). Enter the correct answer below. 237 2 418 41.8