This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
B. 37.2^ Step 1: Identify the given values. The prism is an equilateral triangular prism, so the prism angle A = 60^. The refractive index of the glass n = (3)/(2) = 1.5. Step 2: Use the formula for the refractive index of a prism at minimum deviation. The formula is: n = ((A + _m)/(2))((A)/(2)) where _m is the angle of minimum deviation. Step 3: Substitute the known values into the formula. 1.5 = ((60^ + _m)/(2))((60^)/(2)) Step 4: Simplify the denominator. ((60^)/(2)) = (30^) = 0.5 Step 5: Substitute the simplified denominator back into the equation and solve for the sine term. 1.5 = ((60^ + _m)/(2))0.5 ((60^ + _m)/(2)) = 1.5 × 0.5 ((60^ + _m)/(2)) = 0.75 Step 6: Find the angle by taking the inverse sine. (60^ + _m)/(2) = (0.75) (60^ + _m)/(2) ≈ 48.59^ Step 7: Solve for _m. 60^ + _m = 2 × 48.59^ 60^ + _m = 97.18^ _m = 97.18^ - 60^ _m = 37.18^ Step 8: Round the result to one decimal place and compare with the options. _m ≈ 37.2^. The closest option is B. The final answer is 37.2^.