This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright fiyin — let's do this. The question asks to calculate the angle of minimum deviation (_m) for a prism. Given: • Refractive index of the prism, n = 1.4 • The "Reason" section specifies that it is an equilateral prism, which means the prism angle, A = 60^. The formula for the refractive index of a prism in terms of the prism angle (A) and the angle of minimum deviation (_m) is: n = ((A + _m)/(2))((A)/(2)) Step 1: Substitute the given values into the formula. 1.4 = ((60^ + _m)/(2))((60^)/(2)) Step 2: Simplify the denominator. ((60^)/(2)) = (30^) = 0.5 Step 3: Substitute the simplified denominator back into the equation. 1.4 = ((60^ + _m)/(2))0.5 Step 4: Isolate the sine term. Multiply both sides by 0.5: 1.4 × 0.5 = ((60^ + _m)/(2)) 0.7 = ((60^ + _m)/(2)) Step 5: Find the inverse sine (arcsin) of 0.7. (60^ + _m)/(2) = (0.7) Using a calculator, (0.7) ≈ 44.427^. Step 6: Solve for _m. (60^ + _m)/(2) = 44.427^ Multiply both sides by 2: 60^ + _m = 2 × 44.427^ 60^ + _m = 88.854^ Subtract 60^ from both sides: _m = 88.854^ - 60^ _m = 28.854^ Step 7: Round the result to the nearest whole number. _m ≈ 29^ The calculated angle of minimum deviation is 29^. This matches option A. The final answer is A. Send me the next one 📸