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
Step 1: Identify the angles of incidence and refraction from the diagram. The normal line is N-N'. The angle of incidence (_P) is the angle between the incident ray (in medium P) and the normal. From the diagram, _P = 45^. The angle of refraction (_Q) is the angle between the refracted ray (in medium Q) and the normal. From the diagram, _Q = 30^. Step 2: Identify the given velocity. The velocity of the wave in medium Q is v_Q = 2.0 × 10^-1 m s^-1. Step 3: Apply Snell's Law. Snell's Law states the relationship between the angles and velocities in two different media: ( _P)/( _Q) = (v_P)/(v_Q) We need to find v_P, the velocity of the wave in medium P. Rearranging the formula: v_P = v_Q ( _P)/( _Q) Step 4: Substitute the known values into Snell's Law. v_P = (2.0 × 10^-1 m s^-1) × ( 45^)/( 30^) Step 5: Calculate the sine values. 45^ = sqrt(2)2 ≈ 0.7071 30^ = 0.5 Step 6: Perform the calculation. v_P = (2.0 × 10^-1) × (0.7071)/(0.5) v_P = (0.2) × 1.4142 v_P = 0.28284 m s^-1 Step 7: Express the answer in scientific notation and compare with the given options. v_P ≈ 2.8 × 10^-1 m s^-1 This matches option D. The final answer is D: 2.8 × 10^-1 m s^-1.