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
Hey Blessing, good to see you again. Step 1: Identify the given information and relevant laws. The refractive index of air (medium 1) is n_1 = 1. The refractive index of the glass block (medium 2) is n_2 = (3)/(2) = 1.5. The angle between the reflected ray and the refracted ray is 90^. Let _i be the angle of incidence, _r be the angle of reflection, and _t be the angle of refraction. According to the law of reflection, the angle of incidence equals the angle of reflection: _i = _r. The given condition is _r + _t = 90^. Substituting _r = _i, we get _i + _t = 90^. From this, we can express the angle of refraction as _t = 90^ - _i. Step 2: Apply Snell's Law. Snell's Law states: n_1 (_i) = n_2 (_t) Substitute the known values and the expression for _t: 1 · (_i) = 1.5 · (90^ - _i) Step 3: Simplify the equation using trigonometric identities. We know that (90^ - x) = (x). So, (_i) = 1.5 (_i) Divide both sides by (_i): ((_i))/((_i)) = 1.5 (_i) = 1.5 Step 4: Calculate the angle of incidence. To find _i, take the inverse tangent of 1.5: _i = (1.5) _i ≈ 56.31^ The angle of incidence is approximately 56.31^. Send me the next one 📸