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 given values and the formula. The problem asks for the refractive index of the slab material. We are given the angle of incidence (i) and the angle of refraction (r). We assume the light is entering the slab from air, so the refractive index of the first medium (air) is n_1 = 1. Given: Angle of incidence, i = 40^ Angle of refraction, r = 26^ Refractive index of air, n_1 = 1 We use Snell's Law: n_1 (i) = n_2 (r) where n_2 is the refractive index of the slab material. Step 2: Substitute the given values into Snell's Law. 1 · (40^) = n_2 (26^) Step 3: Calculate the sine values. (40^) ≈ 0.6428 (26^) ≈ 0.4384 Step 4: Solve for n_2. 0.6428 = n_2 · 0.4384 n_2 = (0.6428)/(0.4384) Step 5: Perform the division. n_2 ≈ 1.4663 Step 6: Round the result to an appropriate number of significant figures. n_2 ≈ 1.47 The refractive index of the slab material is 1.47.