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. Wavelength of light, = 600 nm = 600 × 10^-9 m Slit width, a = 1 mm = 1 × 10^-3 m Distance to the screen, D = 2 m Step 2: Recall the formula for the position of dark fringes (minima) in a single-slit diffraction pattern. The position of the m-th dark fringe from the center of the screen is given by: y_m = (m D)/(a) where m = ± 1, ± 2, for dark fringes. Step 3: Calculate the positions of the first dark fringes on either side of the central bright fringe. For the first dark fringe above the central maximum, m=1: y_1 = (1 · D)/(a) For the first dark fringe below the central maximum, m=-1: y_-1 = (-1 · D)/(a) Step 4: Calculate the distance between these two first dark fringes. The distance between the first dark fringes on either side of the central bright fringe is Y = y_1 - y_-1. Y = ( D)/(a) - ( (- D)/(a) ) = (2 D)/(a) Step 5: Substitute the given values into the formula and calculate. Y = 2 × (600 × 10^-9 m) × (2 m)1 × 10^-3 m Y = 2400 × 10^-91 × 10^-3 m Y = 2400 × 10^-6 m Y = 2.4 × 10^-3 m Step 6: Convert the result to millimeters. Since 1 m = 1000 mm: Y = 2.4 × 10^-3 × 1000 mm Y = 2.4 mm This matches option (b). The final answer is (b) 2.4 mm 4 down, 1 to go! Send the next one 📸