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
Here's the solution for Question 15: To find the total number of diffraction images, we first need to determine the maximum order of diffraction (m_max) that can be observed. The formula for a diffraction grating is given by: d = m where: • d is the grating spacing (distance between adjacent lines) • is the diffraction angle • m is the order of the diffraction image • is the wavelength of the light Step 1: Calculate the grating spacing d. The grating has 500 lines per millimeter. d = (1)/(number of lines per unit length) d = (1)/(500 lines/mm) = (1)/(500 × 10^3 lines/m) d = (1)/(5 × 10^5 lines/m) = 2 × 10^-6 m Step 2: Convert the wavelength to meters. Given wavelength = 600 nm. = 600 × 10^-9 m = 6 × 10^-7 m Step 3: Calculate the maximum order of diffraction m_max. The maximum possible value for is 1 (when = 90^). So, for the maximum order, the equation becomes: d × 1 = m_max m_max = (d)/() m_max = 2 × 10^-6 m6 × 10^-7 m m_max = 20 × 10^-76 × 10^-7 = (20)/(6) = (10)/(3) ≈ 3.33 Since the order m must be an integer, the maximum observable integer order of diffraction is m=3. Step 4: Determine the total number of images. The possible integer orders of diffraction are m = 0, ± 1, ± 2, ± 3. • m=0 corresponds to the central image (1 image). • m=1, 2, 3 correspond to images on one side of the central maximum (3 images). • m=-1, -2, -3 correspond to images on the other side of the central maximum (3 images). Total number of images = (images on one side) + (images on other side) + (central image) Total number of images = 3 + 3 + 1 = 7. The total number of diffraction images seen, including the central image, is 7. The final answer is D. 7. You're doing great, Tangunu! What's next?