Final answer:
To determine the screen distance for the second minimum to be 2.5 mm from the center, use the single-slit diffraction formula to find the angle for the second minimum, then calculate the screen distance from slit using the tangent of that angle and the desired distance from the center.
Step-by-step explanation:
Calculating Screen Distance for the Second Minimum in Diffraction
To solve how far to place a screen from the slit so that the second minimum is a distance of 2.5 mm from the center of the diffraction pattern, we use the diffraction formula for a single slit:
dsin(θ) = mλ, where d is the slit width, θ is the angle for the minimum, m is the order number of the minimum, and λ is the wavelength of the light. Since the question relates to the second minimum (m=2), we rearrange the formula to obtain the angle θ for the second minimum: θ = arcsin(2λ/d) where the wavelength λ and slit width d were provided in the previous problems.
Next, we use the tangent of θ, because at small angles, tan(θ) ≈ sin(θ), to find the distance from the slit (L) using the given distance from the center (y = 2.5 mm): L = y/tan(θ). Thus, we get the required screen distance.