COMEDK 2023 Shift 1 Paper

To find the linear width of the central maximum in a diffraction pattern, we can use the formula related to the diffraction due to a single slit. The angular width of the central maximum is given by θ=2λ/b, where λ is the wavelength of the light (in meters) and b is the width of the slit (in meters). The linear width of the central maximum on the screen (which we'll denote as W ) is then given by W=2L‌tan(θ∕2)≈2L(θ/2) for small angles, where L is the distance from the slit to the screen.
Given:
The wavelength of light, The width of the slit, b=2‌mm=2×10−3m.
The distance from the slit to the screen, L=2m.
First, calculate the angular width of the central maximum:
For small angles, where θ is in radians, the approximation tan(θ∕2)≈θ/2 can be used. Thus, the linear width of the central maximum on the screen is:
Therefore, the correct answer is Option B: 1.28‌mm.