Width Of Central Maximum Single Slit Diffraction — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Width of Central Maximum (Single Slit Diffraction) Applies to Fraunhofer diffraction through a single slit where the screen is far from the slit (or a lens is used to focus rays), and the small-angle approximation holds. The condition for the first diffraction minimum is given by a sin(θ) = nλ, where n=1. Therefore, sin(θ) = λ/a. For small angles, θ ≈ y/D, where y is the linear distance from the center to the first minimum. Substituting approximations: y/D = λ/a => y = λD/a. The central maximum spans from the first minimum on one side to the first minimum on the other. Thus, width β₀ = 2y = 2λD/a. The slit width 'a' must be comparable to or larger than the wavelength 'λ', but small enough to produce observable diffraction. Assumes small diffraction angles (sin θ ≈ tan θ ≈ θ). Light must be coherent and monochromatic. Confusing the width of the central maximum in diffraction (2λD/a) with the fringe width in Young's Double Slit Experiment (λD/d). The central diffraction max is twice as wide as the other secondary maxima. Forgetting that if the apparatus is immersed in a medium with refractive index n, the wavelength becomes λ/n, reducing the width. Assuming the intensity is uniform across the width; it actually follows a sinc-squared function profile.