Single-Slit Diffraction: JEE Main Complete Guide

Diffraction is the bending of light around obstacles, and the single-slit experiment is its simplest quantitative model. JEE Main tests diffraction in one to two questions per session — typically asking for minima positions, central maximum width, or comparing diffraction with interference patterns. Students who confuse the two (diffraction minima at nλ, interference minima at (n+½)λ, or vice versa) consistently drop marks. This guide sets both straight and covers every diffraction topic the exam uses.

Single-Slit Diffraction Pattern

A slit of width a, light of wavelength λ, screen at distance D. The key result: minima (dark fringes) occur at angles where a sinθ = nλ (n = ±1, ±2, …). Position of nth dark fringe on screen: y_n = nλD/a (for small angles). Width of central maximum (distance between first minima on either side): W = 2λD/a. This is the most tested result — note it is 2λD/a, not λD/a. The secondary maxima occur approximately at a sinθ = (2n+1)λ/2, giving intensities that fall off rapidly.

Critical distinction: single-slit diffraction minima → a sinθ = nλ. Double-slit interference minima → d sinθ = (n+½)λ. Double-slit interference maxima → d sinθ = nλ. Students frequently swap these. Mnemonic: for interference, the "n" in the condition gives you the bright fringe order (constructive for nλ, destructive for (n+½)λ); for diffraction, "n" gives you the dark fringe. Take a free wave optics mock. For interference and Young's double slit, see our interference and diffraction guide.

Comparing Diffraction and Interference

In a single-slit diffraction pattern: (1) one broad central bright maximum of width 2λD/a; (2) narrower secondary maxima on either side with intensity falling to about 5% of central peak; (3) intensities of secondary maxima ∝ 1/n². In Young's double-slit interference: (1) equal-intensity fringes of width λD/d; (2) no central maximum is special in width — all fringes are the same. When both effects coexist (real double slit of finite width a, separation d), the interference pattern is modulated by the diffraction envelope. Missing orders occur where an interference maximum coincides with a diffraction minimum: d/a = integer.

Resolving Power of Optical Instruments

Two point objects are just resolved when the central maximum of one falls on the first minimum of the other — Rayleigh's criterion. Telescope (circular aperture of diameter D): θ_min = 1.22λ/D (in radians). Microscope: resolving power = 2n sinα/λ where n is refractive index and α is semi-angle of cone of light. JEE question type: find the minimum distance between two point objects at distance L that can be resolved by a telescope of aperture D. Answer: d = Lθ_min = 1.22λL/D. To improve resolution: increase D (larger telescope mirror) or decrease λ (use UV or electron microscopes). Electron microscopes use de Broglie wavelength λ = h/p, which can be nanometres — far better resolution than visible light.

Diffraction by Circular Aperture and Airy Disc

The bright central spot in the diffraction pattern of a circular aperture is called the Airy disc. Its angular radius = 1.22λ/D. JEE uses this in optics-of-eye and telescope questions: the pupil of the eye (≈ 3 mm diameter) limits resolution. For λ = 550 nm (green), θ_min ≈ 1.22 × 550 nm / 3 mm ≈ 2 × 10⁻⁴ rad. At 1 m distance, the minimum resolvable separation = 0.2 mm — consistent with the 0.1–0.2 mm visual acuity of the human eye. For the complete wave optics strategy see our wave optics guide and our wave optics diffraction guide.