Interference & Diffraction: JEE Main Physics Guide

Wave optics — interference, diffraction, and polarisation — contributes two to three questions in every JEE Main session. It is one of the most formula-friendly chapters in the entire syllabus: the conditions for bright and dark fringes, fringe width, and diffraction minima are compact and unambiguous. This guide takes you through every concept and question type JEE Main has tested in the past five years.

Young's Double Slit Experiment

YDSE setup: two narrow slits separated by distance d, at distance D from the screen, illuminated by coherent light of wavelength λ. Path difference at a point at height y from central maximum: Δ = yd/D. Condition for bright fringe: Δ = nλ → y_n = nλD/d. Condition for dark fringe: Δ = (2n−1)λ/2 → y_n = (2n−1)λD/(2d). Fringe width β = λD/d. This is the most important formula in the chapter — every YDSE question is either a direct use of this or a variation.

Angular fringe width = λ/d. If the entire apparatus is immersed in a medium of refractive index n, λ becomes λ/n, so fringe width decreases by factor n: β' = λD/(nd). If one slit is covered by a thin slab of refractive index μ and thickness t, the central maximum shifts toward that slit by: y_shift = (μ−1)t·D/d. JEE Main tests the direction and magnitude of this shift regularly. For the geometric optics complement to wave optics, see our Ray & Wave Optics Guide.

Intensity in YDSE

Intensity at a point: I = 4I₀·cos²(δ/2), where δ = 2πΔ/λ is the phase difference and I₀ is intensity from each slit. At maxima: I = 4I₀. At minima: I = 0. When slits have unequal intensities I₁ and I₂: I_max = (√I₁ + √I₂)², I_min = (√I₁ − √I₂)². JEE Main uses the ratio I_max/I_min to find the ratio of slit widths (intensity is proportional to slit width for single slit illumination). Take a free mock test on wave optics to practise YDSE intensity and shift problems.

Single Slit Diffraction

Single slit of width a: condition for dark fringes (minima): a·sinθ = nλ, n = ±1, ±2, ... Width of central maximum (distance between first minima on either side): 2λD/a. Note: wider slit → narrower central maximum. This inverse relationship is tested conceptually in JEE Main. Secondary maxima appear approximately halfway between consecutive minima, with rapidly decreasing intensity.

The diffraction pattern from a single slit modulates the interference pattern from double slits — a missing order occurs when the double slit interference maximum coincides with the single slit diffraction minimum. Missing order condition: d/a = n (integer). JEE Main asks for which order fringe is missing given the d/a ratio.

Resolving Power

Rayleigh criterion: two point sources are just resolved when the central maximum of one falls on the first minimum of the other. Resolving power of a telescope: RP = 1/θ_min = D/(1.22λ), where D is the aperture diameter. Resolving power of a microscope: RP = 2μ·sinθ/λ (for oil-immersion objective, μ is refractive index of medium). JEE Main tests resolving power conceptually and numerically: which telescope resolves two nearby stars, or how does resolving power change with wavelength.

Polarisation Basics

Transverse waves can be polarised; longitudinal waves (sound) cannot. A polaroid transmits only light with electric field along its transmission axis. Malus's law: I = I₀·cos²θ, where θ is angle between incident polarisation direction and the polaroid axis. For unpolarised light through a polaroid: I = I₀/2. Brewster's law: at Brewster's angle θ_B = arctan(n), reflected light is completely polarised. JEE Main tests Malus's law numerically and Brewster's angle conceptually.

Exam Strategy

Wave optics is one of the most reliable scoring chapters. The formulas are few, the question types are predictable, and the calculations are manageable in under three minutes. Practise identifying whether a question is about interference, diffraction, or polarisation in the first 10 seconds of reading — then apply the corresponding formula set. For a complete optics study plan, pair this with our Refraction & Lenses Guide. Upgrade for ₹149/month for 120+ wave optics questions sorted by difficulty.