Single-Slit Diffraction
I = I₀(sin α/α)². First minimum at a sinθ = λ. Central max width 2λ/a.
Key Notes
When monochromatic light passes through a single slit of width a, it spreads out and produces a diffraction pattern on a distant screen.
The pattern consists of a bright central maximum flanked by alternating dark minima and weaker secondary maxima.
Minima occur where a sin θ = nλ (n = ±1, ±2, ...). NOT n = 0 — that's the central max.
The central maximum is twice as wide as any secondary maximum. Its angular half-width is λ/a.
Intensity envelope: I(θ) = I₀(sin α / α)², where α = πa sin θ / λ. Secondary maxima approximately at α = ±1.43π, ±2.46π, ...
First secondary max ≈ 4.5% of central max. Diffraction is more pronounced when a is comparable to λ.
Fraunhofer diffraction = far-field (source and screen at infinity). Fresnel diffraction = near-field. JEE assumes Fraunhofer.
Formulas
Minima
Positions of dark fringes.
Angular half-width of central max
Half-angular width — from centre to first minimum.
Linear width on screen
Distance from centre to first minimum on a screen at distance D.
Central-max width
Full width of the central bright band.
Intensity profile
Single-slit Fraunhofer intensity envelope.
Important Points
Single-slit minima follow a sin θ = nλ; YDSE bright fringes follow d sin θ = nλ. The formulas look similar but mean opposite things — minima vs maxima.
Decreasing slit width a makes the pattern wider (more diffraction); increasing a makes it sharper.
If slit is illuminated with white light, the central max is white but the side maxima show coloured fringes (longer λ spreads more).
Combined YDSE + single-slit diffraction: the YDSE fringes appear inside the diffraction envelope. Missing orders when d sin θ matches both nλ (bright) and m'λ (single-slit minimum).
Width of central max doubles if a halves; doubling λ also doubles central-max width.
Single-Slit Diffraction notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.