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Single-slit diffraction and polarisation are short topics that sit next to Young's double slit, and many errors come from borrowing the double-slit formula. This post covers the two results you need for single slits, Malus's law for polaroids, Brewster's angle, and the errors research has documented.
Is this on my syllabus?
The JEE (Main) 2026 syllabus lists "diffraction due to a single slit, width of central maximum" and "polarization: plane-polarized light, Brewster's law, uses of plane-polarized light and Polaroid". The NEET (UG) 2026 syllabus has the same lines. The CBSE 2025-26 curriculum lists single-slit diffraction with the width of the central maximum as a qualitative treatment, and does not list polarisation in Chapter 10, though the current NCERT wave optics chapter still explains polaroids and Malus's law. Check your year's syllabus before deciding how deep to go.
Where are the dark and bright bands?
NCERT treats the slit as many small in-phase sources across its width a and adds their contributions. For light falling normally:
Minima at angles θ ≈ nλ/a, with n = ±1, ±2, ±3...
Central maximum at θ = 0, with weaker secondary maxima at about (n + ½)λ/a.
The central bright band runs from the first minimum on one side to the first on the other, so its angular width is 2λ/a. On a screen at distance D, its linear width is 2λD/a.
Worked example. Light of wavelength 600 nm passes through a slit 0.20 mm wide onto a screen 1.5 m away.
First minimum: θ = λ/a = (600 × 10⁻⁹)/(0.20 × 10⁻³) = 3.0 × 10⁻³ rad.
Position on screen: y = Dθ = 1.5 × 3.0 × 10⁻³ = 4.5 mm.
Width of central maximum: 2 × 4.5 = 9.0 mm.
If the slit is narrowed to 0.10 mm, the width doubles to 18 mm.
That last step catches many students: a narrower slit gives a wider pattern.
Why do students find this hard?
Ambrose, Shaffer, Steinberg and McDermott (1999) studied university students who had already taken optics. Many could not account for the pattern a single or double slit makes, did not know whether to use ray (geometrical) or wave (physical) optics, and sometimes combined both. A student who thinks "light goes straight through, so the bright patch is the size of the slit" is using the ray model where it fails.
How does Malus's law work?
NCERT explains that a polaroid passes only the electric field component along its pass axis. Two facts follow:
Unpolarised light through one polaroid: intensity halves, whatever the angle.
Polarised light through a second polaroid at angle θ to the first: I = I₀cos²θ, where I₀ is the intensity after the first polaroid. This is Malus's law.
Worked example. Unpolarised light of intensity I passes through polaroids P₁ and P₂, with their axes at 60°.
After P₁: I/2.
After P₂: (I/2) × cos²60° = (I/2) × ¼ = I/8.
Three polaroids. P₁ and P₃ are crossed, and P₂ sits between them at angle θ to P₁. NCERT works this case: the intensity after P₃ is (I₀/4) sin²2θ, where I₀ is the intensity after P₁. It is greatest at θ = 45°, where it equals I₀/4, or I/8 of the original unpolarised light. Inserting a polaroid between two crossed ones lets light through, which surprises students who think "crossed means dark".
What is Brewster's angle?
When unpolarised light reflects from glass at one particular angle, the reflected light is completely plane-polarised. At this angle tan θ_B = n, and the reflected and refracted rays are at 90° to each other. For glass with n = 1.5, θ_B = tan⁻¹ 1.5 ≈ 56.3°. Brewster's law is listed for JEE Main and NEET-UG, so learn the 90° result as well as the formula.
Research on polarisation shows the same pattern as diffraction. In interviews with Croatian final-year students, Matejak Cvenić and colleagues (2021) found explanations often built on remembered but misread textbook diagrams of polarisation, with no prior model behind them.
Common mistakes and how to avoid them
Using the Young's double slit formula β = λD/d for the single-slit central band. It is 2λD/a. Our guide to Young's double slit problems covers the two-slit case.
Thinking a wider slit spreads light more. Width and spread are inversely related.
Applying Malus's law to unpolarised light. The first polaroid always halves it.
Using cos θ instead of cos²θ. The amplitude goes as cos θ; intensity goes as its square.
Measuring θ from the wrong line. In Malus's law θ is between pass axes; in Brewster's law it is from the normal.
Wave patterns are easier to understand when you change the slit width and watch. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read, and our post on Huygens and the wave theory of light gives the background.
A practice routine for this chapter
Day 1: derive the first-minimum condition by splitting the slit into two halves.
Day 2: five central-maximum width problems, changing one variable each time and predicting the change first.
Day 3: five Malus's law problems, including two with three polaroids.
Day 4: three Brewster's angle problems, each with a sketch showing the 90° between rays.
Day 5: write a side-by-side list of single-slit and double-slit formulas.
Today, solve the slit example again with red light of 700 nm and check that the central band widens.
