Class 12 · Chapter 10
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
12 formulas across 3 topics in Wave Optics.
Updated 2026-07-09 · v1.0.0
Two coherent light sources create a stable pattern of bright and dark fringes — the position of each fringe depends only on path difference, measured in a fixed geometric setup.
Δx = d sinθ ≈ dy/D
Geometry of two slits separated by d, screen at distance D, small-angle approximation for the fringe position y
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| d | separation between the two slits | m | [L] |
| D | distance from slits to screen | m | [L] |
| y | distance of the point from the central maximum on the screen | m | [L] |
Valid when
Δx = nλ (n = 0, ±1, ±2, ...) → bright fringe
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n | order of the fringe | dimensionless (integer) | [M⁰L⁰T⁰] |
Δx = (2n − 1)λ/2 (n = 1, 2, 3, ...) → dark fringe
Common mistakes
β = λD/d
Distance between two consecutive bright (or dark) fringes, from the constructive-interference condition applied at consecutive n
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| β | fringe width — spacing between consecutive bright or dark fringes | m | [L] |
Valid when
I = I₁ + I₂ + 2√(I₁I₂) cosφ
Superposition of two waves with amplitudes A₁, A₂ and phase difference φ; I ∝ (resultant amplitude)²
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| I₁, I₂ | intensities of the two individual sources | W/m² | [MT⁻³] |
| φ | phase difference between the two waves at the point | rad | [M⁰L⁰T⁰] |
Valid when
I(max) = (√I₁ + √I₂)² , I(min) = (√I₁ − √I₂)²
Setting cosφ = +1 and −1 respectively in the resultant intensity formula
Valid when
Fringe shift = (n − 1)tD/d (equivalently (n−1)t/λ fringes)
The slab introduces an extra path length (n−1)t in that arm, shifting the entire fringe pattern without changing the fringe width
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| t | thickness of the inserted slab | m | [L] |
Valid when
Common mistakes
Diffraction is what happens when the slit itself isn't infinitesimally narrow — different parts of the SAME slit interfere with each other, producing a central bright band flanked by much weaker secondary maxima.
a sinθ = nλ (n = ±1, ±2, ...) → minima
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| a | width of the single slit | m | [L] |
Valid when
Common mistakes
Width of central maximum = 2λD/a
Twice the distance to the first minimum on either side of the centre
Valid when
θ(min) = 1.22 λ/D (Rayleigh's criterion, circular aperture)
Two point sources are just resolvable when the central maximum of one falls on the first minimum of the other's diffraction pattern
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| θ(min) | minimum angular separation for two objects to be resolved | rad | [M⁰L⁰T⁰] |
| D | diameter of the aperture (lens/mirror/pupil) | m | [L] |
Valid when
Worth remembering
Polarisation only makes sense for transverse waves — it's direct experimental proof that light is transverse, not longitudinal, since sound waves can never be polarised.
I = I₀ cos²θ
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| I₀ | intensity of light after passing through the first (polariser) | W/m² | [MT⁻³] |
| θ | angle between the polariser's and analyser's transmission axes | rad | [M⁰L⁰T⁰] |
Valid when
Common mistakes
tanθ(B) = n₂/n₁ , θ(B) + θ(r) = 90°
At the polarising (Brewster) angle, the reflected and refracted rays are exactly perpendicular to each other
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| θ(B) | Brewster's (polarising) angle of incidence | rad | [M⁰L⁰T⁰] |
| θ(r) | angle of refraction at the Brewster angle | rad | [M⁰L⁰T⁰] |
Valid when
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