CBSE · Class 12 · Physics · Chapter 10

Wave Optics — Formula Sheet

Board Formulas

13 formulas

1.Huygens' Principle★
$Every point on a wavefront acts as a source of secondary wavelets$
Envelope of secondary wavelets after time t gives the new wavefront. Explains reflection, refraction, diffraction.
2.Path Difference and Phase Difference
$Δ ϕ = \frac{2 π}{λ} Δ$
$Δ$ : Path difference (m) · $Δ ϕ$ : Phase difference (rad)
Phase difference = (2π/λ) × path difference. Full wavelength = 2π radians.
3.Constructive Interference (bright fringe)★
$Δ = nλ, n = 0, \pm 1, \pm 2, \dots$
Waves arrive in phase, amplitudes add. Intensity is 4I_0 for two equal sources.
4.Destructive Interference (dark fringe)
$Δ = (2 n + 1) \frac{λ}{2}, n = 0, 1, 2, \dots$
Waves arrive out of phase by π, amplitudes cancel. Intensity is zero for equal amplitudes.
5.Resultant Intensity of Two Waves
$I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
I_max = (√I₁+√I₂)²; I_min = (√I₁-√I₂)². Ratio predicts fringe visibility.
6.Fringe Width in Young's Double Slit★
$β = \frac{λ D}{d}$
$β$ : Fringe width (m) · $λ$ : Wavelength (m) · $D$ : Slit-to-screen distance (m) · $d$ : Slit separation (m)
Distance between two consecutive bright (or dark) fringes.
7.Position of nth Bright Fringe
$y_{n} = \frac{nλ D}{d}$
Central maximum at y = 0. Fringes are equally spaced.
8.Position of nth Dark Fringe
$y_{n} = \frac{( 2 n - 1 ) λ D}{2 d}, n = 1, 2, \dots$
First dark fringe at y = λD/(2d).
9.Single-Slit Diffraction (dark fringes)
$a sin θ = nλ, n = 1, 2, 3, \dots$
Position of minima in single-slit diffraction pattern. n = 0 is the central maximum, NOT a minimum.
10.Width of Central Maximum (Single Slit)★
$w_{0} = \frac{2 λ D}{a}$
Twice the width of any secondary maximum. Wider slit ⇒ narrower central peak.
11.Rayleigh Criterion (Angular Resolution)
$θ_{min} = \frac{1.22 λ}{D}$
Minimum angular separation of two point objects to be resolved by a circular aperture of diameter D.
12.Brewster's Law
$tan θ_{B} = n$
At the polarising angle θ_B, the reflected ray is 100% plane-polarised (perpendicular to plane of incidence).
13.Malus's Law★
$I = I_{0} cos^{2} θ$
Intensity of polarised light after passing through a polariser at angle θ to its polarisation axis.