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Chapter 02 · Part IV · Optics
Revised on ____________________

Chapter 02 · Wave Optics

Add the amplitudes, and mind the half wavelength

sheets
diagrams
results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

Interference, in general

AMPLITUDES ADD, NOT INTENSITIES

I.Resultant intensity I = I₁ + I₂ + 2√(I₁I₂) cos φ

II.Phase from path φ = 2πλ Δ

III.Maxima and minima I_max = (a₁ + a₂)² , I_min = (a₁ − a₂)²

IV.Equal sources I = 4I₀ cos² ( φ2 )

V.Contrast I_maxI_min = ( a₁ + a₂a₁ − a₂ )²

VI.Coherence a locked phase relation — not merely one colour

Two independent lamps of the same wavelength produce no fringes: their relative phase scrambles billions of times a second. This is why Young split one beam instead of using two sources.

Young's double slit

THE MEDIUM SHRINKS EVERYTHING

I.Path difference Δ = d sin θ ≈ d yD

II.Bright fringes Δ = n λ

III.Dark fringes Δ = (n − 12) λ

IV.Fringe width β = λ Dd

V.In a medium n β → βn every wavelength becomes λ/n

VI.Slab over one slit shift = (n − 1) t Dd toward the covered slit

VII.Missing orders da = an integer

VIII.White light the centre is white, then violet inward

III

Thin films

ONE REFLECTION FLIPS, THE OTHER DOES NOT

I.Extra path on reflection λ2 at the denser-medium face only

II.Bright in reflection 2 n t cos r = (m + 12) λ

III.Dark in reflection 2 n t cos r = m λ

IV.Transmission the two conditions swap

V.Anti-reflection coat t = λ4 n n between air and glass

VI.A very thin film dark in reflection t → 0 leaves only the λ/2

Diffraction and resolution

a sinθ = nλ IS A MINIMUM

I.Single-slit minima a sin θ = n λ n = 1, 2, 3 … never 0

II.Central maximum width = 2 λ Da twice every other fringe

III.Circular aperture θ_min = 1.22 λD resolution — set by aperture, not magnification

IV.Grating d sin θ = n λ here it is a maximum

Polarisation, and where the marks go

TRANSVERSE ONLY

I.Through a polariser I = I₀2 unpolarised light, any orientation

II.Malus's law I = I₀ cos² θ already-polarised light

III.Brewster's angle tan θ_B = n reflected ray fully polarised

IV.Then the reflected and refracted rays are perpendicular

Where marks are lost in this chapter

1Dropping the λ/2 at a denser-medium reflection. Every bright and dark condition inverts with it.

2Reading a sin θ = nλ as a maximum. For one slit it locates the minima; for two slits d sin θ = nλ is a maximum.

3Adding intensities for coherent beams. Add amplitudes and square, or the dark fringe never reaches zero.

4Quoting the vacuum wavelength inside a liquid. In a medium λ → λ/n, and β shrinks with it.