8 · Interference — Hub

Two light waves meet. Where crest meets crest it is bright. Where crest meets trough it is dark. This is interference. Daily example: colours on a soap bubble and on an oil film on wet road.

Steady interference needs coherent waves. Coherent means same frequency and a constant phase difference. One source is split into two. Two separate lamps cannot give a steady pattern.

This page is a hub. Full theory and solved PYQs live in the five subpages below. Total 27 PYQs (2019–2024).

The 5 subpages (read in this order)

1. YDSE, coherence, energy, fringe shift → Interference — YDSE

Coherence conditions (2019). Why two separate sources fail (2022). Full YDSE intensity $I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\delta$, bright and dark conditions, fringe width $\beta = \lambda D/d$, equal-width proof (2024). Energy-conservation question (×2: 2022, 2023). Fringe definition + theory (×4: 2019–2024). Three numerics: $\lambda$ from fringe width (2024), fringe width from $D$, $d$, $\lambda$ (2019), glass-vs-diamond thickness (2023).

Fig: YDSE geometry — path difference $d\sin\theta$, screen at $D$, fringe width $\beta = \lambda D/d$.

2. Newton rings → Interference — Newton Rings

Characteristics list (×2: 2022, 2024). Formation with air film and the Stokes $\lambda/2$ step, geometry $t = r^2/2R$, derivation $D_n^2 = 4n\lambda R$ for dark rings (×3: 2019, 2022, 2023). Wavelength-measurement method (2019). Three numerics: $\lambda$ from $R$, $D_m$, $D_n$ (2019), $R$ from diameters (2019), $\lambda$ from diameters (×2: 2022, 2023). Refractive-index measurement with liquid film.

Fig: Newton rings — lens radius $R$, film $t = r^2/2R$, centre dark because of one $\lambda/2$ reversal.

3. Fresnel biprism → Interference — Biprism

Working (two virtual coherent sources from one slit) and how $\lambda$ is measured with it (×3: 2022–2024). Purpose of the biprism (×2: 2019, 2024). Virtual-source separation from prism data $d = 2a(n-1)A$. Four numerics: $\beta$ from $d$, $D$, $\lambda$ (2022); $d$ from $\beta$, $D$, $\lambda$ (2019; ×2: 2022, 2023; 2024).

Fig: Biprism — one slit $S$ gives two virtual sources $S_1$, $S_2$ (separation $d$); fringes of width $\beta = \lambda D/d$ on screen.

4. Lloyd’s mirror → Interference — Lloyd’s Mirror

Single slit + its mirror image as the coherent pair, Stokes $\lambda/2$ flip on reflection, dark centre, half field. Lloyd’s vs biprism table (2022). Three fringe-width numerics (2022, 2023, 2024 — all $\beta \approx 0.59$ mm).

Fig: Lloyd's mirror — $S$ interferes with its mirror image $S'$; the reflected beam carries the $\lambda/2$ flip.

5. Thin films, Stokes, Haidinger & Fizeau → Interference — Thin Films

Parallel-film conditions in reflected and transmitted light, Stokes relations $r = -r’$, $tt’ + r^2 = 1$, wedge films ($\beta = \lambda/2\mu\alpha$), Haidinger (equal inclination) and Fizeau (equal thickness) fringes. Soap-film colour numeric (2019), thin-film theory (×2: 2022, 2023; 2024).

Fig: Thin film — front reflection flips ($\lambda/2$), back reflection does not; $2\mu t\cos r$ picks the colour.

Most-repeated Interference questions

Quick map of all 27 PYQs. Full solutions live in the subpages.

Exam tip: if the question says “steady pattern”, first line must be coherence. If it gives fringe width, first line must be $\beta = \lambda D/d$. If rings, first line must be Stokes $\lambda/2$ and centre dark. If it says Lloyd’s, first line must be the $\lambda/2$ flip and dark centre.

Reference. Brij Lal, Subrahmanyam & Avadhanulu — Optics Ch-13, 14, 15; Ajoy Ghatak — Optics Ch-13, 14.