Physics by Lamhi: Not Your Boring Physics

CLASS 12 · CHAPTER 10 · OPTICS

QUICK REVISION

Wave Optics

Every key result from this chapter, boxed and ready for a last look before the exam. No derivations here, just what to recall and when to use it — for the full explanation, see the detailed notes.

1. Huygens' Principle

Every point on a wavefront is a source of secondary wavelets; the new wavefront is their common tangent envelope.

2. Coherent Sources

A sustained (visible, unmoving) interference pattern needs a constant phase difference between the two sources. Independent sources (e.g. two bulbs) drift randomly and wash the pattern out.

3. Young's Double-Slit Experiment

Path difference (small angle)
Δ≈dyD\Delta \approx \dfrac{dy}{D}
Bright fringe
Δ=nλ ⇒ yn=nλDd\Delta = n\lambda \ \Rightarrow\ y_n = \dfrac{n\lambda D}{d}
Dark fringe
Δ=(n+12)λ\Delta = \left(n+\tfrac12\right)\lambda
Fringe width
β=λDd\beta = \dfrac{\lambda D}{d}
  1. d small (slits close together): β large — fringes wide apart, clearly visible.
  2. d large (slits far apart): β tiny — fringes packed too close to resolve, effectively invisible.

β is inversely proportional to d. This is the exam trap: “slits further apart” does NOT mean “wider pattern,” it means a tighter one.

See it live: interactive double-slit simulation →

4. Diffraction at a Single Slit

First minimum
asin⁡θ=λa\sin\theta = \lambda

Central maximum is twice as wide (angularly) as each secondary maximum.

5. Polarization

Malus's law
I=I0cos⁡2θI = I_0\cos^2\theta

θ = 0°: full transmission. θ = 90° (crossed polarizers): zero transmission.

Full derivations and worked examples: detailed notes →