Chapter 10 · Introduction

Chapter 10 — Wave Optics

Light is a wave: its wavefronts advance by Huygens' rule, two coherent beams can add to darkness, and a narrow slit spreads light into bands — effects that let us measure the wavelength of light with a ruler.

Hold a CD or a DVD under a lamp and its surface flashes with rainbow colours, although the disc contains no dye at all. A soap bubble swirls with colour just before it bursts; a thin film of oil turns a puddle into a rainbow; a laser pointer shone through a narrow slit paints a row of bright and dark bars on the wall. None of this can be explained by rays travelling in straight lines. All of it follows from one fact: light is a wave, with a wavelength of about half a micrometre, and waves that overlap add up — sometimes to more light, and sometimes to none.

In Chapter 9 we treated light as rays. Here we look underneath the rays. We start with Huygens' principle, a simple rule for how a wavefront moves, and use it to derive the laws of reflection and refraction and the meaning of the refractive index as a ratio of speeds. Then we ask when two beams of light can interfere — they must be coherent — and study Thomas Young's famous double-slit experiment, whose evenly spaced fringes measure the wavelength of light. Finally we let light through a single narrow slit and find the diffraction pattern that limits every optical instrument, and end with polarisation, which shows that light is a transverse wave. Along the way, the JEE/NEET extension boxes add optical path length, the fringe shift caused by a thin film, and Brewster's law.

Wavefronts→Huygens' principle→Reflection & refraction, $n=c/v$→Coherent sources→Young's fringes, $\beta=\lambda D/d$→Single-slit diffraction
🎯 By the end of this chapter you can…
  • define a wavefront and a ray, recognise spherical, cylindrical and plane wavefronts, and state Huygens' principle;
  • use Huygens' construction to derive the laws of reflection and refraction, show that $n=c/v$, and explain why frequency is unchanged while wavelength becomes $\lambda/n$;
  • add two waves using $I=I_1+I_2+2\sqrt{I_1I_2}\cos\phi$, and explain the difference between coherent and incoherent sources;
  • derive the positions of the fringes in Young's double-slit experiment and the fringe width $\beta=\lambda D/d$, and describe the intensity pattern and white-light fringes;
  • find the minima of single-slit diffraction, $a\sin\theta=n\lambda$, and the width $2\lambda D/a$ of the central maximum, and compare interference with diffraction;
  • explain plane-polarised light and polaroids, and apply Malus's law $I=I_1\cos^2\theta$, including the three-polaroid case;
  • solve board, JEE Main, JEE Advanced and NEET problems on all of the above.
Teaser — Two Sources, One Pattern

Two point sources on the left send out circular waves of the same wavelength, like two fingers dipping into a pond. The colours show the total disturbance (red crest, blue trough). Switch to the average intensity to see the still, dark lines where crest always meets trough. Then make the sources incoherent — their phases jump at random — and watch the pattern wash out.

2.50
separation—
dark lines (nodal lines)—
sources—

Sections in this chapter

10.1

Huygens' Principle and the Laws of Reflection and Refraction

Wavefronts and rays, secondary wavelets, Snell's law derived from wave speeds, frequency and wavelength in a medium.

$\dfrac{\sin i}{\sin r}=\dfrac{v_1}{v_2}$, $\ \lambda'=\dfrac{\lambda}{n}$
Open section →10.2

Coherent Sources, Interference and Young's Double-Slit Experiment

Coherent and incoherent addition, constructive and destructive interference, fringe positions, fringe width and the intensity pattern.

$\beta=\dfrac{\lambda D}{d}$, $\ I=4I_0\cos^2\dfrac{\phi}{2}$
Open section →10.3

Diffraction at a Single Slit and Polarisation

Minima and secondary maxima, the width of the central maximum, and the diffraction envelope of Young's fringes; polarisation by polaroids and Malus's law.

$a\sin\theta=n\lambda$, $\ w=\dfrac{2\lambda D}{a}$
Open section →
✅ Before you start
You will need the ray-optics ideas of Chapter 9 — refractive index, Snell's law, critical angle and total internal reflection — and the picture of light as an electromagnetic wave from Chapter 8. Section 10.2 adds two waves using phasors, as in the AC circuits of Chapter 7, and uses the cosine rule. From Class 11 Physics you need wave speed, frequency and wavelength ($v=\nu\lambda$), phase and phase difference, and the principle of superposition (Class 11 Physics, Chapter 14 — Waves). From mathematics you need trigonometry (including $\cos^2\theta=\tfrac12(1+\cos2\theta)$) and small-angle approximations $\sin\theta\approx\tan\theta\approx\theta$; no calculus is needed in this chapter.
← 9.4 Refraction through a Prism and Optical Instruments10.1 Huygens' Principle and the Laws of Reflection and Refraction →