ClassApna

Class 12 Physics Notes

Wave Optics Class 12 Notes

Complete, exam-ready notes on wave optics: Huygens' principle, reflection and refraction of plane waves, interference and Young's double-slit experiment, diffraction and polarisation — written for CBSE boards, JEE and NEET revision.

Class12SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is wave optics in one line?

Wave optics treats light as a wave, explaining interference, diffraction and polarisation — phenomena that the ray (geometrical) model cannot account for.

Huygens' Principle

Huygens' principle

Every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront at a later time is the envelope of all these secondary (Huygens') wavelets travelling at the wave speed.

  • A wavefront is a surface of constant phase.
  • Spherical wavefronts come from a point source; plane wavefronts from a distant source.
  • Using Huygens' construction, the laws of reflection and refraction (Snell's law) are derived geometrically.

Reflection and refraction

Huygens' construction shows the angle of incidence equals the angle of reflection, and gives Snell's law sin⁡isin⁡r=v1v2\frac{\sin i}{\sin r} = \frac{v_1}{v_2} with refractive index n=cvn = \frac{c}{v}.

Interference of Light

Coherent sources

Sources with a constant phase difference emit coherent waves that produce a stable interference pattern of bright and dark fringes. Two independent light sources are incoherent — they need a single source split in two.

  • Constructive interference (bright fringe): path difference = an integral multiple of wavelength.
  • Destructive interference (dark fringe): path difference = a half-integral multiple of wavelength.
  • The principle of superposition governs the resultant amplitude or intensity.

Young's Double-Slit Experiment

β=λDd\beta = \frac{\lambda D}{d}
Fringe width

Fringe width

β\beta

The spacing between successive bright (or dark) fringes. Narrower slits dd and longer wavelengths λ\lambda widen the fringes; moving the screen farther increases β\beta.

  • Path difference to a point at angle θ:
  • Δ=dsin⁡θ\Delta = d\sin\theta
  • .
  • Bright fringes when
  • dsin⁡θ=nλd\sin\theta = n\lambda
  • , dark when
  • dsin⁡θ=(n+12)λd\sin\theta = (n + \tfrac{1}{2})\lambda
  • .
  • Intensity at a point:
  • I=I0cos⁡2(πdsin⁡θλ)I = I_0 \cos^2\left(\frac{\pi d \sin\theta}{\lambda}\right)
  • .

Monochrome needed

A clear, high-contrast fringe pattern needs coherent monochromatic light. White light gives overlapping coloured fringes with a white central maximum.

Diffraction

Diffraction

The bending and spreading of light as it passes an edge or through a narrow slit. Single-slit diffraction produces a central maximum flanked by weaker secondary maxima.

sin⁡θ=nλa,width of central max=2λDa\sin\theta = \frac{n\lambda}{a},\quad \text{width of central max} = \frac{2\lambda D}{a}
Single-slit diffraction minima

Interference vs diffraction

Interference arises from a few coherent sources (bright fringes roughly equal width and intensity). Diffraction arises from many sources on one slit (central maximum broad and brightest, secondary maxima taper off).

Polarisation

Polarisation

Confining the vibrations of a light wave to a single plane. This is possible for transverse (light) waves, not longitudinal waves — polarisation proves light is transverse.

  • Brewster's law: at the polarising angle
  • tan⁡ip=n\tan i_p = n
  • , the reflected and refracted rays are at right angles.
  • A polaroid transmits vibrations along its transmission axis; crossed polaroids block light completely.
  • Intensity after a polaroid at angle θ (Malus's law):
  • I=I0cos⁡2θI = I_0 \cos^2\theta
  • .

Solved Examples

Example: In Young's experiment, slits are 0.2 mm apart and the screen is 1 m away with green light of wavelength 500 nm. Find the fringe width.

Solution: β=λDd=500×10−9×10.2×10−3=2.5 mm\beta = \frac{\lambda D}{d} = \frac{500\times 10^{-9} \times 1}{0.2\times 10^{-3}} = 2.5\,\text{mm}.

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

Fringe width

β=λDd\beta = \frac{\lambda D}{d}

Bright fringe

dsin⁡θ=nλd\sin\theta = n\lambda

Single-slit minima

sin⁡θ=nλa\sin\theta = \frac{n\lambda}{a}

Malus's law

I=I0cos⁡2θI = I_0\cos^2\theta

Brewster's law

tan⁡ip=n\tan i_p = n

Refractive index

n=cvn = \frac{c}{v}

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • Fringe width β = λD/d; use consistent units (metres).
  • Coherent monochromatic light gives a stable fringe pattern.
  • Single-slit central maximum width = 2λD/a.
  • Polarisation proves light is a transverse wave.
  • Brewster angle: tan i_p = n, with reflected and refracted rays perpendicular.

FAQ

Common questions

What is the difference between interference and diffraction?

Interference results from a few coherent sources and gives equally spaced fringes; diffraction results from many sources on a single slit and gives a broad central maximum with decaying secondary maxima.

Why does white light give coloured fringes?

Each wavelength interferes at slightly different path differences, so the bright fringes for different colours land at slightly different positions, producing coloured bands around a white centre.

What does polarisation tell us about light?

Only transverse waves can be polarised, so the ability to polarise light confirms it is a transverse wave and not longitudinal.

How do I increase the fringe width?

Increase the wavelength or the screen distance, or decrease the slit separation — fringe width β = λD/d.

Continue learning

Related notes

Ray Optics and Optical Instruments NotesClass 12 Physics NotesPhysics Tutor in Mohali

Test yourself

MCQ mock test

Exam-style questions for this chapter — no login required. Submit to see your score instantly.

Chapter mock test

Check how much of this chapter you have actually locked in — exam-style questions with instant scoring.

15 questions (of 24)~23 minNo login needed

Mastering this chapter with live help

Notes help, but doubts clear fastest in a live class. Narayan Gurukul Academy (ClassApna) runs small-batch CBSE, JEE and NEET coaching from our Mohali centre and online — with daily doubt support and mock tests.

Book a Free DemoSee plans & pricing

One-on-one guidance available · Live online classes across India