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Wave Optics

Young's double slit carries most of it: fringe width, fringe position and intensity. It has grown since the early papers.

Questions in the bank
119
q/paper in 2025–26
1.17
Numeric answer
38%
Notes pages
6

Tier: Core

When you’ll see it

Two coherent sources, a slit, a polaroid or light in a medium, and the question asks where fringes fall, how bright a point is, or how much light passes.

How this chapter is tested

This is a core chapter, set about once a paper, and it has grown. The largest group is Young's double slit: where the fringes fall, how bright the screen is at a point, and how far a thin sheet over one slit moves the pattern. The rest are single-slit diffraction, polarisation, the brightness of two overlapping beams, and what happens to light inside a medium.

Almost every question rests on one short relation, so the arithmetic is brief. Marks are lost on a factor: an intensity ratio used where the amplitude ratio is needed, the double slit's fringe width used for a single slit's central maximum, which is twice as wide, or the half lost at the first polaroid forgotten.

Many answers are typed numbers, so a factor slip has no option to expose it. Two waves adding as amplitudes is the idea from Waves, and the resolving-power results feed the instruments at the end of Ray Optics.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Wavefronts and light in a medium

    Rays are normal to the wavefront; entering a medium keeps the frequency and divides the speed and the wavelength by μ.

  • Coherent sources and resultant intensity

    Coherent beams add as amplitudes, I = I₁ + I₂ + 2√(I₁I₂) cos φ; incoherent beams add intensities; a plate in one path adds (μ − 1)t.

  • Fringe width and positions

    β = λD/d; bright fringes at whole multiples of β, dark ones halfway between; in a liquid divide λ by μ; two wavelengths first coincide where n₁λ₁ = n₂λ₂ in lowest terms.

  • Double slit intensity and sheet shifts

    Path difference from yd/D or from Pythagoras, then I = I_max cos²(φ/2); a sheet over one slit adds (μ − 1)t and slides the pattern towards the covered slit.

  • Single slit and resolving power

    Dark fringes at a sin θ = nλ, a central maximum 2λD/a wide, and a round aperture that resolves down to 1.22λ/D.

  • Polarisation

    The first polaroid halves unpolarised light, each later one passes cos²θ of what reaches it; reflected light is fully polarised when tan i_B = μ.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Intensity ratio used as amplitude ratio

    An intensity ratio of 1 : 9 is an amplitude ratio of 1 : 3. Take the square root before finding the brightest and darkest fringes.

  • Single slit and double slit swapped

    For one slit a sin θ = nλ is dark, and the central maximum is 2λD/a, set by the slit width a. λD/d belongs to the double slit's gap.

  • The half at the first polaroid

    Only the first sheet halves unpolarised light; light already polarised goes straight to I cos²θ. Each cos² uses the angle from the sheet just before.

  • Half the phase, and μ − 1

    I = I_max cos²(φ/2), not cos²φ, and a path of λ/3 is a phase of 2π/3. A sheet adds (μ − 1)t of path, not μt.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Wave Optics notes

Drill every Wave Optics question

119 questions from the bank, across 6 subtopics.

Drill the 119 questions

Drill one subtopic at a time

The 6 subtopics, in teaching order.

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