A light wavefront lies horizontally in uniform air. Which direction do its rays take?

Perpendicular to that surface. Rays follow the advancing front, rather than running along it.

Light slows when entering stationary glass. What happens to its frequency?

It stays unchanged. The incoming light sets the vibration rate; slower travel shortens the wavelength.

Two same-colour lamps have randomly changing relative phase. What happens to their interference bands?

They average out. Equal frequencies alone cannot keep bright and dark positions steady.

Equal, equally polarised beams start in phase. What intensity results from a half-wavelength path difference?

Zero. Their electric-field amplitudes cancel.

Which 400 nm and 600 nm bright orders first meet beyond the centre?

Third and second. Three times 400 equals two times 600.

A uniform plate delays one beam. What happens to adjacent bright-fringe spacing?

It stays unchanged. The same added delay shifts every fringe equally.

At fixed wavelength, what happens to the central bright region when the slit widens?

It narrows. A wider slit brings the first dark boundaries closer to the centre.

At 60° to the incoming field, what fraction of intensity passes through an ideal analyser?

One quarter. The field halves, and intensity depends on the field amplitude squared.

Teach Wave Optics in eight steps.

For each idea: show it, ask before you tell, then say one line.

Gather paper, a pencil and a ruler.

Common misconceptions & worked visual for this chapter · 15 practice questions with answers

Why it matters

Soap bubbles show colourful interference bands in daylight.
Sound spreads around everyday obstacles because its wavelength is relatively long.
Matching colours alone do not make two lamps produce steady interference bands.

What to teach

How to teach it

How waves travel

Equal wavelets advance from an old wavefront to a perpendicular propagation direction.

1. Wavefronts and Huygens’ principle

A wavefront joins points at the same stage of vibration.

Show: Look at the diagram’s old wavefront. Follow the equal wavelets towards their forward edges.
Ask: Where will the next wavefront lie after these wavelets spread?
Say: Each point sends out a wavelet. The next wavefront touches their forward edges and advances perpendicular to the old front.
Used in: A converging lens makes a parallel beam when its light source sits at the focus.

If your child says…“Light travels along the wavefront.”

Ask: Does the propagation arrow run along the old wavefront or across it?
What’s true: In a medium identical in every direction, light travels perpendicular to its wavefront.

$f_{\mathrm{air}}=\frac{3.0\times10^8}{600\times10^{-9}}=5.0\times10^{14}\,\mathrm{Hz}$

$v_{\mathrm{glass}}=\frac{3.0\times10^8}{1.5}=2.0\times10^8\,\mathrm{m\,s^{-1}}$

$f_{\mathrm{glass}}=f_{\mathrm{air}}=5.0\times10^{14}\,\mathrm{Hz}$

$\lambda_{\mathrm{glass}}=\frac{2.0\times10^8}{5.0\times10^{14}}\,\mathrm{m}$

2. Wave refraction

Light can change speed and wavelength while keeping the same frequency.

Show: Write these lines for 600 nm light entering stationary glass with refractive index 1.5. Say that f means frequency, v means speed, and λ means wavelength. Take air’s refractive index as 1.
Ask: With frequency unchanged, what wavelength does the slower light have inside this glass?
Say: The wavelength becomes 400 nm. Divide the speed in glass by the unchanged frequency.
Used in: Spectacle lenses refract light to help eyes focus clearly.

If your child says…“Slower light must vibrate less often.”

Ask: Which sets the vibration rate: the incoming light or its speed inside glass?
What’s true: The incoming light sets the frequency, so slower travel means a shorter wavelength.

How waves combine

Common-source slits above wave pairs with fixed or changing relative phase.

3. Coherence

Matching frequencies and a steady phase difference allow lasting interference bands.

Show: Follow the diagram from the common source through both slits to the screen. Compare the wave pairs below: fixed phase on the left, changing phase on the right.
Ask: Which wave pair shown will keep its bright and dark bands in fixed positions?
Say: Both waves need the same frequency and a fixed offset between their cycles. A changing offset moves the bands. Rapid, random changes make them average out.
Used in: Holograms use coherent light to record interference patterns that preserve depth information.

If your child says…“Same colour means steady bands.”

Ask: Which wave pair keeps the same gap between corresponding crests?
What’s true: Random changes in relative phase make interference bands average out.

Whole-wavelength and half-wavelength path differences produce reinforcement and cancellation of equal fields.

4. Path difference and interference intensity

Waves add their amplitudes.

Show: Look at the diagram’s equal waves, which start in phase and share polarisation. Compare the extra whole-wavelength path with the extra half-wavelength path.
Ask: Which shown path difference makes the point bright, and which makes it dark?
Say: A whole-wavelength delay doubles the combined field amplitude. Intensity follows amplitude squared, giving four times either beam’s intensity. A half-wavelength delay gives opposite fields and zero intensity.
Used in: Interfering laser beams revealed detector-arm length differences, helping detect gravitational waves.

If your child says…“Half a wavelength gives half the maximum brightness.”

Ask: What remains when equal opposite amplitudes add?
What’s true: Equal beams starting in phase cancel at a half-wavelength path difference when their polarisations match.

Two rows of fringe marks with different gaps and aligned first shared positions.

5. Young’s fringes

Different colours can share bright-fringe positions.

Show: Compare the diagram’s 400 nm and 600 nm rows, starting at their aligned centres. Find their first shared mark beyond the centre.
Ask: Will equal fringe numbers align beyond the centre?
Say: Longer wavelengths give wider gaps. At the first shared mark, the 400 nm row crosses three gaps. The 600 nm row crosses two, so different orders meet.
Used in: Fringe spacing measures wavelength, helping compare colours.

If your child says…“Different colours meet at the same fringe number.”

Ask: How many gaps does each row cross before its marks first line up again?
What’s true: Different wavelengths need different nonzero orders to reach a shared bright position.

Three fringe rows showing original gaps, closer gaps and an equally shifted pattern.

6. Changing Young’s pattern

Immersion changes spacing; delaying one beam shifts fringes.

Show: Compare the diagram’s three rows. Find which row changes the gaps and which shifts the marks from the original centre.
Ask: Will another uniform delay change the gaps?
Say: A constant delay shifts fringes without changing gaps.
Used in: Fringe shifts reveal glass thickness differences, helping check uniformity.

If your child says…“Delaying one beam changes the gaps.”

Ask: In the shifted row, which gaps changed?
What’s true: A constant added phase shifts every fringe equally.

Spreading and vibration direction

Two slit widths produce different central maxima; paired contributions explain the first dark boundary.

7. Single-slit diffraction

A narrow slit spreads light.

Show: Find the diagram’s paired points and first minimum. Compare both central bands at unchanged wavelength and screen distance.
Ask: Will light from all parts of this slit reinforce at every screen position?
Say: Paired contributions cancel at the first minimum because they arrive half a wavelength apart. Narrowing the slit widens the central bright band.
Used in: Larger telescope apertures reduce diffraction spreading, helping distinguish closely spaced stars.

If your child says…“A wider slit spreads light more.”

Ask: Would bringing the first dark boundaries closer make the central bright region wider or narrower?
What’s true: Narrowing the slit moves its first dark boundaries farther from the bright centre.

An analyser passes the incoming electric field’s component along its tilted transmission axis.

8. Polarisation and Malus law

A polariser selects a vibration direction.

Show: Follow the diagram’s beam through the polariser and analyser. Find the incoming field and its component along the analyser’s transmission axis.
Ask: As the diagram’s analyser turns towards crossed axes, what will happen to the emerging intensity?
Say: The analyser passes the field component along its axis, and intensity follows its square. Intensity entering the analyser is I₀, and intensity leaving it is I. With θ the angle between the transmission axes, $I=I_0\cos^2\theta$ .
Used in: Polarising sunglasses reduce reflected glare, making objects easier to see.

If your child says…“Half the field means half the intensity.”

Ask: What happens to a half when you square it?
What’s true: Halving the electric-field amplitude leaves one quarter of the intensity.

A real problem

Light interference helped detect gravitational waves.

LIGO first detected gravitational waves directly in 2015.

Interference between returning laser beams revealed differences between the detector arms’ lengths.

The detected disturbance came from merging black holes.

ESA LIGO Scientific Collaboration NASA

Soap bubble showing colourful interference bands in daylight.

Concept Lab · Common misconception

The tempting mistake in Wave Optics

Open standalone misconception page →

Does a dark fringe mean the light's energy disappeared?

Wrong

Two waves destroy their energy when they make a dark fringe.

Why it feels right. The intensity at that position drops to zero.

Right

Interference redistributes intensity across the pattern.

Worked example

Double-slit intensity has bright peaks and dark troughs. Interference shifts where the light reaches the screen.

In a double-slit pattern, at a dark fringe equal waves arrive half a cycle apart.
At neighbouring bright fringes they reinforce, so energy is concentrated in other regions.

Ask your child eight quick questions.

One per step. The answer and the reason are given.

A light wavefront lies horizontally in uniform air. Which direction do its rays take?

Perpendicular to that surface. Rays follow the advancing front, rather than running along it.
Light slows when entering stationary glass. What happens to its frequency?

It stays unchanged. The incoming light sets the vibration rate; slower travel shortens the wavelength.
Two same-colour lamps have randomly changing relative phase. What happens to their interference bands?

They average out. Equal frequencies alone cannot keep bright and dark positions steady.
Equal, equally polarised beams start in phase. What intensity results from a half-wavelength path difference?

Zero. Their electric-field amplitudes cancel.
Which 400 nm and 600 nm bright orders first meet beyond the centre?

Third and second. Three times 400 equals two times 600.
A uniform plate delays one beam. What happens to adjacent bright-fringe spacing?

It stays unchanged. The same added delay shifts every fringe equally.
At fixed wavelength, what happens to the central bright region when the slit widens?

It narrows. A wider slit brings the first dark boundaries closer to the centre.
At 60° to the incoming field, what fraction of intensity passes through an ideal analyser?

One quarter. The field halves, and intensity depends on the field amplitude squared.

15 more questions with answers, 1 with pictures

Teach Wave Optics in eight steps.

Why it matters