# Light: the Wave Model > Newton's particles against Huygens' waves, Young's double slit, diffraction gratings, polarisation and Malus's law. From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/light-wave-model/. Updated 2 November 2026. Year 11 and Year 12 boxes go deeper than the Year 10 text around them. ### Story time: The candle and the two slits In 1801, Thomas Young covered a window with card, poked a pinhole in it, and let a thin beam of sunlight into a dark room. In the beam he held a card with two narrow slits cut very close together. If light were a stream of tiny particles, the wall should have shown two bright stripes, one behind each slit. Instead, the wall showed a whole row of bright and dark bands. Young had seen the same pattern in water: two sets of ripples overlapping make places where they add up and places where they cancel. Light was doing the same thing. Particles cannot cancel each other out, but waves can. **In short:** The wave model says light travels as a wave. Young's double slit experiment proved it: light from two slits makes bright and dark bands through interference. Diffraction and polarisation also show that light behaves as a transverse wave. ## Two old models of light | | Newton's **particle** (corpuscular) model | Huygens' **wave** model | |---|---|---| | Light is | tiny particles fired from the source | a wave spreading out | | Reflection | particles bounce off | waves reflect | | Refraction | particles are pulled into the denser medium and **speed up** | waves **slow down** in the denser medium and change direction | | Diffraction and interference | cannot explain | explains | Newton's fame meant his model was widely accepted for over 100 years. Two experiments ended that: - **Young's double slit** (1801) showed interference, which only waves can do. - **Foucault** (1850) showed light is **slower** in water, as Huygens predicted. ## Huygens' principle Huygens said **every point on a wavefront acts as a source of tiny new wavelets**. The new wavefront is the line that touches all the wavelets. This explains: - **Refraction**: wavelets in the slower medium spread less, so the wavefront bends. - **Diffraction**: at a narrow gap, the wavelets spread out in all directions beyond it. ## Diffraction **Diffraction** is the spreading of a wave as it passes through a gap or around an edge. It is strongest when the gap is about the **same size as the wavelength**. Narrower gap, more spreading. Light's wavelength is tiny (400 to 700 nm), which is why we rarely notice light diffracting. ## Interference and Young's double slit When two waves meet, they add together: - **Constructive interference**: crest meets crest, giving a **bright** band. This happens when the **path difference** is a whole number of wavelengths. - **Destructive interference**: crest meets trough, giving a **dark** band. This happens when the path difference is a whole number of wavelengths plus a half. $$\text{Bright: } d\sin\theta = m\lambda \qquad \text{Dark: } d\sin\theta = \left(m + \tfrac{1}{2}\right)\lambda$$ - $d$ = distance between the slits - $\theta$ = angle from the centre line to the band - $m$ = 0, 1, 2, ... (the order of the band) For small angles, the spacing between neighbouring bright bands on a screen a distance $L$ away is: $$\Delta x = \frac{\lambda L}{d}$$ ### Worked example: A laser through two slits Red light (650 nm) passes through slits 0.25 mm apart onto a screen 2.0 m away. $\Delta x = \dfrac{650 \times 10^{-9} \times 2.0}{0.25 \times 10^{-3}} = 5.2 \times 10^{-3}$ m, so the bright bands are 5.2 mm apart. The bands spread out **more** with a longer wavelength (red more than blue), a bigger distance to the screen, or slits that are closer together. ## Diffraction gratings A **diffraction grating** has thousands of slits per centimetre. It uses the same equation, $d\sin\theta = m\lambda$, but gives much **sharper, brighter** and more widely spaced bright lines. That makes gratings ideal for measuring wavelengths in spectroscopes. If a grating has $N$ lines per metre, the slit spacing is $d = \dfrac{1}{N}$. ## Polarisation Light is a **transverse** wave: its electric field vibrates at right angles to the direction of travel. In ordinary (**unpolarised**) light, the field vibrates in every direction across the beam. A **polarising filter** only lets through vibrations in one direction. The light that comes out is **plane polarised**. - Unpolarised light through one filter: intensity **halves**. - Two filters with axes at right angles (**crossed**): no light gets through. Only transverse waves can be polarised, so polarisation is strong evidence that light is a transverse wave. Sound, which is longitudinal, cannot be polarised. ## Malus's law When polarised light of intensity $I_{max}$ meets a filter whose axis is at angle $\theta$ to the light's direction of polarisation: $$I = I_{max}\cos^2\theta$$ ### Worked example: Two filters Unpolarised light of intensity 80 W/m² passes through two filters whose axes are 30° apart. - After the first: $80 \div 2 = 40$ W/m². - After the second: $40 \times \cos^2 30° = 40 \times 0.75 = 30$ W/m². **Mind map** ```text Wave Model of Light Two old models Newton: particles Huygens: waves Foucault: slower in water Huygens' principle Every point makes wavelets Explains refraction Diffraction Spreading at gaps Biggest when gap ≈ λ Interference Path difference mλ: bright Young's double slit d sin θ = mλ Δx = λL / d Gratings Many slits Sharp bright lines Polarisation Transverse waves only I = I max cos² θ Unpolarised: halves ``` ### Year 11: Path difference in practice Point P on a screen is 3.0 µm further from one slit than the other. With 600 nm light, the path difference is $\dfrac{3.0 \times 10^{-6}}{600 \times 10^{-9}} = 5$ wavelengths, a whole number, so P is a **bright** band (the 5th order). If the path difference were 5.5 wavelengths, P would be **dark**. The central band ($m = 0$) is always bright, because both paths are the same length there. ### Year 12: Gratings, maximum orders and three filters **Highest order.** Since $\sin\theta$ cannot be bigger than 1, the largest order you can see is the whole number part of $\dfrac{d}{\lambda}$. A grating with 600 lines per mm has $d = 1.67 \times 10^{-6}$ m. With 500 nm light, $\dfrac{d}{\lambda} = 3.3$, so you can see up to the 3rd order. **Separating colours.** Two close wavelengths are easier to tell apart in a higher order, because the angle difference grows with $m$. **Three filters.** Two crossed filters block everything. Put a third one between them at 45°, and some light gets through: $\dfrac{I_0}{2} \times \cos^2 45° \times \cos^2 45° = \dfrac{I_0}{8}$. The middle filter changes the direction of polarisation in two smaller steps. **Rotating a filter.** Turning the second filter through a full circle passes through two crossed positions (90° and 270°), so the light drops to zero twice, and is brightest twice. **Working backwards.** For a transmitted fraction, $\cos^2\theta = \dfrac{I}{I_{max}}$: for 30%, $\cos\theta = \sqrt{0.30}$, so $\theta = 56.8°$. After a first filter halves unpolarised light, $0.20I_0 = 0.5I_0\cos^2\theta$ gives $\cos^2\theta = 0.4$. **Testing Malus's law.** Plot $I$ against $\cos^2\theta$. If the law holds, the graph is a straight line through the origin with gradient $I_{max}$. **Dark bands.** The $n$th dark band from the centre has a path difference of $\left(n - \frac{1}{2}\right)\lambda$. If the second dark band has path difference 975 nm, then $1.5\lambda = 975$ nm and $\lambda = 650$ nm. **Close wavelengths.** Find each angle from $d\sin\theta = m\lambda$ and subtract. With $d = \frac{1}{6.0 \times 10^5}$ m, the sodium lines 589.0 nm and 589.6 nm in the second order are at 44.98° and 45.03°, about 0.05° apart. **Keeping the spacing.** From $\Delta x = \dfrac{\lambda L}{d}$, keeping $\Delta x$ the same means $L$ must change in proportion to $\frac{1}{\lambda}$. Changing from 650 nm to 520 nm moves the screen from 1.2 m to 1.5 m. **White light.** Every colour makes a bright band at the centre, so the centre is white. The other bands are coloured, with violet nearest the centre and red furthest out, because red has the longest wavelength. **Narrow slits.** Each slit must be narrow (close to the wavelength) so the light diffracts and spreads enough for the two beams to overlap and interfere. **Polarisation and photoelectrons.** Rotating a filter in front of a metal changes the intensity, so the number of photoelectrons (the current) changes. Their maximum kinetic energy does not, because the frequency is unchanged. ## Quick summary - Newton modelled light as particles. Huygens modelled it as waves. - Young's double slit interference and Foucault's slower speed in water supported the wave model. - Diffraction is the spreading of waves at gaps, strongest when the gap is close to the wavelength. - Bright bands where $d\sin\theta = m\lambda$. Band spacing on a screen $\Delta x = \dfrac{\lambda L}{d}$. - Diffraction gratings give sharp bright lines, used to measure wavelengths. - Polarisation shows light is transverse. Malus's law: $I = I_{max}\cos^2\theta$. ## Quiz Try these questions from the chapter quiz. 1. Which scientist proposed that light is made of tiny particles? - A. Newton - B. Huygens - C. Young - D. Maxwell - Answer: A. Newton. Newton's corpuscular model treated light as a stream of particles. 2. Young's double slit experiment supported the wave model because it showed: - A. Reflection - B. Interference - C. Light travels in straight lines - D. Light has mass - Answer: B. Interference. Bright and dark bands from interference can only be explained by waves. 3. Newton's particle model predicted that light travels in water: - A. At the same speed as in air - B. Faster than in air - C. Slower than in air - D. Not at all - Answer: B. Faster than in air. Newton thought particles were pulled into the denser medium and sped up. Experiments showed the opposite. The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/light-wave-model/#quiz