E. The Wave Nature of Light · The Wave Nature of Light

The Wave Nature of Light: Unit Review

E1.1 E1.2 E2.1 E2.2 E2.3 E2.4 E3.1 E3.2 E3.3 E3.4 A1.1 A1.8 A1.10 A1.11 A1.12 A1.13 A2.1About 40 minutes

Learning goals

I can use the wave model to explain refraction, diffraction, interference and polarization of light.
I can solve two-source, double-slit, single-slit, grating, thin-film, air-wedge, polarization and resolution problems.
I can explain how light-wave technologies work and assess their impact on society and the environment.

Words to know

interference
The combining of overlapping waves by superposition.

diffraction
The spreading of waves through openings and around obstacles.

polarization
Restricting a transverse wave's vibrations to one direction.

coherent
Having the same frequency and a constant phase relationship.

Let's review!

In this unit you used the wave model to explain refraction and dispersion, studied diffraction with Huygens' principle, analysed the two-point-source pattern, and followed the debate between the particle and wave models. You worked through Young's double slit, single-slit diffraction and gratings, explained colours in thin films and measured with air wedges, showed light is transverse with polarization, found the resolution limit set by diffraction, described how oscillating dipoles radiate, and assessed technologies that use light's wave nature.

This review has a few questions from every lesson. Try each one, then press Show answer to check.

How to use this review

Do two or three sections at a time with your calculator in degree mode (switch to radians only for resolution answers). For every problem, first decide which situation you have (two sources, double slit, single slit, grating, thin film or air wedge) and write the matching equation before substituting. Convert nm and mm to metres. For thin films, count the inversions first. For each question you miss, write down why and go back to that lesson. Finish with the 10-question quiz.

How the unit fits together. Wave basics, diffraction and the two-source pattern built the evidence for the wave model; the light experiments, thin films, polarization, resolution and electromagnetic waves follow from it.

The key equations of the unit in one place. Notice that d sin θ = mλ gives bright fringes for slits and gratings, while w sin θ = nλ gives dark fringes for a single slit.

Just for fun

You've now met light as a wave that bends, spreads, cancels, adds and filters itself. In the next unit it turns up as a particle. Light, it seems, refuses to be put in a single box, or even through a single slit.

Light as a Wave: Refraction, Index of Refraction and Dispersion

Find the wavelength in water (n = 1.33) of light that has λ = 589 nm in air.

Find the speed of light in a plastic with n = 1.40.

Light enters glass (n = 1.50) from air at 50°. Find the angle of refraction.

Why does a prism separate white light into colours?

Diffraction and Huygens' Principle

Water waves of λ = 2.0 cm pass through gaps of 2.0 cm and 8.0 cm. Which gap gives more diffraction?

State Huygens' principle.

Why can you hear but not see around a corner?

Interference in Two Dimensions: The Two-Point-Source Pattern

Point P on the 3rd nodal line is 20.0 cm from S₁ and 15.0 cm from S₂. Find λ.

Sources 4.0 cm apart, λ = 1.0 cm. Find the angle to the first nodal line.

Sources 5.0 cm apart, λ = 2.0 cm. How many nodal lines in total?

Light: Wave or Particle? Testing Two Models

What did each model predict about the speed of light in water?

Which measurement settled the speed question, and what did it show?

Why was Poisson's bright spot strong evidence for the wave model?

Young's Double-Slit Experiment

λ = 520 nm, d = 0.26 mm, L = 2.5 m. Find Δx.

d = 0.20 mm, L = 1.6 m, Δx = 4.8 mm. Find λ.

λ = 600 nm, d = 0.040 mm. Find the angle to the 3rd dark fringe.

Why must the two slits be coherent?

Single-Slit Diffraction

λ = 640 nm, w = 0.080 mm, L = 2.0 m. Find the width of the central maximum.

λ = 500 nm, w = 0.010 mm. Find the angle to the first dark fringe.

What happens to the pattern if the slit is made narrower?

Diffraction Gratings and Spectroscopy

A grating has 750 lines/mm. Find the first-order angle for 600 nm light.

What is the highest order for that grating and wavelength?

A grating with 500 lines/mm gives a first-order line at 15.0°. Find λ.

Thin-Film Interference: Soap Bubbles, Oil Slicks and Anti-Reflective Coatings

Find the minimum thickness of a soap film (n = 1.33) in air that strongly reflects 480 nm light.

Find the minimum thickness of a MgF₂ coating (n = 1.38) on glass (n = 1.52) that cancels 600 nm reflections.

Why does a draining soap film turn black at the top?

Air Wedges and Measuring with Light

Plates 10 cm long, spacer 0.040 mm, λ = 600 nm. Find Δx.

Plates 8.0 cm long, λ = 500 nm, Δx = 0.50 mm. Find the spacer thickness.

Why is the fringe at the contact line dark?

Polarization of Light

Unpolarized light of 120 W/m² passes two polarizers at 45° to each other. Find the final intensity.

Find Brewster's angle for glass with n = 1.60 in air.

What does polarization tell us about light?

Resolution: How Diffraction Limits What We Can See

Find θ_min for an 8.0 cm telescope lens at 500 nm.

What is the smallest feature separation it can resolve on the Moon (3.84 × 10⁸ m away)?

Give two ways to improve resolution.

Electromagnetic Waves from Oscillating Charges

An FM station broadcasts at 88.1 MHz. Find λ and the half-wave antenna length.

What kind of charge motion produces EM radiation?

Name the source of X-rays in an X-ray tube.

Light-Wave Technologies and Their Impact on Society

Why must a hologram be made with laser light?

Find the pit depth for a disc read at 650 nm through plastic with n = 1.58.

List three things a strong risk–benefit analysis includes.

Check your understanding

Quiz

When light passes from air into glass, which quantity stays the same?

A point on the 2nd nodal line of a two-source pattern has a path difference of…

In Young's experiment, which change doubles the fringe spacing?

The equation w sin θ = nλ gives…

A grating has 500 lines/mm. Its spacing d is…

An anti-reflective coating (n between air and glass) has a minimum thickness of…

Fringes in an air wedge get closer together when…

Unpolarized light passes through two crossed polarizers. The transmitted intensity is…

Which evidence shows that light is a transverse wave?

10.

Which explains why radio telescopes are much larger than optical telescopes?

For parents and teachers

Which lesson to revisit:

Wrong speed or wavelength in a medium, or frequency changing: Light as a Wave: Refraction, Index of Refraction and Dispersion.
Mixing up when diffraction is noticeable: Diffraction and Huygens' Principle.
Using nλ instead of (n − ½)λ for nodal lines, or miscounting nodal lines: Interference in Two Dimensions.
Unsure why the wave model won, or which model predicted what: Light: Wave or Particle?
Errors with Δx = Lλ/d or d sin θ = mλ, or unit conversions: Young's Double-Slit Experiment.
Using Lλ/w instead of 2Lλ/w, or thinking w sin θ = nλ gives bright fringes: Single-Slit Diffraction.
Forgetting d = 1/N, using small angles for gratings, or rounding the highest order up: Diffraction Gratings and Spectroscopy.
Choosing the wrong thin-film formula (inversions miscounted) or forgetting λ/n: Thin-Film Interference.
Using λ instead of λ/2 per fringe in air wedges: Air Wedges and Measuring with Light.
Missing the factor ½ for unpolarized light or using cos θ instead of cos² θ: Polarization of Light.
Radian/degree confusion in θ = 1.22λ/D: Resolution.
Thinking any moving charge radiates, or E-field direction errors: Electromagnetic Waves from Oscillating Charges.
One-sided or physics-free technology answers: Light-Wave Technologies and Their Impact on Society.

Praise careful setup: naming the situation and writing the right equation before calculating is the most important habit in this unit.