• Intensity is power spread over an area (I = P/A), and it obeys an inverse-square law with distance for a point source.
• Refraction happens when light crosses a boundary between materials — it changes speed, and (unless it hits the boundary straight on) it changes direction too.
• Refractive index (n) tells you how much a material slows light down compared to a vacuum. Snell's Law (n₁sinθ₁ = n₂sinθ₂) connects refractive index to the angles either side of a boundary.
• The critical angle is the special angle of incidence (inside a dense material) at which the refracted ray grazes along the boundary at exactly 90°.
• Total internal reflection (TIR) happens beyond the critical angle, when going from a denser to a less dense material — 100% of the light reflects, none escapes.
• The refractive index experiment uses a ray box, a perspex block, and careful angle-marking to measure n practically.
• Plane polarisation restricts a transverse wave's oscillations to a single plane. Only transverse waves can be polarised — longitudinal waves never can.
• Light can be polarised by filters, reflection, or refraction, and polarisation has real uses — from sunglasses to stress-testing materials to analysing sugar solutions.

Think about a wave — light, sound, whatever — as a courier carrying energy. Intensity just measures how much energy that courier delivers, per second, to each square metre of surface it hits. That's it. It's power density.

Now here's the part that trips people up conceptually: intensity isn't just about how much energy the source is pumping out — it's about how concentrated that energy is when it lands. The same 100 W lightbulb feels blinding up close and barely noticeable from across a football field, even though it's emitting the exact same power the whole time. What's changing is the area that power is spread across.

Amplitude and Frequency

Intensity also depends on the wave's amplitude and frequency — specifically, it's proportional to the square of each:

Spherical Waves & the Inverse Square Law

A point source (like a bare lightbulb or a speaker) radiates energy equally in all directions — forming an expanding sphere of wavefronts. The area of that sphere at radius r is 4πr². So as the wave travels outward, the same total power P is spread across a bigger and bigger sphere:

Refraction occurs whenever light crosses a boundary between two transparent materials of different density — like going from air into glass, or from water into air. Two things happen simultaneously at that boundary: the light's speed changes, and (unless it hits the boundary dead-on) its direction changes too.

Here's the crucial insight: the bending isn't some separate, mysterious effect — it's a direct consequence of the speed change. One side of the wavefront hits the new material and slows down before the rest of the wavefront does, so the whole wavefront pivots, like a marching band changing direction when one end walks onto muddy ground.

The Bending Rules

Refractive Index — the Formula

The refractive index, n, is a number that tells you exactly how much slower light travels in a material compared to in a vacuum.

Because light can never travel faster in a material than it does in a vacuum, v is always less than c — which means n is always greater than 1. A "high refractive index" material (like diamond, n ≈ 2.4) is called optically dense — it slows light down a lot. Air is so close to a vacuum that we just treat its refractive index as approximately 1 in calculations.

Snell's Law

Snell's Law is the equation that links the angle of incidence and angle of refraction to the refractive indices of the two materials involved:

Now imagine you're inside a dense material (like glass) shining light out towards a less dense material (like air), and you slowly increase the angle of incidence. As you do, the angle of refraction increases too — and it increases faster than the angle of incidence, because you're going from dense to less dense (bending away from the normal).

Eventually, at some specific angle of incidence, the refracted ray gets bent so far that it skims exactly along the boundary itself — refracted at 90°. That special angle of incidence is called the critical angle, C.

This formula drops straight out of Snell's Law. Set n₁ = n (the dense material), θ₁ = C, n₂ = 1 (air), and θ₂ = 90° (refraction along the boundary):

So what happens if you increase the angle of incidence beyond the critical angle? The refracted ray can't bend past 90° — there's no way for it to "escape" the boundary anymore. Instead, 100% of the light reflects back into the denser material. None of it transmits through. This is total internal reflection.

Aim: To investigate the refraction of light through a perspex (or glass) block and determine its refractive index.

Equipment

• Ray box — provides a narrow beam of light
• Perspex/glass block — the material being investigated
• Protractor — measures the angles
• Sheet of paper, pencil, ruler — for marking the ray's path

Method (Step by Step)

1. Place the block on paper and draw around its outline with a pencil.
2. Direct a ray of light from the ray box at the side face of the block.
3. Mark small crosses (×) at: a point on the incoming ray, where the ray enters the block, where it exits the block, and a point on the exiting ray about 5 cm beyond the block.
4. Draw a dashed normal line (at right angles to the surface) at the point of entry.
5. Remove the block and join up the marked points with straight ruled lines.
6. Replace the block in its outline and repeat for several different angles of incidence.

Analysing the Results

Once you have several pairs of (angle of incidence, angle of refraction) readings, you calculate n for each pair using n = sinθ₁/sinθ₂, or — for better accuracy — plot a graph of sin(θ₁) against sin(θ₂). Because Snell's Law says n₁sinθ₁ = n₂sinθ₂, rearranging gives sinθ₁ = n·sinθ₂ (with air as material 2, n₂=1). This means the gradient of that straight-line graph equals n — much more reliable than trusting a single pair of readings.

This topic is really about one question: which directions is a wave allowed to wiggle in?

A transverse wave (like light) oscillates perpendicular to its direction of travel. But "perpendicular" doesn't mean just one direction — it means any direction within the flat plane perpendicular to travel. Picture looking straight down the barrel of a wave travelling towards you: the oscillations could point up-down, left-right, or any diagonal in between. Ordinary light is a jumble of waves oscillating in all of these directions at once — this is called unpolarised light.

Method 1 — Polarising Filters

A polarising filter has a transmission axis — only oscillations aligned with that axis get through. Pass unpolarised light through one filter, and you get plane-polarised light out the other side (whatever survives lines up with the transmission axis). Now if you place a second filter after it, rotated 90° to the first, absolutely no light gets through — the first filter already restricted the light to one plane, and the second filter demands a perpendicular plane, so nothing satisfies both.

Method 2 — Polarisation by Reflection

When unpolarised light reflects off a non-metallic surface (like water, glass, or a wet road), it becomes partially polarised — the reflected light oscillates more in the plane parallel to the reflecting surface than in other planes.

This is exactly why polaroid sunglasses work: if the reflecting surface (road, lake) is horizontal, the glare reflecting off it is partially polarised horizontally. Sunglasses with a vertical transmission axis block most of that horizontal glare, letting through the vertically-oscillating light that carries the useful image of what's underneath.

Method 3 — Polarisation by Refraction

Light can also become partially polarised when it refracts (transmits) from one medium into another. This time, the refracted light is polarised in the plane perpendicular to the transmitting surface — the opposite orientation to the reflected polarisation. So at any boundary, the reflected beam and the refracted beam end up partially polarised at right angles to each other.

Real-World Uses of Polarisation

• I can state and use I = P/A to calculate intensity
• I understand why intensity follows an inverse square law with distance for a point source
• I can apply I ∝ A² and I ∝ f² together in combined problems
• I can explain why light bends towards/away from the normal when entering different media
• I can define refractive index and explain why n is always greater than 1
• I can apply Snell's Law correctly, keeping material 1 and material 2 in the right order
• I can define the critical angle and derive sin(C) = 1/n from Snell's Law
• I know the two conditions required for total internal reflection
• I can describe the method for measuring refractive index of a perspex block
• I can identify relevant safety precautions for the refraction experiment
• I can define plane polarisation and explain why only transverse waves can be polarised
• I can describe all three methods of polarising light: filters, reflection, refraction
• I can explain how polaroid sunglasses reduce glare
• I can describe real-world applications: stress analysis and chemical concentration analysis