Reflection and Refraction

When a wave reaches a boundary — the edge of one material and the start of another — it does not simply stop. It may bounce back off the boundary (reflection), or it may pass through and change direction (refraction). These two behaviours explain a great deal of everyday physics: why you can see yourself in a mirror, why a straw looks bent where it enters a glass of water, why a swimming pool looks shallower than it really is, and how lenses and prisms work. This lesson, part of Topic P5 (Waves in matter) of OCR Gateway Science A, sets out the law of reflection, distinguishes specular from diffuse reflection, explains refraction as a change of speed at a boundary, and shows how to draw the ray diagrams examiners ask for. Higher-tier students will also see how refraction is explained using wavefronts.

By the end of this lesson you should be able to state and use the law of reflection, distinguish specular and diffuse reflection, explain refraction in terms of a change of wave speed at a boundary, predict which way a ray bends, and draw labelled ray diagrams for both.

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Reflection and the Law of Reflection

Reflection is when a wave hits a boundary and bounces back into the material it came from. The most familiar example is light reflecting off a mirror, but all waves reflect — sound echoes off walls, and water waves bounce off the side of a tank.

To describe reflection we draw a normal: an imaginary line at right angles ($90°$90°) to the surface at the point where the wave hits. All angles are measured from the normal, never from the surface itself. The ray arriving is the incident ray, and the ray leaving is the reflected ray. We then define:

• the angle of incidence ($i$i) — between the incident ray and the normal;
• the angle of reflection ($r$r) — between the reflected ray and the normal.

The law of reflection states:

$\text{angle of incidence} = \text{angle of reflection} \qquad (i = r)$angle of incidence=angle of reflection(i=r)

The incident ray, the reflected ray and the normal all lie in the same plane. The diagram below shows a ray reflecting off a plane (flat) mirror.

Exam Tip: Always measure angles from the normal, not from the mirror surface. A favourite exam trap gives you the angle between the ray and the mirror; you must subtract from $90°$90° to get the angle from the normal before applying $i = r$i=r.

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Specular and Diffuse Reflection

Whether a surface gives a clear reflection or just scatters light depends on how smooth it is.

• Specular reflection happens at a very smooth surface, such as a mirror or still water. Parallel incident rays are all reflected in the same direction, so a clear, sharp image is formed. This is the "mirror" kind of reflection.
• Diffuse reflection happens at a rough surface, such as paper, a wall or rough water. The surface is made of tiny facets pointing in many directions, so parallel incident rays are reflected in many different directions (scattered). No clear image forms — but it is why you can see non-shiny objects from any angle.

Crucially, the law of reflection still holds at every single point in diffuse reflection — each tiny part of the rough surface obeys $i = r$i=r using its own local normal. The rays scatter only because those local normals point in different directions, not because the law is broken.

Exam Tip: In diffuse reflection the rays scatter because the surface is rough, not because the law of reflection fails. State that $i = r$i=r at every point, but the normals point in different directions, so the reflected rays go different ways.

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Refraction: A Change of Speed at a Boundary

Refraction is the change in direction of a wave when it crosses a boundary between two materials and changes speed. The change of speed is the cause; the change of direction is the result.

Why does the speed change? Different materials let waves travel at different speeds. Light, for instance, travels fastest in a vacuum (and air), more slowly in water, and slower still in glass. A material in which light travels more slowly is described as optically denser. (Optical density is about how much the material slows light; it usually, but not always, follows ordinary density.)

When a wave crosses a boundary at an angle to the normal, one side of the wave reaches the new material — and changes speed — before the other side. This makes the wave swing round, like a marching band wheeling when soldiers on one side take shorter steps. The rule for which way it bends is:

• entering a slower (optically denser) material — for example, light passing from air into glass or water — the ray slows down and bends towards the normal;
• leaving into a faster (less dense) material — for example, light passing from glass or water back into air — the ray speeds up and bends away from the normal.

A useful memory aid is to imagine a car driving from a smooth road onto mud at an angle: the wheel that reaches the mud first slows first, so the car slews towards the normal as it enters the slower medium.

One special case: if a wave meets the boundary along the normal (at $90°$90° to the surface, head-on), it still changes speed but does not change direction, because both sides of the wave reach the boundary at the same instant. The diagram below shows a ray of light refracting as it passes through a glass block.