Reflection & Refraction

Reflection & Refraction

When a wave reaches a boundary between two materials, it can bounce off (reflect), bend as it passes through (refract), or be absorbed. Get those behaviours straight, plus one golden rule about where angles are measured from, and boundary questions fall into place. The module ends on a question that sounds like a riddle: why can you see your face in a mirror but not in a sheet of paper, when every ray leaving both of them obeys exactly the same law?

The words for it

Six terms. The first is the one everything else is measured against, and it is where the marks go:

Label the reflection

This ray diagram shows a wave reflecting off a mirror. Drag each label to the right feature: the dashed line, the ray coming in from the left, the ray leaving to the right, and the pink angle.

The law of reflection

The law itself is short and exact: angle of incidence = angle of reflection Both are measured from the normal, and it is worth knowing why that convention exists rather than treating it as a rule to obey. A normal can be drawn at any point on any surface, flat or curved, and it is always unique. "The direction of the surface" is not: on a curved mirror it changes from point to point, and there is no single line to measure from. Measure from the normal and one law covers flat mirrors, curved mirrors and every lens you will ever meet.

Angle of reflection

A ray hits a mirror with an angle of incidence of 40°. What is the angle of reflection, in degrees?

Measured from where?

A ray of light strikes a mirror at 25° to the MIRROR SURFACE. What is the angle of incidence, in degrees?

Bounce, or bend?

Both happen at a boundary, and they are often happening at once. What separates them is whether the wave gets into the second material at all:

Straight through

A ray of light enters a glass block travelling exactly along the normal, at 0° to it. Inside the glass it definitely travels more slowly. Does it change direction?

• No. Every part of the wavefront reaches the boundary at the same instant and slows together, so there is nothing to pivot the wave round: it slows without turning
• Yes, towards the normal, because it has slowed down and slowing always bends a ray towards the normal
• Yes, away from the normal, because entering a denser material spreads the ray out
• No, and this shows that a ray travelling along the normal does not slow down either

The mirror and the paper

Hold up a mirror and you see your face. Hold up a sheet of white paper, which reflects nearly as much light, and you see nothing at all. Both surfaces obey the law of reflection perfectly. Specular reflection, from a smooth surface: every point has a normal pointing the same way, so parallel rays arriving stay parallel on the way out, and the pattern of the light survives the journey. That preserved pattern is the image. Diffuse reflection, from a rough surface: paper is rough on the scale of light, so the normals at neighbouring points tilt in different directions. Each individual ray still leaves at exactly its own angle of reflection. They simply all leave at different angles, so the pattern is scattered. Nothing is broken in the second case. The law holds ray by ray, and the image is lost anyway.

What happens here?

Order the experiment

Put the steps for investigating reflection with a ray box in order.

• Place the mirror on paper and draw along its front edge
• Draw the normal at 90° to that line, where the ray will hit
• Shine a ray from the ray box at that point and mark the incident and reflected rays with dots
• Take the mirror away and rule the two rays through the dots
• Measure both angles from the normal and compare them

Which are true?

Select ALL THREE statements that are TRUE.

• Every ray reflecting off a sheet of paper obeys the law of reflection exactly. The surface is simply rough enough that neighbouring normals point in different directions
• A wave crossing a boundary along the normal changes speed but not direction
• The angle a ray makes with a mirror surface and its angle of incidence always add up to 90°
• Diffuse reflection happens because rough surfaces break the law of reflection
• Refraction happens because the wave changes frequency as it crosses the boundary
• The angle of incidence is measured between the incident ray and the surface

The boundary rules

In reflection, the angle of incidence equals the angle of _____, both measured from the _____, which is the line drawn at 90° to the surface. In refraction, a wave that slows down as it crosses a boundary bends _____ the normal, and one that speeds up bends away from it. A rough surface gives _____ reflection, scattering the light without any ray breaking the law.

Mirror or paper?

Exam practice. In about 50 words, explain why you can see your face in a mirror but not in a sheet of white paper, even though both reflect light and both obey the law of reflection. Include:

• what is different about the two surfaces at a very small scale
• what that does to the normals, and therefore to parallel rays arriving together
• the names for the two kinds of reflection