Reflection at a plane boundary

The law of reflection

• When a wave meets a plane (flat) boundary it can be reflected — it bounces back into the medium it came from.

$$\theta_i = \theta_r$$

• $\theta_i$ — the angle of incidence

• $\theta_r$ — the angle of reflection

• Both angles are measured from the normal, not from the surface.

  • The normal is the construction line drawn at right angles to the surface at the point where the wave strikes.
  • Drawing it, and labelling it "normal", is expected in every ray diagram.

• The incident ray, the reflected ray and the normal all lie in the same plane.

What does and does not change on reflection

• The wave stays in the same medium, so:
  • the speed is unchanged,
  • the frequency is unchanged,
  • therefore the wavelength is unchanged.
• Only the direction changes.
• On a wavefront diagram, the reflected wavefronts have the same spacing as the incident ones — a useful check on your drawing.

Phase change on reflection

The standard asks about phase changes at a boundary, and there are two cases for a pulse on a rope or spring:

• Reflection from a fixed end (a denser medium, or a wall):

  • the pulse is inverted — a crest comes back as a trough,
  • this is a phase change of half a wavelength (often stated as $180°$).

• Reflection from a free end (a less dense medium, or a loose ring on a pole):

  • the pulse comes back the same way up,
  • there is no phase change.

• The memory hook: a fixed end flips the pulse; a free end does not.

• In both cases the pulse keeps its shape and its width — reflection does not change the wavelength.

Drawing a reflection ray diagram

• Draw the surface and mark the point where the ray strikes it.
• Draw the normal at that point, at $90°$ to the surface, as a dashed line.
• Measure the angle of incidence from the normal with a protractor.
• Measure the same angle on the other side of the normal and draw the reflected ray.
• Add arrows to both rays showing the direction of travel.