Waves at boundaries
Definition
Reflection
The change in direction of a wave at a boundary so that it remains in the original medium.
Definition
Refraction
The change in direction of a wave caused by a change in speed as it passes from one medium into another.
- When a wave reaches a material interface, its energy may be reflected, transmitted or absorbed, and a transmitted wave may also be refracted.
- A material interface is the boundary between two materials or between two regions with different wave properties.
- The proportions of energy in each outcome depend on the two materials, the wavelength and the angle at which the wave meets the boundary.
Reflection
- A reflected wave remains in the original material and travels away from the boundary.
- For a straight boundary, the angle of incidence equals the angle of reflection: i=ri=ri=r.
- Both angles are measured from the normal, an imaginary line at 90∘90^\circ90∘ to the surface.
- Reflection changes the direction of travel, but the wave remains in the same material, so its speed, frequency and wavelength stay unchanged.
Transmission and refraction
Definition
Transmission
The passage of electromagnetic radiation through a substance or across a boundary.
- A transmitted wave carries energy beyond the boundary.
- If its speed changes and it arrives at an angle to the normal, its direction changes by refraction.
- The source continues to set the frequency, so frequency does not change at the boundary.
- Because v=fλv=f\lambdav=fλ, a change in speed at constant frequency causes the wavelength to change.
- A wave that slows bends towards the normal, whereas a wave that speeds up bends away from the normal.
Absorption
Definition
Absorption
The transfer of energy from electromagnetic radiation to a material when the radiation is taken in rather than reflected or transmitted.
- Absorption reduces the amplitude and energy of the wave that continues through or returns from the material.
- The absorbed energy commonly increases the material's temperature, although it may produce another response in a detector.
- A surface can partly absorb and partly reflect or transmit the same incident wave, so these outcomes are not mutually exclusive.
Energy at an interface
- Energy is conserved at the boundary, so the incident wave energy is shared between reflected, transmitted and absorbed energy.
- In symbols, Eincident=Ereflected+Etransmitted+EabsorbedE_{\text{incident}}=E_{\text{reflected}}+E_{\text{transmitted}}+E_{\text{absorbed}}Eincident=Ereflected+Etransmitted+Eabsorbed.
- A wave with a smaller transmitted amplitude has not necessarily lost energy from the system; some energy may have been reflected or absorbed.
Example
Tracking wave energy
- A wave transfers 120 J120\ \text{J}120 J to a boundary, where 35 J35\ \text{J}35 J is reflected and 50 J50\ \text{J}50 J is transmitted.
- Use energy conservation: Eabsorbed=120−35−50E_{\text{absorbed}}=120-35-50Eabsorbed=120−35−50.
- The material absorbs 35 J35\ \text{J}35 J.
Exam technique
- For a description question, name the outcome and state what happens to the wave: it returns, crosses the boundary, changes direction or transfers energy to the material.
- For an explanation of refraction, link the change in speed to the change in direction.
Common Mistake
- Measure incidence and reflection angles from the normal, not from the surface.
- Do not state that refraction always means bending; a wave travelling along the normal changes speed and wavelength without changing direction.
Self review
- What happens to a wave during reflection?
- How are the angles of incidence and reflection related?
- Why can a transmitted wave change wavelength without changing frequency?
- What happens to wave energy during absorption?
- How is incident energy divided at a material interface?
