Reflection, Refraction, and the Wave Equation

Reflection, Refraction, and the Wave Equation

When waves meet boundaries between different materials, they can be reflected, refracted, or absorbed. Understanding these behaviours and the laws that govern them is essential for GCSE Physics.

Reflection

When a wave hits a boundary and bounces back, this is reflection. The law of reflection applies to all waves (light, sound, water waves):

The angle of incidence equals the angle of reflection.

angle i = angle r

Both angles are measured from the normal — an imaginary line perpendicular to the surface at the point where the wave hits.

Key points:

• The normal is drawn at 90 degrees to the surface
• The incident ray approaches the surface
• The reflected ray leaves the surface
• The angle of incidence is between the incident ray and the normal
• The angle of reflection is between the reflected ray and the normal
• The wavelength, frequency, and speed of the wave do not change after reflection

Specular reflection occurs on smooth surfaces (mirrors) — all reflected rays are parallel, producing a clear image. Diffuse reflection occurs on rough surfaces — reflected rays scatter in different directions, so no clear image is formed.

Refraction

Refraction is the change in direction of a wave as it passes from one medium to another, caused by a change in speed.

When light travels from a less dense medium to a more dense medium (e.g. air to glass):

• The light slows down
• It bends towards the normal
• The angle of refraction is less than the angle of incidence
• The wavelength decreases (because speed decreases but frequency stays the same)

When light travels from a more dense medium to a less dense medium (e.g. glass to air):

• The light speeds up
• It bends away from the normal
• The angle of refraction is greater than the angle of incidence
• The wavelength increases

Important: The frequency does not change during refraction. Only the speed and wavelength change.

If a wave hits the boundary along the normal (angle of incidence = 0), it passes straight through without changing direction, even though its speed changes.

Required Practical: Investigating Refraction

Aim: To investigate how light refracts through a rectangular glass or Perspex block.

Method:

1. Place a rectangular glass block on a sheet of paper and draw around it

2. Use a ray box to shine a narrow beam of light at the block at a measured angle

3. Mark the incident ray and the emerging ray with crosses

4. Remove the block and draw the refracted ray through the block by joining the entry and exit points

5. Draw normals at both surfaces

6. Measure the angle of incidence and the angle of refraction at the first surface

7. Repeat for different angles of incidence

Results: As the angle of incidence increases, the angle of refraction also increases, but by a smaller amount (for light entering a denser medium). The emerging ray is parallel to the incident ray but displaced sideways.

The Wave Speed Equation

wave speed = frequency x wavelength

v = f x lambda

This equation applies to all waves. Since the frequency stays constant during refraction, the change in speed is accompanied by a proportional change in wavelength:

v1 / v2 = lambda1 / lambda2

Example: Light has a wavelength of 600 nm in air (speed 3 x 10^8 m/s). In glass, the speed is 2 x 10^8 m/s. What is the wavelength in glass?

lambda2 = lambda1 x (v2 / v1) = 600 x (2 x 10^8 / 3 x 10^8) = 600 x 2/3 = 400 nm

Wave Fronts and Refraction

Refraction can be explained using wave fronts. When a wave front enters a denser medium at an angle:

• The part of the wave front that enters first slows down first
• The rest of the wave front continues at the original speed
• This causes the wave front to pivot, changing direction

This is analogous to a car with one wheel going onto mud — that side slows down and the car turns towards the mud.

Total Internal Reflection (Higher Tier)

When light travels from a dense medium to a less dense medium and the angle of incidence is greater than the critical angle, the light does not refract out — it is completely reflected back inside. This is total internal reflection.

• At the critical angle, the refracted ray travels along the boundary (angle of refraction = 90 degrees)
• Above the critical angle, total internal reflection occurs
• Below the critical angle, the light refracts out (with some partial reflection)

Applications:

• Optical fibres — light bounces along the inside of a thin glass fibre by total internal reflection, used in telecommunications and endoscopes
• Prisms in binoculars and periscopes

Exam Tips

• Always draw and label the normal — angles are measured from the normal, not from the surface
• Remember: frequency NEVER changes during refraction; speed and wavelength change together
• In the required practical, describe how you would draw the normal and measure angles
• For total internal reflection, state that light must travel from dense to less dense AND the angle must exceed the critical angle