9.3.5 Thin Film Interference

• Thin film interference causes the iridescence seen in:
  • Nature on peacock feathers
  • Glossy flower petals
  • Soap bubbles
  • The shiny side of a CD
  • Thin layers - or films - of oil on water
• This phenomenon occurs when light waves reflecting off the top and bottom surfaces of a thin film interfere with one another

The colourful pattern observed on a CD is a result of thin film interference

Conditions for Thin Film Interference

• To see the interference light must be incident on a material which:
  • Is very thin
  • Has a higher refractive index than the medium surrounding it

• The effect is caused initially by reflection
• When a wave reflects at a boundary, a phase change is seen, such that:

A wave reflected at a boundary undergoes a phase change of half a wavelength, or π rad

• If a ray of light meets a medium with a higher refractive index, reflection occurs
  • But if the medium is transparent to light, the wave also refracts as it enters
• It will then reflect from the ‘back’ of the medium, before passing out of the ‘front’
• The reflected and refracted waves of light interfere with each other
  • The phase changes at boundaries depend on the refractive indices of the two media

Phase changes at the top and bottom of a thin film

• When light is reflected at an optically denser medium, which has a higher refractive index, it undergoes a phase change of π rad, or 180°
  • This is equivalent to half a wavelength
• When the wave is reflected at an optically less dense medium, there is no phase change
• Although soap bubbles and layers of oil floating on water are incredibly thin, they do have a thickness, which we can usefully express in terms of the wavelength
  • For example, distance travelled by the light, d = 2λ.

Uses of Thin Film Interference

• Thin films can prevent light from being reflected
• Due to the conservation of energy, this increases the light which is transmitted through a medium
• This effect is utilised in:
  • Camera lenses - these often have a coating to prevent reflection
  • Solar cells - this is to ensure a high proportion of incident light can be captured

• A thin film, such as a soap bubble, can be modelled as a very thin, parallel-sided rectangle, with thickness d and refractive index higher than that of air, i.e. n > 1

A thin film can be modelled as a parallel-sided, rectangular ‘slice’ with a thickness of ‘d’

• At point A, a ray of light is incident on the thin film, this light:
  • Reflects with a phase change of π
  • Refracts into the film
• At point B, the ray of light:
  • Reflects with no phase change
  • Continues to point C where it refracts
• The observer sees both rays, at points A and C, which can now be seen to interfere
  • The path difference is 2d, the extra distance that the second ray has travelled

• Constructive interference occurs when:

The thickness of the coating is

• This is because the light from the bottom of the film has travelled an extra distance (there and back)
• Since the first ray has undergone a phase change of π, or half a wavelength, , the condition for constructive interference is:

Path difference, 

• Where:
  • d = thickness of the film (m)
  • m = an integer (generally taken as m = 0)
  • λ₀ = wavelength of light in soap (m)
• The value of λ₀ can be obtained using the relationship:

• Where:
  • λ = wavelength of light in a vacuum (m)
  • n = refractive index of the film
• The condition for constructive interference can, therefore, be rewritten in terms of λ as:

• Rearranging this gives:

• Destructive interference occurs when:

The thickness of the coating is

• This is because the light from the bottom of the film has travelled an overall distance of λ
• This time, the condition for destructive interference is:

Path difference, 

• The value of λ₀ can be obtained using the relationship:

• The condition for destructive interference can, therefore, be rewritten in terms of λ as:

• Rearranging this gives:

• In this case, the light appears coloured as one wavelength is missing
• Hence, different colours are removed at different angles so a multi-coloured fringe pattern is observed

Step 1: List the known quantities

• • Refractive index of coating, n = 1.31
  • Wavelength, λ = 540 nm

Step 2: Use the data booklet to find the conditions for thin-film interference

Constructive Interference	Destructive Interference

Step 3: Consider the phase changes at the boundaries

• • Firstly, at the boundary with the coating, which has higher optical density, phase change = π
  • Secondly, at the boundary with the lens, which has higher optical density, phase change = π

Step 4: Determine the correct equation to use 

• • To prevent reflection, this requires destructive interference, so the equation to use is:

• • For a minimum thickness, m = 0

Step 5: Rearrange to make thickness, d, the subject and calculate

= 100 nm