Thin Film Interference and Soap Bubbles Easy Explanation

When light falls on a thin transparent film like a soap bubble, oil on water or a thin glass plate, some reflects from the top surface and some from the bottom surface. These two reflected waves interfere. Depending on film thickness and wavelength, some colours are strengthened and some are cancelled, so the film looks coloured.

Thin film interference matters because it explains natural beauty and useful technology. The colours of soap bubbles, oil slicks and peacock feathers come from this effect. Engineers use it to make anti-reflection lenses, mirrors for lasers and decorative coatings.

Key Concepts

Phase change on reflection: a wave reflecting from a denser medium undergoes a phase change of pi, equivalent to path change lambda divided by 2. No phase change occurs when reflecting from a rarer medium. Optical path is refractive index multiplied by geometric path. For nearly normal incidence, path difference between the two reflected rays is approximately 2 mu t, where mu is film refractive index and t is thickness, plus or minus lambda divided by 2 due to phase change.

• Top reflection from air to soap film: denser, phase change pi.
• Bottom reflection from film to air: rarer, no phase change.
• Net extra lambda divided by 2 must be included.

Formulas

For reflected light with one phase change, bright fringes satisfy 2 mu t cos r equals (2m plus 1) lambda divided by 2, and dark fringes satisfy 2 mu t cos r equals m lambda, where m is 0, 1, 2 and so on, t is thickness, mu is refractive index and r is angle of refraction in the film. For normal incidence cos r is approximately 1. In transmitted light the bright and dark conditions are reversed.

Worked Example

A soap film of refractive index 1.33 is illuminated by light of wavelength 600 nm at normal incidence. Find the minimum thickness for bright reflection.

For one phase change, bright condition: 2 mu t equals lambda divided by 2 for m equals 0.

So t equals lambda divided by 4 mu equals 600 divided by (4 multiplied by 1.33).

Denominator equals 5.32. t equals 112.8 nm approximately. A film about 113 nm thick will reflect 600 nm strongly. Different thickness will favour different colours, which is why bubble colours change as it drains and thins.

Common Misconceptions

• Colours come from pigments in soap: Wrong. Pure soap film is transparent; colours are purely interference of white light.
• Both reflected rays get phase change: Wrong. Only reflection from denser medium gives pi change; counting it wrong swaps bright and dark conditions.
• Thick glass plate should also show same colours easily: Wrong. Large thickness exceeds coherence length of ordinary light, so fringes wash out.

Real-World Applications

Camera lenses and spectacles use magnesium fluoride coatings of thickness lambda divided by 4 to cancel reflection by destructive interference. Oil spill monitoring uses colour patterns to estimate thickness. Dichroic mirrors in projectors and lasers use multilayer thin films to reflect selected colours. Non-reflecting museum glass and solar panel coatings improve transmission using the same principle.

Soap bubble colours arise because top and bottom reflections interfere with one phase reversal, giving path difference 2 mu t. As thickness varies across the bubble, different wavelengths satisfy bright conditions at different places.