Thin Film Interference Calculator: Soap Film, Oil Slick and Anti-Reflection Coating Colours
Why thin films show colours, and how coatings cut reflection.
Engineering student calculators
Free textbook calculators with every step shown, so you can check your own working. Pick one, type in your numbers and see the formulas worked out. Or switch to Ask a question for an explained answer. No account needed.
Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.
How this calculator works
Enter the refractive indexes of the film and the materials above and below it.
Enter the thickness, the wavelength and the angle.
The calculator gives the path difference, the phase flips, the reflection and the colours.
Formulas used
- \delta = 2 n_f t\cos\theta_t
- \delta = (m + \tfrac12)\lambda\ \text{(one phase flip, constructive)}
- t = \frac{\lambda}{4 n_f}
Worked example
With the default numbers in the calculator above:
- Optical path difference (2 n t cos of the angle in the film): 798 nm
- Path difference in wavelengths: 1.4509
- Half-wave phase flips on reflection (top surface and bottom surface): 1 at the top, 0 at the bottom: an odd number, so one extra half wave
- Reflected light of this wavelength: Strong reflection (close to constructive)
- Visible wavelengths reflected most strongly: 532 nm
- Quarter-wave thickness for this wavelength: 103.38 nm
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
Why does a soap bubble show colours?
Light reflected from the front and back of the film interferes. The thickness decides which colours add up, and it changes across the film.
When is there a half-wave phase flip?
When light reflects from a material with a higher refractive index than the one it is travelling in.
How does an anti-reflection coating work?
A coating a quarter wavelength thick, with an index between air and glass, makes the two reflections cancel.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any physics text (thin film interference).
Need a calculator we do not have?
Embed this calculator on your own page
Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.
Need this drawn, designed or checked?
Drafting Central is a mechanical engineering and drafting business working with customers across Australia and around the world. A calculator gives you the numbers; we can turn them into drawings and designs.
Need help with a real project?
Talk to Drafting Central →