Thin Film Interference Calculator (Soap Bubbles, Oil Slicks, Anti-Reflection Coatings)
Wavelengths a thin film of a given thickness and refractive index reflects most strongly, the thinnest film that makes or cancels a reflection, and its brightness at one wavelength.
Results
The dashed line marks the value you entered.
What this tool does
Light reflected from the front and back of a film travels slightly different paths, and the two beams reinforce or cancel depending on the thickness compared with the wavelength inside the film. A soap film or oil slick shows colours because some wavelengths reinforce while others cancel, and the colours shift as the film thins. An anti-reflection coating on a lens uses the opposite case: a layer a quarter of a wavelength thick, with an index between air and glass, cancels the reflection at its design wavelength. This is the normal-incidence result; at an angle the path is longer and the colours shift towards blue.
Formula
2 n t = (m + ½) λ (one flip: bright) · 2 n t = m λ (no net flip: bright) · quarter-wave coating t = λ ÷ 4n
Variables
| Symbol | Meaning | Unit |
|---|---|---|
nf | Refractive index of the film | — |
tf | Film thickness | nm |
lw | Wavelength of the light | nm |
cs | Phase change on reflection | — |
L1 | Wavelength reflected most strongly (longest) | nm |
L2 | Next wavelength reflected strongly | nm |
L3 | Third wavelength reflected strongly | nm |
TB | Thinnest film that reflects that wavelength best | nm |
TD | Thinnest film that cancels the reflection of that wavelength | nm |
BR | Reflected brightness at that wavelength (0 dark – 100 brightest) | % |
Worked example
- Refractive index of the film1.33
- Film thickness300 nm
- Wavelength of the light550 nm
- Phase change on reflection1
- Wavelength reflected most strongly (longest)1596 nm
- Next wavelength reflected strongly532 nm
- Third wavelength reflected strongly319 nm
- Thinnest film that reflects that wavelength best103.4 nm
- Thinnest film that cancels the reflection of that wavelength206.8 nm
- Reflected brightness at that wavelength (0 dark – 100 brightest)98 %
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.