Thin Film Interference Calculator

Thin‑film interference: what this calculator solves

Thin films (soap bubbles, oil slicks, optical coatings) can look colorful because light reflected from the top and bottom film surfaces combines. Depending on the film thickness t, refractive index n, and wavelength λ, the two reflected rays can add (constructive interference) or cancel (destructive interference).

This calculator returns the film thickness that produces a chosen interference condition in reflected light for a specified wavelength at normal incidence, using an integer order m (with m = 0 giving the smallest non‑negative thickness for the selected condition).

Model and formulas (normal incidence)

At normal incidence, the extra optical path inside the film for the ray that reflects from the bottom interface is 2 n t. Whether that corresponds to constructive or destructive reflection depends on phase reversals upon reflection.

Phase reversal assumed by this calculator

The equations below assume exactly one reflection undergoes a π phase shift (a “half‑wave” phase reversal). This occurs when one interface reflects from lower→higher refractive index and the other does not (typical example: air → film → substrate with indices arranged so that only one reflection is from lower to higher).

Conditions for reflected light (one phase reversal)

With one phase reversal, the reflected‑beam conditions are:

Solving for thickness t gives the formulas implemented by the calculator:

• Constructive reflection: t = ((m + 1/2) λ) / (2 n)
• Destructive reflection: t = (m λ) / (2 n)

How to use the inputs

• Wavelength λ (nm): enter the wavelength of interest. Visible light is roughly 380–750 nm.
• Film refractive index n: typical values: water ~1.33, many polymers ~1.4–1.6, glass ~1.5, TiO₂ ~2.3–2.6 (depends on wavelength).
• Order m (integer): counts solutions spaced by half‑wavelengths in optical path difference. m = 0 gives the thinnest solution for constructive reflection; for destructive reflection with one phase reversal, m = 0 yields t = 0.
• Desired reflection: choose whether you want constructive (brighter reflection at that λ) or destructive (suppressed reflection at that λ).

Interpreting the result

The output thickness is the film thickness that makes the chosen wavelength interfere constructively or destructively in reflection under the stated assumptions. Real “color” under white light happens because many wavelengths are present at once; a single thickness can enhance some wavelengths while suppressing others, and the effect changes with viewing angle.

Worked example

Suppose you want a film with refractive index n = 1.33 (water‑like) to produce constructive reflection at λ = 550 nm (green) for the smallest nonzero thickness (m = 0), assuming one phase reversal.

Use t = ((m + 1/2) λ) / (2 n):

t = ((0 + 1/2) · 550) / (2 · 1.33) = 275 / 2.66 ≈ 103.4 nm.

If instead you wanted the next constructive solution (m = 1), thickness increases by λ/(2n): t = ((1.5) · 550)/(2 · 1.33) ≈ 310.5 nm.

Comparison table (example values)

For λ = 550 nm and n = 1.33 under the calculator’s one‑phase‑reversal assumption:

Assumptions & limitations

• Normal incidence: the calculator uses the normal‑incidence path difference 2nt. At angle, the condition becomes approximately 2 n t cos(θ_film), shifting results.
• Reflected light only: transmission conditions differ (they swap constructive/destructive relative to reflection depending on phase shifts).
• One phase reversal only: if zero or two reflections undergo a π phase shift (depending on surrounding refractive indices), the constructive/destructive formulas interchange.
• Single wavelength: real sources may be broadband; perceived color depends on the full spectrum and the eye/sensor response.
• Dispersion and absorption ignored: n may vary with wavelength and some films are absorbing, changing the reflected intensity and effective phase.
• Multiple reflections neglected: the simple two‑beam model ignores higher‑order internal reflections that matter for high‑reflectivity coatings and etalons.