Calculate reflectance, transmittance, and spectral response of thin film optical coatings. Includes AR coating design, spectral plot, and material reference.
Thin film optics governs how light reflects and transmits through coatings only a few hundred nanometers thick. When light hits a thin film, reflections from the front and back surfaces interfere — constructively (bright reflection) or destructively (anti-reflection). By choosing the right film material (refractive index) and thickness, engineers can minimize reflection to below 0.1% or create highly reflective mirrors.
The most common application is anti-reflection (AR) coatings on eyeglasses, camera lenses, and solar cells. A single-layer AR coating works best when n₁ = √(n₀ × n₂) and the film thickness equals λ/(4n₁) — a quarter-wave optical thickness. MgF₂ (n = 1.38) on glass (n = 1.52) reduces reflection from 4% to about 1.3% at one wavelength. Multi-layer stacks using high and low refractive index materials can achieve broadband AR below 0.2%.
This calculator models single-layer thin film interference using the Fresnel equations and Airy formulas. It shows reflectance at any wavelength, angle, and film parameters, plus a full visible-spectrum reflectance chart to visualize the coating's performance across colors.
Use this calculator when you want to see how refractive index, thickness, and wavelength shape the performance of a single optical coating.
It is useful for anti-reflection intuition, coating comparisons, and understanding why a thin film can suppress reflection at one wavelength while shifting color or performance elsewhere. It also helps show why a visually simple coating problem can become wavelength-sensitive very quickly.
Phase: δ = 2πn₁d cos(θ₁)/λ. Fresnel: r₀₁ = (n₀cosθ₀ − n₁cosθ₁)/(n₀cosθ₀ + n₁cosθ₁). Total: R = |r₀₁ + r₁₂e^(2iδ)|² / |1 + r₀₁r₁₂e^(2iδ)|². AR condition: n₁ = √(n₀n₂), d = λ/(4n₁).
Result: R = 1.37%, T = 98.63%
MgF₂ (n=1.38) on glass (n=1.52) at 100nm thickness: near quarter-wave at 550nm. Reflectance drops from 4.3% (bare glass) to 1.37%. Ideal AR would use n₁ = √1.52 ≈ 1.233 at 111nm.
Thin-film coatings are easiest to reason about when you focus on optical thickness rather than physical thickness alone. A small change in refractive index or design wavelength can move the destructive-interference minimum enough to change the apparent color and the useful AR bandwidth.
The most common mistake is assuming a single-layer design stays optimal across all wavelengths and angles. Real optical systems often need broadband or multi-angle performance, which usually requires multi-layer stacks. Material availability also limits the ideal quarter-wave index condition in practical coating design. Manufacturing tolerances can also shift the final coating away from the exact design minimum.
A film whose optical thickness (n × d) equals λ/4. Reflected waves from front and back surfaces travel a half-wavelength different path, producing destructive interference (minimum reflection).
Zero reflection requires n₁ = √(n₀n₂). For air-to-glass: √1.52 ≈ 1.23. No common material has n = 1.23 (MgF₂ at 1.38 is closest), so some residual reflection remains.
AR coating that works across a wide wavelength range (e.g., 400-700nm). Single layers are narrow-band; multi-layer stacks (2-6 layers) achieve broadband performance.
Typically 80-150nm for a single layer or a few hundred nanometers total for a multi-layer stack. The exact number depends on the design wavelength and the refractive index of the coating material.
Yes. At steeper angles, the effective optical path changes, shifting the AR minimum and reducing performance at the original design wavelength.
Low-n: MgF₂ (1.38), SiO₂ (1.46). High-n: TiO₂ (2.4), ZrO₂ (2.1), Ta₂O₅ (2.15). Multi-layer designs alternate high and low-n layers.