Thin-Film Optical Coating Calculator

This thin-film optical coating calculator will calculate the optical path difference and reflectivity at the coating interface.

Coating thickness99.6377 nmλ/4n — a QUARTER wave measured inside the film, which is thinner than a quarter wave in air by the refractive index

Reflectance with the coating1.26008%at the design wavelength

Reflectance of the bare surface4.258%uncoated glass in air reflects about 4% per surface, and a lens with ten surfaces would lose a third of the light without coatings

Improvement70.407% less reflectiontransmission rises from 95.742% to 98.74%

Ideal coating index1.23288√(n₀n_s) gives EXACTLY zero reflectance at the design wavelength. Yours is 1.38, which is 11.933% away — and no durable material has an index as low as 1.23, which is why magnesium fluoride at 1.38 is the practical standard rather than the perfect one

Thickness at that ideal index111.5272 nm

Why a quarter wavethe two reflections cancellight reflecting off the film's far side travels an extra half wavelength there and back, arriving exactly out of phase with the front reflection. Destructive interference removes it

Where the light goesinto transmissionthe cancelled light is not absorbed — energy is conserved, so suppressing the reflection necessarily increases what passes through

Reflectance at 450 nm1.6204%away from the design wavelength

Reflectance at 550 nm1.2601%the design point

Reflectance at 650 nm1.4368%away from the design wavelength

Why coated lenses look purplethe coating misses the endsa single layer nulls only one wavelength, so it works best in the green where the eye is most sensitive and reflects more blue and red. Their mixture is the familiar purple sheen

The formula

t = λ/4n; ideal n = √(n₀n_s); R = ((n₀n_s − n²)/(n₀n_s + n²))²

A quarter wave, measured inside the film

Light reflecting from the back of a coating travels an extra half wavelength going there and returning, so it arrives exactly out of phase with the reflection from the front and cancels it. The film must therefore be a quarter wavelength thick as measured INSIDE the coating, which is thinner than a quarter wave in air by the refractive index.

The cancelled light is not destroyed. Energy is conserved, so suppressing the reflection necessarily increases the transmission — which is the entire point for a camera lens with ten air-glass surfaces that would otherwise lose about a third of the light.

Why the perfect coating does not exist

Exactly zero reflectance needs a coating index of √(n₀n_s), which for crown glass in air is about 1.23. No durable material comes close; magnesium fluoride at 1.38 is the practical standard and leaves around 1.3% rather than nothing.

A single layer also nulls only one wavelength. Coatings are optimised for the green, where the eye is most sensitive, and reflect more at the blue and red ends — whose mixture is the purple sheen on a coated lens. Multi-layer stacks flatten this at the cost of complexity.