Fresnel Reflection Calculator

Reflection loss at an uncoated interface, and through a window

Refractive index varies with wavelength, so the values in the list are nominal only: the visible d-line for the glasses and fluorides, and the mid-infrared for ZnSe, silicon and germanium. Use the figure from your own datasheet at your own wavelength. Incident medium is 1.000 for air, and around 1.33 for water.

Reflection at one surface
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% of incident power
Through one surface
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Through a window
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Window loss
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Calculation method and assumptions +

Light meeting a change in refractive index reflects part of its power, whether or not the material absorbs. At normal incidence the reflected fraction depends only on the two indices.

R = ( (n₁ − n₂) / (n₁ + n₂) )²
Twindow = (1 − R) / (1 + R)

R is the fraction reflected at one surface and the same value applies going in and coming out, since the expression is symmetric in the two indices.

A window has two surfaces

The single-surface figure is the one usually quoted, and it is not the loss through a window. Light reflects on the way in and again on the way out. Taking those as independent gives (1 − R)², which is slightly pessimistic because some of the light reflected at the second surface bounces back and eventually leaves the front. Summing that series gives (1 − R)/(1 + R), which is the figure reported here. For glass the two differ by less than a fifth of a percent; for germanium, where R is 36 %, they differ by six percentage points.

MaterialR per surfaceThrough a window
Fused silica3.5 %93.3 %
N-BK74.2 %91.9 %
Sapphire7.7 %85.7 %
ZnSe17.0 %70.9 %
Silicon30.0 %53.9 %
Germanium36.0 %47.0 %

Why this matters for a measurement

Reflection is not the only loss but it is the one that is always there and is entirely predictable. An anti-reflection coating on both faces takes a germanium window from 47 % transmission to well above 95 % across its design band, which is why uncoated high-index windows are rare in an optical path. The reflected light also has to go somewhere: a flat window at exactly normal incidence sends it straight back toward the source, which can destabilise a laser, so windows are often mounted at a slight wedge or tilt.

What this does not cover

The calculation is for normal incidence and unpolarised light. At an angle the reflection differs between the two polarisation states, which is the effect the Brewster angle calculator deals with. Absorption inside the material is not included, and for infrared materials over their working band it can matter as much as the surface reflection. Scattering from surface roughness and any coating are also outside this figure.

Application notes

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