Can reflection in the blocking band be accurately approximated using the formula R ≈ 1 - T?

Here is a breakdown of why this happens and how to know which formula to apply.

The Underlying Physics

Whenever light strikes an optical component, the total energy must be conserved. This is defined by the following fundamental equation:

1 = R + T + A + S

Where:

• R = Reflection
• T = Transmission
• A = Absorption
• S = Scattering

By rearranging this equation, we get the true formula for reflection:

R = 1 - T - A - S

When R ≈ 1 - T is Accurate (Dielectric Filters)

If you are working with high-quality dielectric bandpass filters (interference filters), the materials are specifically designed to have near-zero absorption (A) and near-zero scattering (S).

Because A and S are practically negligible, the equation simplifies neatly to R ≈ 1 - T.

These types of filters create their blocking band by acting as highly specialized mirrors for the unwanted wavelengths. In the blocking region, Transmission (T) is essentially zero (often rated at OD4, OD6, or higher), which means that almost 100% of the light in that band is being reflected (R ≈ 1).

When R ≈ 1 - T Fails (Absorptive Filters)

If the component uses absorptive materials (like colored glass) to block unwanted light, it achieves its blocking band by soaking up the light energy and converting it into heat.

In this scenario, Absorption (A) is the dominant factor. While Transmission (T) will still be near zero in the blocking band, the light isn't bouncing back. The Reflection (R) will simply be the natural Fresnel surface reflection of the glass—typically around 4% to 8% if uncoated.

If you used the R ≈ 1 - T formula on an absorptive filter, you would incorrectly calculate that the filter reflects nearly 100% of the blocked light, when in reality it is only reflecting a tiny fraction and absorbing the rest.