Radio Waves / Light: Atmospheric Refraction

Question

The following image differentiates between a visual horizon and a radar horizon.

Sidenote: I'm not too familiar with primary surveillance radar technology, but this image refers to secondary surveillance radar, where the aircraft emits a radio signal at 1090MHz. So this refers to a simple one way radio transmission from the plane to the antenna.

The source claims the radio horizon is extended due to atmospheric duction, which causes electromagnetic radio waves to be refracted towards the ground. Snell's law suggests the refraction can be described using only the velocity:

$\frac{\sin \theta_{1}}{\sin \theta_{2}} = \frac{v_1}{v_2}$

To my understanding electromagnetic radiation and light are the same thing? Radio signals simply have a different frequency than visual light, but both have the same velocity. So shouldn't the visual light be refracted exactly like the radio waves are? Shouldn't the visual horizon be equal to the radio horizon?

Answer 1

The main difference between ducting at visible wavelengths and radio wavelengths is due to water vapour's effect on the refractive index of air.

In the visible part of the electromagnetic spectrum the refractive index of air depends on the variation of the density (temperature) of the air with height and not very much on the amount of water vapour in the air.
In the radio part of the electromagnetic spectrum as well as the refractive index of the air depending on the density of air it also depends a great deal on the percentage of water vapour in the air.
The variation of the fraction of water vapour in the air with height is also much greater than the variation of density of the air so there is a greater change in the refractive index with height in the radio part of the spectrum.

In practice the vertical change in the refractive index of the air in the radio part of the spectrum is about twice as much as that in the visible part of the spectrum.

So both visible and radio waves are refracted by the vertical changes in refractive index but the radio waves are bent/refracted significantly more due to them being affected by the water vapour in the air.

Answer 2

The refractive index of air is frequency dependent, so just as different colours of light are deflected by different amounts in a prism, radio waves and light waves can be deflected by different amounts by the air.