Atmospheric Extinction: Calculating Visible & Radio Wave Opacity

[Gotaskor]

I'm wondering if anyone can help me with something.

I've been asked to calculate, assuming no curvature for the Earth, how far through the atmosphere one could see when stood at sea-level - as in, at what distance would the atmosphere become opaque, both to visible light and to radio waves.

I know that the major factors to look at will be Rayleigh scattering and the attenuation coefficient of the atmosphere.

 

[eljose79]

Any insights or calculations would be greatly appreciated.Hello there,

I would be happy to help you with your question. The distance at which the atmosphere becomes opaque to visible light and radio waves is known as the atmospheric depth. This depth can vary depending on factors such as altitude, weather conditions, and the specific wavelengths of light or radio waves being considered.

To calculate the atmospheric depth at sea level, we can use the Beer-Lambert Law, which relates the intensity of light passing through a material to its thickness and the material's attenuation coefficient. In this case, the material is the atmosphere and the thickness is the distance from sea level to the point where the atmosphere becomes opaque.

The attenuation coefficient of the atmosphere is dependent on the type of radiation being considered. For visible light, we can use the Rayleigh scattering formula, which takes into account the scattering of light by particles in the atmosphere. For radio waves, we can use the absorption coefficient, which represents the amount of energy absorbed by the atmosphere as the waves pass through it.

Assuming an average attenuation coefficient for visible light of 0.2 km^-1 and for radio waves of 0.005 km^-1, we can calculate the atmospheric depth at sea level using the following formula:

Atmospheric depth = (1/attenuation coefficient) x ln(1/transmittance)

For visible light, the transmittance is typically around 0.01%, meaning that only 0.01% of light is able to pass through the atmosphere. Plugging in the values, we get an atmospheric depth of approximately 500 km for visible light.

For radio waves, the transmittance is typically much higher, around 99.9%. Plugging in the values, we get an atmospheric depth of approximately 20 km for radio waves.

It's important to note that these calculations are based on the assumption of no curvature for the Earth. In reality, the curvature of the Earth does play a role in the attenuation of light and radio waves, so these values may vary slightly in real-world conditions.

I hope this helps with your calculations. Let me know if you have any further questions.