Find the true location of the sun in relation to your reference of the horizon if the sun is observed to make an angle of theta with the horizon. This is not an easy question. Use Snell’s law to take into account the aberration and bending of light rays as they pass through the earth’s atmosphere and make assumptions on the index of refraction as the atmosphere packs up. Any ideas on how to do this?

The derivation is rather complicated. You will find it at
http://mintaka.sdsu.edu/GF/explain/atmos_refr/integrate.html

What you are looking for it the and "r" in that reference. They derive a formula for it.

To find the true location of the sun in relation to your reference of the horizon, considering the bending of light due to atmospheric refraction, you can use Snell's law and the information provided in the reference you mentioned.

The reference you provided contains a derivation and the formula you need to find the "r" value, which represents the true altitude of the sun. I recommend visiting the link (http://mintaka.sdsu.edu/GF/explain/atmos_refr/integrate.html) to understand the derivation and to obtain the formula.

To summarize the steps involved:

1. Visit the provided link and study the derivation and formula presented there.
2. Follow the steps outlined in the derivation to calculate "r," which represents the true altitude of the sun.
3. Take into account the observation angle (theta) with respect to the horizon in your calculations.
4. Make necessary assumptions about the index of refraction as the atmosphere changes.
5. Apply Snell's law to account for the bending of light as it passes through the Earth's atmosphere.
6. Use the derived formula to calculate the true location of the sun in relation to your reference of the horizon.

Please note that this derivation entails complex calculations, and it is recommended to have a strong background in physics or mathematics to work through it effectively.