Atmospheric Extinction

In the diagram above, h is the thickness of the atmosphere directly overhead, d is the thickness of the atmosphere you are looking through when you are looking at an object that is at an angle theta above your horizon, and Re is the radius of the earth. Apply the Pythagorean Theorem to the right triangle in the above diagram.

But, the second term on the left is very small compared to the other two terms.

Therefore,

Or,

If you are looking at an object that is 30 degrees above your horizon, you are looking through twice as much atmosphere compared to looking directly overhead.