Horizon related question I'm a student taking an undergrad course in physics and we were discussing light and how it works in relation to vision. This question stumped us. What altitude would you need to reach on the globe before the horizon vanished from your view provided you maintained a line of vision parallel to the surface of the earth.
 A: If I understand the question correctly, to be fully defined you would need to specify the field of view. The horizon would disappear from a viewpoint "parallel to the surface of the earth" right at the earth unless you have a nonzero angle for your field of view. If your field of view is 180 degrees, you could technically "see" the horizon not matter how high you get, although in reality it would become small and faint.
If you draw a diagram, you should find that the horizon appears at the angle below horizontal given by:
$$
\cos(\theta) = \frac{R}{R+h}
$$
for radius of the earth $R$ and height above the ground $h$. Thus, if your field of view is angle $2\theta$
$$
h = \frac{R(1-\cos(\theta))}{\cos(\theta)}
$$
from which you see that when $h = 0$, $\theta = 0$, and as $h$ goes to infinity, $\theta$ goes to a right angle. The limitations on the field of view are thus needed to answer this question exactly.
Note that this is an ideal analysis that assumes no topography and no atmospheric refraction. As you may know if you have ever treated yourself to flat earth material (I actually enjoy solving their "proofs" from time to time), it is actually difficult to see the horizon since the curvature of light due to atmospheric refraction is often of a similar magnitude, and even greater than, the curvature of the earth.
