As light enters the atmosphere from distant space on its journey to the eye of an observer, or the aperture of a telescope, it will be refracted by an amount that depends on the length of the path through the atmosphere. When viewing objects directly over head, this effect is almost imperceptible. But when viewing the Moon, planets or stars towards the horizon, atmospheric refraction can be dramatic. As anyone watching a crescent Moon set in the west will tell you, the distortions wrought by refraction can noticeably distort the shape of the Moon, and alter its setting time by prolonging the time when its limb is occulted by the horizon. This also happens for the Sun, and you have to allow several extra minutes to the time when the limb sets below the geometric horizon, before the optical image of the limb follows!
The table below gives you an idea of how severe the refraction effect is for a standard Earth atmosphere at sea level.
Degrees above the horizon..................refraction angle ................................................................. 15 4 arcminutes 10 6 arcminutes 5 10 arcminutes 1 1 degree .................................................................The refraction angles were computed using an approximation formula:
angle ( arcseconds) = 58 x Tan(Z) - 0.067 x Tan^3(Z)
Where Z is the angle between the Zenith and the horizon ( 15 degrees above the horizon means that Z = 75 degrees) For viewing angles within 10 degrees of the horizon, the formula gives only a rough indication of how large the effect is, but I think the above table gives a sense that the closer your object is to the horizon, the larger this distortion is.