2019 March 2
What is refraction?
Light entering or leaving a new medium perpendicular to its surface passes straight though without any deviation (Figure 1 – ray A).
At other angles the ray will be refracted and the greater the angle of incidence the greater the amount of refraction (Figure 1 – rays B & C). Notice how the light is bent towards the normal (green lines) on entering the glass and away from it on leaving. This is due to the glass having a higher refractive index than the surroundings and the resultant change in the light’s speed.
The refractive index and hence amount of refraction is slightly different for different wavelengths (colours) of light and consequently white light can be dispersed into its constituent colours to form a spectrum.
Refraction of light in the atmosphere
The schematic in figure 2 shows rays of light from stars at different altitudes above the horizon passing through the atmosphere. The structure of the atmosphere has been very much simplified and the amount of refraction greatly exaggerated. Notice in particular the following:
- The light from star A, directly overhead, is not refracted and its light reaches the observer without any deviation to its path.
- The lower the altitude of a star the greater the length of air it has to pass through.
- The lower the altitude of a star the more obliquely its light strikes the atmosphere.
These last two points combine to cause the amount of refraction to increase rapidly as an object approaches the horizon. As a result star B appears at position B’ and star C is lifted to C’.
How much is light refracted?
a = the true altitude of the object.
a = the object’s true altitude in degrees.
P = atmospheric pressure in kPa.
T = temperature in Celsius.
|90o||0’ 0”||15o||3’ 41”|
|80o||0’ 11”||10o||5’ 25”|
|70o||0’ 22”||5o||9’ 40”|
|60o||0’ 35”||2o||16’ 56”|
|50o||0’ 51”||1o||21’ 45”|
|40o||1’ 12”||0o 30’||25’ 0”|
|30o||1’ 45”||0o||28’ 59”|
|20o||2’ 45”||-0o 30’||33’ 41”|
On the horizon
Let’s consider the setting Sun. As it approaches the horizon the amount of refraction is around 0.5o, which is roughly the Sun’s apparent diameter. When the Sun appears to be sitting on the horizon, just rising or setting, it is really below the geometric horizon and is only lifted into visibility by atmospheric refraction. Figure 3 shows this situation. If we could miraculously make the Earth’s atmosphere vanish at the apparent moment of sunset or sunrise then the Sun would actually disappear from view as it is really already below the horizon. Obviously this uplift applies to any astronomical object such as stars, planets and the Moon, not just the Sun.
The effect of all this is to lengthen the time an object is above the horizon. In particular, the day becomes longer with the Sun appearing to rise earlier and set later than it would in the absence of an atmosphere.
Consider the last two entries in the refraction table above. These show the position when Sun seems on to be on the horizon, but is actually below it. Because the altitudes differ by 0.5o which is about the Sun’s apparent diameter, the lower limb of the Sun is lifted by roughly 34’ and the upper by ‘only’ 29’. With the refraction at the Sun’s lower limb being greater than that at the upper, the lower limb is uplifted by about 16% more than the upper and the normally round solar disk is flattened into an oval shape. This is very much the ideal situation; in reality discrete layers in the atmosphere can have different effects often causing a jagged edge to the solar limb. Also local conditions can cause the amount of refraction to vary significantly at such low altitudes. The same effect can be seen with the Moon.
Tracking across the sky
Consider the case of a star moving across the sky. This is usually shown as a smooth curve with the star rising in the eastern part of the sky, reaching its highest point on the meridian and then sinking towards the western horizon. This is a reasonable approximation to reality and is perfectly correct in the absence of the atmosphere. Taking refraction into account we find that any star, except at the zenith, is higher than it would be and the difference varies with its altitude. Consequently its path across the sky is more complex.
Does this matter? The answer is yes if you have a telescope drive that is attempting to track the stars. The continually changing amount of refraction means that the telescope will not keep a star perfectly centred in the field of view. For purely visual observing this is something that is easy to cope with but for photography it does present a challenge. With an equatorial mount that needs to be aligned on the celestial pole the best thing to do is to align on the refracted pole not the geometric one. Most methods that use star alignment will do this automatically but if you are using a mechanical method such as an inclinometer you could make an adjustment for refraction particularly at low latitudes.
At the beginning of this tutorial we noted that the amount light is refracted varies slightly with its wavelength (colour). This can cause a star’s image to be spread out into a very small spectrum with red at the top and blue at the bottom. This effect, only really visible in a telescope, increases as an object’s altitude decreases. Figure 5 shows the effect on Polaris at an altitude of 52o. The image here is greatly enlarged and because it is taken through an inverting telescope the colours are reversed from those above with red at the bottom and blue at the top.
The situation with planets is more difficult particularly at the long focal lengths and large image scales used in imaging. Here the single image is comprised of multiple images of different colours all slightly out of alignment with one another blurring the detail. For a more detailed discussion of atmospheric dispersion and ways of counteracting it Martin Lewis has written an in depth article available here and there is also one by Damian Peach here.
Even though atmospheric refraction can often go unnoticed the effects it causes can be quite significant. From affecting the way a telescope tracks to smearing planetary images and even extending daylight, its effects can be surprising.