There is a lot of confusion about what downward refraction will do to the apparent position of an object.  Many people think that the word “downward” suggests it will make the object appear lower.  We examine the actual effect in this article.

Light bends when it passes from one medium to another if the mediums have a different Index of Refraction(IoR).  This is quantified in Snell’s Law.  Understanding Snell’s Law allows the manufacture of many things such as eyeglasses, camera lenses, prisms, and magnifying glasses.  Earth’s atmosphere also has a varying IoR due to a number of physical properties such as:

• Pressure
• Temperature
• Humidity
• The wavelength of the light
• Carbon Dioxide content
• Several other factors to a lesser degree

Calculating the Index of Refraction based on environmental conditions must take all variables into account.  This is very difficult to get exact, however, there are several very good formulas to calculate an extremely close Index of Refraction.

• Cauchy Equations
  • This is an older equation that works well only for select materials
• Sellmeier formula
  • Better, broader application
• Ciddor Equation and Edlén Equation
  • These two are very good for the conditions regularly experienced in the atmosphere

The IoR is almost exactly 1.0 extreme elevations and increases as elevation decreases.  At standard conditions for temperature and pressure, the IoR is 1.000 29.  The IoR at ground level is close to the value.  Since the IoR increased from extreme elevations to the ground there is a gradual change in the IoR.  This is sometimes called “pressure gradient” but since there are more factors than just pressure a better term is “Index of Refraction gradient”.  Regardless, there is a gradient and it causes light to bend.

The difference between 1.000000 and 1.00029 is small, but when light travels through many miles of this graduated medium the effect can be significant enough that it makes measurable differences in observations.

The distance and angle the light travels through the atmosphere is an important factor.  Light traveling from straight above the observer will experience effectively zero refraction from the IoR gradient.  This is because the angle of incidence of the light as it passes between different gradient regions is almost exactly 90°.  By Snells Law, if the angle of incidence is 90° there is no refraction.  Additionally, the distance from where the atmosphere has substantial pressure to the viewer is smallest from directly above.

Similarly, light originating between 30 degrees and 90 (straight up) degrees will experience very little change due to refraction.  As the light travels through the more of atmosphere this effect increases, light originating from very close to the horizon experiences the largest effects due to refraction.  When making observations of objects very near horizon the margin of error must be carefully considered.  However, the amount of this effect will vary from day to day and location to location as atmospheric conditions are different every day and for different locations.

Light always bends toward the higher IoR, this is quantified in Snell’s Law.  The IoR is higher closer to the ground so light is bent toward the ground, or downward.

The IoR gradient is not generally a smooth continuum all the way to the ground.  There are different levels where the IoR may decrease for a section instead of increasing.  Close to the ground, the IoR can be very volatile.  This volatility can cause large effects when viewing objects that have traveled a long distance through this volatile layer.  When viewing objects that are well above this layer the effects are significantly diminished.

The total change in IoR from extreme elevation to the ground is always a net increase.  Therefore the overall refraction is always downward.  This article will only examine the simple case of constant downward refraction.  Scale is not being considered and no math is being applied, this may be done in a future article.

To start we examine what would be seen if there were no refraction.  This is never the case since the earth has an atmosphere.  However, it is a useful starting point.  We consider the light at the topmost corner of the building as it travels to our observer.  Since there is no refraction, the light travels straight and the observer sees the object in the correct location.

Next, we add in the downward refraction.  The same light that would have been seen by the observer starts out in the same direction but gets bent down and misses the observer.  It reaches the ground in front of the observer.

The light that does reach the observer starts at a higher angle and gets bent downward.  The observer still sees the object because light still makes it to the observer.  It’s just different light.

However, the angle that the light enters the observer’s eyes or camera lens arrives at a different angle.  This is critically important as it changes the perceived location of the object.  In our downward refraction case here, the angle is slightly elevated than if the light were not refracted.  The result is that the object appears to be more elevated than it really is.

Conclusion: General downward refraction over a long distance makes objects appear elevated.  This is most important when viewing things that are just a few degrees above the horizon.