# Why do sunbeams diverge even though the sun is much more than a few kilometers away?

Consider this picture of sun beams streaming onto the valley through the clouds.

Given that the valley is only (at a guess) 3km wide, with simple trigonometry and the angles of the beams, this gives the result that the position of the light source is being a few tens of km away at most.

What is wrong with the analysis?

• Apparently, these are perspective effects. See atoptics.co.uk/atoptics/ray1.htm (and sublinks). Commented Dec 25, 2014 at 11:47
• Solution route estimation: Parallax method, Spacetime warps, curves (?), Reflection, Scattering, etc. Commented Dec 25, 2014 at 11:51
• The rays are parallel, but because they are at an angle they get nearer to the camera as they approach the ground, so they look bigger as they approach the ground. The divergence can be used to calculate the angle of the sunlight relative to the ground, but not to calculate the distance of the Sun. Commented Dec 25, 2014 at 12:20
• Convergence of the rays will only tell you where the Sun is located on the two-dimensional photograph. To tell where the rays would converge in three-dimensional space, you would need all of the 3D information that is typically concealed by a 2D representation. Commented Dec 25, 2014 at 17:07
• Since the question is "What is wrong with the analysis?" and not "how is the effect called", I would answer in a sientific way: "since you have only a 2 dimensional projection of a 3 dimentionanl event/situation, you lost information, and cant (at least not easy) make this analysis." In Fact, the sun would be on the triangulated position on the Photo even w/o the clouds and beams. oops, thats RBarrys commment, it poped up to late, sory Commented Dec 25, 2014 at 23:48

The train's destination is not above the ground, but rather far away, and perspective means that the tracks appear not to be parallel but instead to converge to the vanishing point.

The same applies to the beams of light above them. The Sun is very far away and the beams are pretty much parallel, but they're pointing towards you, and perspective makes them appear to converge towards the vanishing point - which in this case is the Sun's location in the sky.

The technical term for these beams is "crepuscular rays." Occasionally, when the Sun is very low on the horizon, you can see "anticrepuscular rays," where the beams seem to converge to a different point on the opposite side of the sky to the Sun. Here's an example: (source)

This happens for the same reason - the rays are really parallel, and there's another vanishing point in the opposite direction from the Sun.

• Wow, great way to put things into perspective. Commented Dec 26, 2014 at 7:14
• That's a beautiful picture and a great way to illustrate the solution. It certainly derailed the mistaken analysis, and set us back on the right track. Commented Dec 26, 2014 at 7:29
• Can we have a photo of anticrepuscular rays? Commented Dec 26, 2014 at 7:39
• @JanDvorak done! Commented Dec 26, 2014 at 7:58
• OK! I'm going to accept this as the answer, since it does seem to be the answer! If any of you are involved in education this might be an interesting question to ask your students. It certainly illustrates the fallacy of applying logic and mathematics to incomplete information and drawing wildly wrong conclusions.
– user56903
Commented Dec 26, 2014 at 10:11

In addition to the excellent answers already given, here is another famous picture of an anticrepuscular ray (or better: shadow). It is not a coincidence that the shadow of the plume extends almost exactly towards the full moon. It is a consequence of the Sun, Earth and full Moon being almost aligned. So all shadows must point towards the moon at such a moment.

Just imagine what a picture would look like with a second shuttle starting a bit more towards the right... a "V" shape with the Moon at the corner...

Image credit: NASA, Pat McCracken.

This also was once the Astronomy Picture of the Day, where you can find some extra explanation.

• A good try, but everyone knows it was the moon aliens that just shot down the rocket with the blue laser!
– user56903
Commented Dec 27, 2014 at 13:14