Go and have a look at Mark Holland's
pretty picture of the Sun, then come back here.
Now, the Sun is about one hundred and fifty million kilometres away and the earth is only about twelve thousand kilometres in diameter. Therefore, the Sun's rays that shine upon the earth should be very nearly parallel. However, in Mark's picture, the Sun's rays are nowhere near parallel.
Why?
UPDATE (29/01/06): The puzzle's been solved. Here's the winning comment, courtesy of
Mike:
I would tend to say that it is due to nothing more than perspective.
Just like looking at a chess board from table height, the lines seem to go towards a vanishing point, so should the rays seem to "narrow" towards the sun.
UPDATE (12/02/06):
Patrick wonders
Hmm. OK, so it's perspective but that just gives us another puzzle. When I look down a set of railway lines (for instance) I don't have to be told that the lines are parallel. But here (kinda sorta) I did. Now, why is that? Would it have been any different had I been standing where Mark Holland had been standing?
This is a harder question, since it isn't really about optics, but is about psychology and how the brain processes information - a subject that I know almost nothing about. I can, however, make a few points that might be worth bearing in mind:
1. Stereoscopic vision.
Try this experiment. On a clear night, look at the sky and pick two stars at random. Which one is closer? You won't have a clue. If the stars were all painted on a dome one light-year away, rather than ranging from a few light-years to thousands of light-years away, you wouldn't be able to tell the difference.
This illustrates my first point. Your stereoscopic vision is a useful tool for judging distances, but it only works for objects that are fairly close by.
With a railway line, you can easily tell that the tracks that pass under your feet are only a meter or two away, but the tracks that vanish into the distance are hundreds of meters away. Your brain is therefore provided with the information to deduce that the tracks are parallel.
In Mark's picture, however, the parts of the Sun's rays closest to you will be, perhaps, ten or twenty miles away, whilst the parts farthest from you might be hundred of miles away. At those distances, your stereoscopic vision doesn't provide any clues that your brain can use to deduce that the Sun's rays are parallel.
2. Other visual clues.
When you look down a railway line, you might see other objects - buildings, people, trees, animals - that you already know look big when they are nearby, but are small when they are far away. In Mark's picture, there are no comparable reference points.
3. Are you really sure that you didn't need to be told that railway lines are parallel?
Perhaps you did, when you were a child, and have incorporated that memory into your knowledge, but have forgotten that you had to be told. For instance, I can remember being taught about perspective when I was eight, and the teacher used the example of railway lines disappearing into the distance, but she didn't mention that the same logic applied to the Sun's rays. I can well imagine that my knowledge that railway lines are parallel are due largely to that lesson, or to other people repeating the point, but not making the same point about the Sun's rays.
