# B Are the Sun's rays reaching us always parallel?

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1. Dec 3, 2017

### navneet9431

My book says that the Sun's rays reaching us are always parallel.

See this image

Are the Sun's rays reaching us always **PARALLEL rays**?

I will be thankful for help!

2. Dec 3, 2017

### phinds

They are not mathematically parallel but for PRACTICAL purposes, yes they are.

3. Dec 3, 2017

### navneet9431

But,what is the reason that they are parallel ?
Can you explain with a rough diagram ?

I will be thankful for help!

4. Dec 4, 2017

### glappkaeft

It's just a consequence of the fact that the suns rays comes from the sun and while the sun is very big it is also very far away so the rays comes from approximately the same spot (within 0.5 degrees) in the sky. You could say that it is because the sun is farther away than it is big.

The best diagram of the relative sizes and distances in the solar system I have http://joshworth.com/dev/pixelspace/pixelspace_solarsystem.html

Last edited: Dec 4, 2017
5. Dec 4, 2017

### Asymptotic

You may find this blog post (and illustration) by Keith Harrison informative.

6. Dec 4, 2017

### Drakkith

Staff Emeritus
The reason that the Sun's rays are nearly parallel to each other has nothing to do with its size. It is solely the result of how far away the Sun is. Unfortunately I don't have a good diagram available and don't have the time to make one at the moment. I'll try to get back to this tomorrow or something.

7. Dec 4, 2017

Thanks.

8. Dec 4, 2017

9. Dec 4, 2017

### lekh2003

Practically, yes, but not exactly. Let me give you an analogy which might help.

Imagine a tennis ball machine shooting tennis balls at all angles from the horizontal. These balls can go on forever unless they are caught. If you are standing directly in front of the tennis ball machine, you might be able to catch the tennis balls shooting upwards, directly at you, or at your feet. Simply put, you are catching balls at every angle. No ball's path is parallel.

Now imagine that you are standing 10 kilometers away. The tennis ball machine is still throwing tennis balls towards the floor and even upwards, but these balls probably won't reach you. They are at too extreme angles. Even if they could go on forever and forever, they would never reach you since they aren't facing towards you.

The only balls which you could catch would be the balls coming directly at you. All the balls coming to you are coming at the same angles. Their paths are parallel. For all practical purposes, the balls are parallel. Of course, sometimes the balls could hit your feet and sometimes your head, but this isn't a big enough difference to call the balls "not parallel".

The textbook isn't literally saying that the rays are parallel, it is practically saying that the rays are parallel. I hope that explained it.

10. Dec 4, 2017

### FactChecker

"parallel" means that they are going in exactly the same direction. Any rays which go in straight lines from the Sun to the Earth (93 million miles), must be going in practically the same direction. Rays from the Sun going in any other direction will miss the Earth.

Last edited: Dec 4, 2017
11. Dec 4, 2017

### sophiecentaur

The Geometry (Basic School stuff) is what counts here - along with a sense of what's practical. The value of the angle between two radial lines is given by the ratio of the separation where they arrive and their length. Comparing the width of even the widest practical conventional telescope with the distance from the Sun gives a ratio that's as near as dammit to Zero so rays from a particular point on the Sun can be regarded as pretty near parallel. Looking at it the other way round; the Sun's image subtends an angle of about 0.5Â° on Earth, which means that rays from the Sun are up to about half a degree out of parallel. That's near enough parallel for many practical purposes. When you need more accuracy from a measurement (for instance in Astral Navigation) of the Sun's position in the sky then you have to take this half degree into account. In a Solar Oven, the half degree doesn't matter but when you are taking a photo of the Sun (be careful if you ever try this), that half degree is enough to show the Sun as a small disc and not a single point.
This is just one of many useful approximations that we make in our everyday lives- along with the time shown on our watches, the value of g, the temperature of freezing water etc. etc..

12. Dec 4, 2017

Staff Emeritus
The mentors have changed the title from parallel in all caps, but I still want to know what meaning was intended by putting them in all capitals to begin with? Is it to say they are perfectly parallel? Something else? There is some fishing around for what the OP is asking in general.

13. Dec 4, 2017

### Staff: Mentor

If the light rays in sunlight reaching a small area on the earth were all exactly parallel, shadows would have sharp edges. Instead, they're a bit fuzzy. In a solar or lunar eclipse, the sun's shadow doesn't have a sharp edge, but instead has an umbra and a penumbra.

http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit2/eclipses.html

This is because the rays from the sun are not all exactly parallel. Nevertheless, for some practical purposes you can consider the rays to be approximately parallel.

14. Dec 4, 2017

### phinds

Strictly speaking, that is absolutely not true. As glappkaeft correctly pointed out, it is due to the relationship between size and distance, with the size being trivial relative to the distance. If the size were substantial relative to the distance, they would not appear parallel. Think about it, @Drakkith. What would be situation be if the sun were the same distance from the Earth (93 million miles), but 50 million miles in diameter? Would the size then be irrelevant?

15. Dec 4, 2017

### Andy Resnick

No, because the sun is an extended object, subtending 32 arcminutes. The fallacy that sunlight is collimated leads to the erroneous claim of Archimedes 'death ray' being practical.

16. Dec 4, 2017

### sophiecentaur

It looks as if it was actually possible. If it had really been achieved in the Archimedes incident, even in a half hearted way, it would definitely have impressed the enemy and the story would instantly have been exaggerated. ("Let's get the hell outa here!!")They weren't Scientists so they could have believed, from a small area of smouldering timbers, that the whole fleet could have been burned. Warfare at sea, in those days, was a pretty close-up affair and ships moved fairly slowly. The MIT demonstration would possibly have be representative of the scale of the actual event. As a weapon, it would have been a bit specialised and would have needed reliably clear blue Mediterranean skies. So it would not have been suitable for most European engagements. Also, the relative positions of target and mirror would need to have been just right. Strange it was never repeated, apparently - giving justification to the skepticism about it.

Last edited: Dec 4, 2017
17. Dec 4, 2017

### Drakkith

Staff Emeritus
Hold on, I think there's some confusion about what "parallel" or "collimated" rays mean in this context. A collimated bundle of rays are parallel to each other, as I'm sure most people understand. However, when we speak of collimated rays, we usually mean a collimated bundle of rays, and this bundle is, as far as I know, always emitted from the same point on the object. I've never read anything talking about a bundle of collimated rays where the rays are emitted from different points on the object except perhaps starlight. However the OP's book is talking about the light from the Sun, not starlight.

For the purposes of this post I use the following definition of a ray bundle: "the portion of a fan of rays, each of which are emitted from the same point on an object, that are captured by an optical system."

The fact that the Sun is an extended object means that while the ray bundles from each point are all approximately collimated (due to the Sun's distance), they are not parallel to each other. The difference in their angles varies by up to about 0.5 degrees for ray bundles emitted from opposite edges of the Sun. The underlined section of the OP's book is correct in that it means that the rays in each bundle of light emitted from the Sun are essentially parallel to each other. Because of this, the image of the Sun will be formed at the mirror's focal point, again, as the book says (focal plane actually, but I'll use focal point to keep things simple). The angular size of the Sun does not affect this. You could quadruple the angular size of the Sun and the image would still be formed at the focal point of the mirror.

However, if the rays in each bundle diverged at up to 0.5 degrees, the image would be shifted away from the mirror and would no longer be formed at the focal point. As the angle is increased, the image is formed further and further away from the mirror, which corresponds to bringing the object closer. Note that bringing an object closer to the mirror also increases its angular size, which highlights the difference in keeping an object at the same distance and increasing its size versus bringing it closer. Both result in an increased angular size, but the former does not affect the position of the image.

@navneet9431, basically, the reason the image of the Sun is formed at the focal point is because of how far away the Sun is. If you were to move closer to the Sun the image would begin to be shifted away from the mirror and the focal point. I hope the following (poor) illustrations help:

The first three pictures show how rays are (or aren't) emitted from the Sun. The picture in your book with all the rays parallel to each other is a simplification. The real situation is more like the 3rd picture, with a fan of rays being emitted from each point and spreading out into space. The 4th picture shows how ray from a single bundle behave when an object is very far away versus when it is nearby. Notice how in the bottom illustration the image is formed further back, past the focal point of the mirror. By the time that ray bundles from the Sun arrive at the Earth, they are a close approximation of the top illustration and the image of the Sun is formed almost exactly at the focal point of the mirror.

Note that in the final image the ray bundles aren't drawn as being collimated, but they should be. I only drew it to show that light emitted from two different points on the Sun are brought to a focus at different locations on the image plane. If we make the object larger without bringing it closer, the size of the image increases, but the location of the image plane does not change. If we instead bring the object closer, the size of the image again increases, but now the rays in each bundle start to become noticeably divergent, like the bottom illustration in picture 4, and the image moves away from the focal point. Also, ignore the unlabeled focal point dot in that final image. It should be drawn at the image plane, but I made a mistake.

18. Dec 4, 2017

### sophiecentaur

There is no way that an image of the Sun in any normal optics can be regarded as a "point". The focussed image is in the Image Plane and not at a point.
All those diagrams are 'correct', just not all of them are relevant to the question. You can select any rays you choose, depending what you want to know.

I really thing we are over cooking this, in the light of the OP's quoting an elementary book for the question.

19. Dec 4, 2017

### Drakkith

Staff Emeritus
I know. I already addressed this in my post:

20. Dec 4, 2017

### Drakkith

Staff Emeritus
Yes, but most of the ray choices do not help anyone understand why the rays are parallel, which rays are parallel, or why the image is formed at the focal plane of the mirror, all of which is relevant to what the book is trying to explain.