# Reflection in spherical mirrors

1. Nov 10, 2012

### rishch

Hey everyone, I'm reading a chapter on reflection of Light and I had some doubts:-

1 Is a real, erect image possible? What about a virtual, inverted image?

2 How can you see a real image without a screen? Can you see it in the air or something?

3 When you move away from a plane mirror the image becomes smaller. However your size remains the same. How then, is the image size equal to the object size?

4 In my textbook it's given that "For spherical mirrors of small apertures R=2f” Why only for spherical of small apertures, why not large apertures too?

5 If a real image is formed between C and F and you capture it on a screen or a tablecloth etc., from which side do you see the image? Do you have to see from the concave mirror side or from the object side? Although to see from the object side I think the screen would have to be translucent or something.

6 When you look in a spoon (concave side) you see an inverted image of yourself. How? Shouldn't a real image be formed? Isn't the image in the spoon virtual? Or can you see a real image in the spoon? I thought that you had to capture real images on a screen?

7 In concave mirror, for object at focal point for all light rays radiating from a point on the object, the reflected rays are parallel to each other. But if you were to take the top point of the arrow-object then draw a ray going straight up you could say it comes from the focal point and would be reflected parallel to the principal axis, not the other reflected rays. What's wrong with that?

8 Why are light rays from an object at infinity all parallel? Couldn't you have a light ray from the sun passing through the focal point that wasn't coincident to the principal axis? Even by a teensy bit?

9 Just because two rays coming from a point on an object, after reflection from a concave mirror, converge at a point or appear to diverge from a point behind the mirror (if the object is between P and F), how do you know that all other reflected rays from that point will also converge or appear to diverge from that same point?

10 If a point object was kept on the principal axis then where would the image be formed? Couldn't it be formed at any point along the principal axis? Same for a point on a non-point object that is on the principal axis. The corresponding point of the image to the object at that point could be anywhere on the principal axis, right?

11 My text book says that at F object is at infinity, enlarged and real and inverted but shouldn't there be no image? The reflected rays are parallel so they should never meet right?

12 My textbook says that for an object at infinity, the image would be at the focus and it would be point sized. So if I looked at the sun in a convex mirror, I'd see a point?

2. Nov 11, 2012

### Simon Bridge

You should be getting good at ray diagrams now - see if you can find one.
Yes. You can even reach out and "touch" it! It helps if you have a big, very clean, mirror.
When you move away from any object it appears smaller - it is the same with the image in a mirror: the size you see is due to perspective.
So they can use a handy approximation that makes the math easy.
Either - depending on the opacity of the screen.
That would be correct - like a back projection movie screen. What the screen does is scatter the light arriving at the image position from the lens. The advantage of this is to make the image visible from a wider range of angles. Handy if you only have a small lens.
Concave mirrors do that.
You thought wrong - see above.

Think about it this way:
You never "see" the object itself - you see the light that is scattered from it. Normally the distinction is not important. This is because, normally, the place the light appears to be scattered from is actually where it is scattered from and our visual system has evolved to take advantage of this.

If there is nothing in the way of the light, then the image position happens to be the same as the object position. If there is something to bend the light, then the image position will usually be someplace else. The think you are looking at appears to be at the location that the light-rays diverge from.

If you can reach out and touch that position - then the image is said to be "real". If there is something solid in the way, then the image is "imaginary".

So when you look at the computer keyboard you are seeing a real image.
You don't need a screen do you?

Nothing. Of course, the mirror would have to be pretty big to reflect light travelling perpendicular to the optic axis. Generally we like to use small aperture approximations to keep things simple.
This is an approximation of course. Note: light from the Sun is not parallel - the Sun is BIG.

Light from a point source - like a spot on the Sun - diverges at such a small angle that it makes no difference on the scale of the Lab.
The same way I know anything about geometry.
No. Draw the ray-diagram for a non-point object to find the image. Consider - the base of the arrow-object is a point object on the principle axis. Where is it's image?
If there were no image then there would be no reflected rays.

What they are saying is, in order to see the image, you'd have to stand way waaay back.
If you place your eye between the mirror and the image, you get a bright blur.
No. The Sun is BIG. You'd get a small image of the Sun very close to the focal point ... but that is still bright enough to set fire to things.

Last edited: Nov 11, 2012
3. Nov 11, 2012

### rishch

I'm trying to figure out how to multi-quote but the button just turns blue. Anyways, I want to mention that I've only learnt about reflection, no refraction, so I've no idea how lenses work.

"You should be getting good at ray diagrams now - see if you can find one."

Well using a mirror I can't seem to find any virtual image that is not erect nor any real image that is not inverted.

"Yes. You can even reach out and "touch" it! It helps if you have a big, very clean, mirror."

You can touch it? Wouldn't you be swiping through air? And the image is just there in the air? I've never seen nor heard of anything like that.

"When you move away from any object it appears smaller - it is the same with the image in a mirror: the size you see is due to perspective."

I guess that it's because as you move back the image also moves away from you (image distance from you is twice your distance from the mirror right?) so it APPEARS smaller.

"So they can use a handy approximation that makes the math easy."

So it's just an approximation that is more accurate for mirrors with smaller apertures?

"Either - depending on the opacity of the screen." and "That would be correct - like a back projection movie screen. What the screen does is scatter the light arriving at the image position from the lens. The advantage of this is to make the image visible from a wider range of angles. Handy if you only have a small lens."

I was asking what side do you have to see the image from. If it's opaque you'd have to see it from the mirror side because the light can't pass through right? And I didn't get the part how a screen arriving at the image position from the lens thing. I don't know how lenses work. Plus how does it make it visible from a wide rage of angles? Didn't get this at all, sorry.

"Concave mirrors do that."

Yes that's what I saw in the spoon but I don't get how? I think it was a real image because I wasn't sticking my nose in the spoon so I was beyond the focus, but how could I see the image in the spoon? I get how I can see my image in a plane mirror, as that's a virtual image that appears to be behind the mirror. I thought real images in concave mirrors were formed in front of mirrors. But I saw the image IN the mirror.

"Think about it this way:
You never "see" the object itself - you see the light that is scattered from it. Normally the distinction is not important. This is because, normally, the place the light appears to be scattered from is actually where it is scattered from and our visual system has evolved to take advantage of this.

If there is nothing in the way of the light, then the image position happens to be the same as the object position. If there is something to bend the light, then the image position will usually be someplace else. The think you are looking at appears to be at the location that the light-rays diverge from.

If you can reach out and touch that position - then the image is said to be "real". If there is something solid in the way, then the image is "imaginary".

So when you look at the computer keyboard you are seeing a real image.
You don't need a screen do you?"

In a real image light rays actual diverge from a point whereas in virtual images they appear to diverge thanks to our eyes. But I thought you could get a real image using a concave mirror. But you couldn't reach out and touch that image right?

"The same way I know anything about geometry."

What does that mean? Is there some geometrical proof or theorem?

"If there were no image then there would be no reflected rays.

What they are saying is, in order to see the image, you'd have to stand way waaay back.
If you place your eye between the mirror and the image, you get a bright blur."

But for an image to form light rays have to converge at some point (real) or appear to diverge from some point (virtual). If they're parallel how does standing far back help?

Thanks a lot for taking the time to answer my questions. I really appreciate it. :) Oh and could someone tell me how to multi-quote?

4. Nov 11, 2012

### Simon Bridge

excuse me ... I'm getting ahead of myself.
Lenses work the same way as mirrors except the light rays go right through instead of bouncing off. So the statements work for both lenses and mirrors.
When the mirror is very good, and big, you see yourself hanging upside down in the air in front of you. I've done this. If you reach out towards the image, the image reaches towards you, and you can "touch" fingers (notice the quotes?) The illusion is so good that the tip of your finger where it passes through the image feels warm. It's a phantom sensation due to your brain anticipating touching something.

However, you cannot do this for a virtual image.

Normal perspective effect - right. The image is the same size as the object would be twice as far away.

Yep. It is, however, a very good approximation.

That's OK I corrected it ... light scatters off the object and gets reflected by the mirror. You've seen the ray diagram. To see a real image with your naked eye you have to have the image between you and the mirror. This will only work for a narrow range of angles. A screen helps by scattering light that hits it. A screen like a sheet of tissue paper you can see the image from all angles, but a screen like a sheet of wood, you have to look at an angle from the mirror side.

Actually, most people find that the image looks like it is painted on or just under the surface of the spoon. This is an optical illusion created by the image processing in your head. With small mirrors or lenses it is very difficult to see the image location without a screen.

Nope - in a virtual image, the rays really do diverge ... they just don't originate at the point they appear to be diverging from. Your eyes need diverging light in order to see something. Your brains image processing uses the difference in the angle that different light rays come from to work out where things are. Mirrors and lenses mess this up.

Of course you can. See above.

5. Nov 11, 2012

### Buckleymanor

Are you sure about this, if you place two mirrors together at a 90 degree angle,(put them into a corner) then look at yourself you get an image that is not inverted.

6. Nov 11, 2012

### Staff: Mentor

There's a nifty gadget that consists of two concave mirrors glued together facing each other, with a hole in the upper mirror so you can look inside. On the inner surface of the lower mirror rests a small object. When you look into the hole at an angle, with the object hidden behind the upper mirror, the image floats just above the hole. One can't resist reaching out to try to grab it.

7. Nov 11, 2012

### Staff: Mentor

And if you want to quote multiple sections from one post: use the "quote" button which quotes the entire post in one block, delete the sections that you don't want to include in your quotes, and insert "/quote" and "quote" tags to split the rest into sections.

8. Nov 11, 2012

### Simon Bridge

I'm sure that the OP investigated a single mirror geometrically and found the expected result
Well of course. (See jtbell post above for a good example.)

Also if I hang upside down the real image will no longer be inverted.
I can also look at it through a lens or via a space-time warp.

9. Nov 11, 2012

### rishch

That sound's interesting. But why couldn't you get such an image for a small mirror? It's the same thing just scaled down right?

Yeah that makes perfect sense.

But not very good when the aperture's more than the radius of curvature?

I get how to see the image from the mirror side you need a screen at the image location to reflect the reflected rays at your eyes, but not why you need one when your standing at the object side. Aren't the light rays already scattering? I thought each point on a real image corresponds to a point on the object and gives out light the same way as that point on the object does? Seeing ray diagrams I'm guessing that it does that, but unlike the actual object it doesn't give out light rays in all directions. Plus, isn't tissue paper opaque?

This is the one thing that makes the least sense to me. I get how the image in a plane mirror getting smaller thing is because of our eyes. But not this. To me the image looks like it's behind the spoon, just like a virtual image but it's contorted and upside down. How can I see the real image without a screen. It's not even floating in the air...

Yes I think I worded my sentence a bit wrong. I meant they appear to diverge from a point

But not for all real images right? And my keyboard is a real image? I thought real images were purely mirror related phenomena and a keyboard is just a....proper image or actual image.

Yes but I couldn't prove that they would all converge at the focus.

Yes that's because the sun is super far away and the mirror is also pretty small (not a earth sized mirror or something) so I imagined if you take it really far away the light rays become very close to parallel. But two parallel lines are never going to come any closer. Infinite distance away, they'll still be parallel.

Yes on a Khan Academy video I saw he says no image and that made sense but my textbook didn't make that much sense. Takes into account that light is still where? And how does it tell anything about what happens if you shift slightly off focus? Why can't you get an object exactly at the focus? And what's a mathematical abstractation? And why can't you get a perfect focus? I seem to have questioned every sentence you said here :tongue:

Thanks for that

Wait, I thought that plane mirrors make virtual images, so if you put two of them at 90 degrees you should still get a virtual image right?

Yep I tried out with only one mirror and couldn't find a real, erect image. But I was thinking something that maybe you put another mirror where the real image is formed and do some other shizbang and maybe you could get one? So it is possible for more than one mirror?

Well technically it still would be right? It's inverted with respect to you.

A space-time warp

Yeah I actually saw that I was searching the net for some answers on these and came across a PF post where Doc Al posted a link to that. I don't get how it works but it's cool. Plus why did they choose a pig of all things :tongue:

10. Nov 11, 2012

### Simon Bridge

You also get a dimmer image because fewer light rays are being intercepted by the mirror.

It would still work - just harder to see.
The piggie image in the pic (above) is an example.
I know you've seen it because you mention it in your post (see below).

There's another problem: your brain does post-processing on what your eyes get before it gets turned into something you "see" ... so it tends to do stuff like reinterpret the picture based on expected results. The process is unconscious and very strong with small mirrors.

Seeing what is there instead of what you expect is a skill that comes with practice.

Or maybe I'm thinking of a different meaning for "aperture"?
scatter - scattering and reflecting are related, but different, phenomena
You don't need one - it just makes it easier to see.
No - these are reflected rays ... you'll only see the image in a narrow range. A screen scatters the light to a wide angle.
Nope - not the same way.
There you go! The range of angles where the image is visible without a screen depends on the location of the image and the size of the mirror. You can work it out by drawing in the extreme rays on your diagram.
Opacity is variable. Have you never seen a back-projected movie screen? Ever built a pin-hole camera? Hold tissue paper up to the light - some light gets through doesn't it?

I'm thinking that what you really need now is more experience ... go get hold of some of these things and have a play with them. Really. I mean it.

Because of perspective.
It's a processing artifact in your visual system. They are more common that people think... as you proceed through optics, and gain experience with the phenomena, you'll see more of them.
Really carefully. One approach would be to use a system of lenses or mirrors ... you'll get an image of the image, but you'll have to use optical principles to determine where the first image had to be for the lens/mirror system to work. Anyway - the image in the spoon is probably less than a millimeter from the surface. Bring the object closer to the focus.

Images are also due to lenses ... you eyes have lenses. You see with your eyes: you are looking at an image the whole time.

We usually think of an image as something that "isn't there" in some sense - but it is useful for understanding optics to realize that, when you look at something in front of you, you are looking at an image that happens to have the same position as the object. Our visual system has evolved to make sure of that (mostly).

It is handy to distinguish between the light diverging by scattering from an object and the light reflected off a mirror, or refracted through some material, and then diverging from some place. The first is referred to as an object - it would be the technical definition of "object", and the second is referred to as an image.

The image is "real" if light also converges on that place.

But it is not infinitely far away... you have been happy by making "infinite" a synonym for "super far away" when it is the object but not when it is the image..
What has the size of the mirror to do with the image position.

Saying "the image is at infinity" is the same as saying "the image cannot be resolved" or "the image is super far away".

Saying that there is no image does not do the physical situation justice.

If you start with an object close to, but on on, the focus, then you have no problem with there being an image. As the object approaches the focus the image gets further away. If you plot a graph of image-distance vs object position you see the curve sweep up to infinity... you won't be able to finish because, at some point, you will run out of lab space to set up the screen.

However - repeat the experiment, this time don't worry about shifting the screen position.
If you start with a sharp picture on the screen, then the screen is at the image position. (you should distinguish between the image and the picture formed on a screen - they are not quite the same thing). If you move the object closer to the focus, the picture on the screen gets blurry ... the closer you get to the focus, the blurrier the picture: from the presence of a blurry picture we deduce the existence of an image.

However - you will always get a picture. Ergo - you will always have an image.
This is even more obvious when you try it with lenses - which are easier to work with than mirrors.

However - I'm done arguing. It is not up to me to convince you of the validity of these ideas. Accept or reject them at your peril. You will need to realize that many people will say that the image is at infinity and a few will say "no image" for the same thing. You'll figure it out for yourself as you gain experience.
being reflected by the mirror. See above.
Careful: there are two uses of the word "focus". Informally, we say that something is "in focus" when the picture on the screen is sharp and the process of producing a sharp picture is called "focusing". But in physics, the word "focus" applies to the focal point.
Because the focal point has zero width and real objects have bigger than zero width. It would require infinite accuracy.
"abstraction" ... as in "made abstract". Something that only exists inside of maths. Like perfection and infinite sums and so on.
Because we cannot grind perfectly smooth mirrors. In fact - you can see it for yourself with a spherical mirror - just draw a big one and draw lots of parallel rays, then use the law of reflection as see if they all go through the same spot.

We use spherical mirrors and lenses because they are cheap to make - but to get a perfect focus the shape has to be a perfect paraboloid ... and there ain't no such thing in real life. Real life is messy and imperfect: you should have noticed this by now :)

The spherical mirror behaves a lot like a parabolic one if we restrict the light to those rays close to the optic axis. Remember that approximation we talked about earlier.

Yep - but wait till you try combinations of curved mirrors!

Here's a puzzle for you: you know how plane mirrors swap left and right but not top and bottom? Well, if you lie on your right-side, then left becomes up and right down, but they are still swapped over in the mirror. How does it know?

Could you make a mirror that swaps up and down but not left and right?
Yes - the picture from above is an example like I said.
What you are doing is using the first image as an object.
Oh - hanging upside down ... the image is still inverted with respect to the object, yes.
Curving space-time is cheating though. I could also film the image with the camera inverted, then the picture on my screen will be right-side up :) I just thought that you needed to clear up single-mirror issues before dealing with multiples and other possibilities.
No idea. I used to have one of these and the pig comes with it ... but it is not attached: you can put anything you like there. Anything brightly colored works well - the object is placed inside the bowl.

If you can get hold of one you should have a play.
For instance, if you tilted the bowl shown in the pic a little more, it looks like you should be able to get the pig image to overlap the black part of the bowl. In practice this cannot happen - you'll have fun figuring out why not :)

But what happens is that the part of the pig that would otherwise have appeared in front of the black part gets cut off ... then you visual centers step in and say "aha! you had me fooled for a minute there but I'm on to you now!" and flips the picture to 2D with the image inside the bowl. It's doing the same thing with your spoon.

11. Nov 11, 2012

### Simon Bridge

This is getting very long. The trouble is that this is not a physics class ... a lot of the things you are still puzzled about will get resolved as you progress in your course or by experimenting with the various optics devices you will encounter.

You should have the core ideas now.
Give it a chance to settle.
... and have fun.

12. Nov 11, 2012

### rishch

*sigh* Okay then I'll do my best. Problem is I don't have any mirrors (except for a plane mirror) and my school doesn't either so I can't try things out on my own :/

13. Nov 12, 2012

### Simon Bridge

You'll have to scrounge some.
Sometimes surplus type stores have those convex mirrors you see on roads - they are often reflective on the other side as well. The more new-age toy stores often have educational kits for optics and you can talk to people who make and repair glass. Keep an eye out. It's very odd that your school doesn't have any... talk to the lab technician: most schools have something old in a box someplace.

If there is a college in range - keep an eye out for their open days and go.

You really won't get a lot of this stuff intuitively until you can mess around with the actual things. Until you do you are stuck just believing the odd things people like me can tell you is true.

(Mind you: I am assuming you are not wealthy enough to buy the equipment yourself...)

14. Nov 12, 2012

### rishch

Well I don't think the lab teacher would let me touch anything. And do colleges just let you in like that? And how much do these things cost?

15. Nov 12, 2012

### sophiecentaur

You can always use a shiny table spoon. It will have a concave and a convex surface so that you can see the difference. A soup spoon would even be fairly spherical.

16. Nov 12, 2012

### d3mm

Car headlamp reflectors. At night you know, when no-one is looking. If you put them back the next night, it will generate some nice 'wtf' reactions.

17. Nov 12, 2012

### Simon Bridge

On open-days colleges will run demonstrations. When I was senior in HS I used to be able to let myself in to the undergrad labs but I don't think people get away with that now ... more security conscious.

Some schools have a student volunteer position called "lab assistant" or something.
Different lab techs have different personalities - I used to hang out with the technical support people for my school from about half-way through the first year. You have to play on the "keen young mind" thing.

Costs seems to be pretty much whatever you can afford. Really good quality, purpose-built, is usually prohibitive but you can google around and, like I said, visit a lot of junk shops and stuff. It boils down to how curious you are.

New - a convex, unframed, mirror, 12" in diameter costs US$26 each from at least one supplier - I found 3.5" mirrors for$6 at Feng Shui suppliers. (The links are examples not endorsements.) I'd just google and see.

Tell people it's for a school project and they may give you a deal - I used to find, if I showed up expecting to pay, people would find a way to give stuff to me for free ... if it was for education. Take advantage of it while it lasts.

Lenses are easier than mirrors - I once got a glass-worker to cut me two circles out of a glass sphere that I could turn into a converging or diverging lens for eg. If you can find an old camera - they have all kinds of neat lenses in them.

There is a conceptual problem with spoons ... see if we can come up with a rig to locate the inverted image formed by one... soup spoon is a good idea.

Here's another person exploring the spoon image:
... they managed to locate it (real, inverted, in front of the spoon) with the help of a pencil tip.

The road-mirror on the hairpin on my street regularly goes missing ;)

I am reluctant to suggest er borrowing equipment in this way... at least not on the record. There's probably a rule about it :/ It's for Science M'Lord, honestly...

18. Nov 13, 2012

### sophiecentaur

Conceptual? Why any more than just a mirror? You have to drink the soup first
I just picked up a soup spoon and managed to locate a real image inside the concave bowl fairly easily. I used the 'no parallax' method that we were taught at School in the fifties. You can get a real image of a pencil tip (inverted, of course) which will appear to be in exactly the same place as a small pointer - when you get it right, the pointer moves in exactly the same way as the image as you move your head from side to side so they are in the same 'place' (a real place in the space within the bowl).
Unfortunately, the spoon is too small to get a nice looking result - like the optical toy - but it certainly proves the point. The old 'shaving mirrors' can be used for the same thing - or even the make-up mirrors on powder compacts will give interesting results.

Rather than an "old camera", there are old, budget lenses for SLR cameras in S/H camera or even junk shops, costing only pence. These can be taken apart and there will be a number of elements inside which will give you hours of fun.

19. Nov 13, 2012

### Simon Bridge

If you've been following - OP has remained insistent that the image in his spoon is in his spoon.
Oh do I have to? Can't I just skip to dessert?
There used to be a toy in the 50's for this? <imagines Sophiecentaur sitting for hours in front of a small mirror wiggling his head back and forth and shouting excitedly: "look mummy, it moves the same way" while his parents muttered worriedly between "yes, well done"'s.> Could have been my childhood.
Ah - forgot about those.

This is taking me back ... we used to have to scrounge all our educational/science equipment when we were little... and we were better off for it! The youth of today are all soft...

20. Nov 13, 2012

### sophiecentaur

Sounds a bit like a Secret Policeman's Ball sketch.

Indeed the image is in the spoon because it is below the rim of it, for a deep spoon. But it is in front of the surface and it doesn't appear behind the spoon. There are a million diagrams like this one on the net to show what happens.