Understanding Reflection of Light on a Concave Mirror

[sophiecentaur]

Thankyou sophiecentuar for your help and all you did for me... really thankyou

sophiecentuar I just wanted to confirm one thing by saying "Exploding Point " you mean the focus of the concave mirror, Right ?

I would say that when you are at r and the image spreads out everywhere would be the exploding point. Thereafter, nothing is easy to see until you are at 2f. Then you get a clear image right in front of you.
But you have to do it yourself to be really convinced. A spoon really does work once you identify what you are seeing.

 

[SHASHWAT PRATAP SING]

I would say that when you are at r and the image spreads out everywhere would be the exploding point. Thereafter, nothing is easy to see until you are at 2f. Then you get a clear image right in front of you.
But you have to do it yourself to be really convinced. A spoon really does work once you identify what you are seeing.

Thanks Sophiecentuar,
Here r is the radius of curvature,right? Just to confirm

This means that on Radius of curvature of a concave mirror,Until we reach the centre of curvature from focus, everywhere would be the exploding point...
thanks for help

 

[swampwiz]

An easy to think about it is that any time the rays appear to be emanating from a single point - even if they got reflected or refracted from some other point (which could be the actual point on the object or a point from which they appear to be emanating due to other previous reflection/refraction) - if the observer is in front of that emanation point, then he will see the light as if it were being originally the object from which the light is emanating. The original point on the object from which the light emanates is termed the "object", and the point from which the rays appear to be emanating (i.e., which is due to the optical system) is termed the "image" - and when considering a compound optical system, the image point from one optical system is considered to be the object for the following one.

In the 3rd case for the figure posted, the image is behind the observer, and thus there is no point of emanation in front of him. Now of course, there is light emanating to him, but it is not from a point, and thus, it will be a blur - and is the same blur that someone gets when trying to focus on something too close to his eye. Someone with hyperopia (i.e., farsightedness) has the condition in which he can focus light coming from a hyper-infinite point - i.e., light that appears to be emanating from a point behind him (i.e., the light is coming at him, but it appears to emanate from a point behind him), so he would be able to focus in that 3rd case (i.e., up to some limit where his hyperopia is not strong enough to focus in at a "closer" hyper-infinite point.

The reason that a standard flat mirror always shows an image that is twice as deep as the distance to the mirror is that the image "point of emanation" is always the same distance (but behind) the mirror as the object is from the mirror, so the image appears to be deep into the mirror at the same distance that the object is in front of the mirror.

 

[SHASHWAT PRATAP SING]

I would say that when you are at r and the image spreads out everywhere would be the exploding point. Thereafter, nothing is easy to see until you are at 2f. Then you get a clear image right in front of you.
But you have to do it yourself to be really convinced. A spoon really does work once you identify what you are seeing.

sophiecentaur here r is the radius of curvature of the concave mirror, right ? Just to confirm...
Please reply whenever you are free...

 

[sophiecentaur]

sophiecentaur here r is the radius of curvature of the concave mirror, right ? Just to confirm...
Please reply whenever you are free...

You really shouldn't need me to say right or wrong. Just put yourself at the centre of curvature and think where an image could be. Rays are coming from everywhere. If the word 'exploding' doesn't apply then what other word would you use?
Another point is that our brain does its very best to make sense of what is going into the eye. It will try hard to deal with any image - even when it is defocussed or distorted so there will be some vague idea about what you see in other places.

 

[SHASHWAT PRATAP SING]

You really shouldn't need me to say right or wrong. Just put yourself at the centre of curvature and think where an image could be. Rays are coming from everywhere. If the word 'exploding' doesn't apply then what other word would you use?
Another point is that our brain does its very best to make sense of what is going into the eye. It will try hard to deal with any image - even when it is defocussed or distorted so there will be some vague idea about what you see in other places.

Thank you sophiecentuar,
The word Exploding fits here...

 

[A.T.]

As it happens a standard camera or eyeball is not designed to do this for the contested region between between focus and cc.

I just tested it with a cheap make-up mirror. It gets a bit blurry beyond F, but you can still clearly recognize your eye until you get really close to C. And it is not flipped between F and C. A smart phone camera works even better.

@SHASHWAT PRATAP SING If you haven't done it yourself yet, I encourage you to try it. If you don't know the focal length of the mirror, move an object back and forth in front of the mirror, until you find the location where its image flips for a distant eye/camera. That's your F and C it 2 times that. Then move the eye/camera between F and C.

 

[sophiecentaur]

its image flips for a distant eye/camera.

yes but it's at r that your own image flips. At that point the rays strike the normals from the other direction.
This is why 'that video' doesn't help at all because it is shot from a different location from the subject.

 

[A.T.]

Keep in mind that if the real image on the retina is flipped, then we see a not flipped picture.

IMO, that's a red herring.

The question was, what you see when your eye is between F and C. And to tell whether you see a flipped or a non-flipped image you need to understand how to relate the ray diagram to what you see.

 

[A.T.]

yes but it's at r that your own image flips.

You mean at the center of curvature or 2f? Then yes, as I said a few pages back:

- For a distant camera the image flip happens when the object is at the mirror's focal point.
- For a camera at the object the image flip happens when the object is at the mirror's center of curvature.

 

[hutchphd]

Between f and cc a camera/eyeball lens with a positive focal length will not create an image. If the lens can be made to have a negative focal length (like a concave lens) then the lens will produce a real image because the reflection from the mirror provides a projected virtual object behind the lens. Note that this real image will not be inverted by the camera/eyeball lens and so you see what you described. Confusing perhaps but not surprising.

 

[A.T.]

Between f and cc a camera/eyeball lens with a positive focal length will not create an image.

It will produce an image, which might not be exactly on the sensor/retina, and thus the picture you see is blurry. But you can still tell if your eyebrow is above or below the eye. Try it.

If the lens can be made to have a negative focal length (like a concave lens) ..

You don't need a negative focal length. You just need a positive focal length greater than the lens-to-sensor-distance/eyeball-diameter, because the rays are already converging, so you need less lensing than for parallel rays.

Look at the diagram below. The eye here still needs a convex lens to focus the converting rays more, so they meet on the retina, and not behind it, where the mirror forms a real image.

Note that this real image will not be inverted by the camera/eyeball lens and so you see what you described.

No. To see what I described (a non-inverted picture) the real image on the retina (or close to it) must be inverted (like in the diagram above).

 

[sophiecentaur]

You mean at the center of curvature or 2f? Then yes, as I said a few pages back:

With you and your eye at 'cc', rays are all incident back at your eye but there's no specific source. With you and your eye at 2f, there is an identifiable (inverted) image of each part of your face / eye formed at the eye. Those two cases are significantly different, although the rays converge in each case.

I still don's see why you stress the optics of the eye in this. 'Inverted' surely implies upside down compared with how you would normally appreciate a scene. Non - inverted is the converse. In my personal sketches, the inversion starts at >cc - just after the image spreads out everywhere (what I have called the explosion). Even very near cc, the upper and lower parts of the image can be appreciated, although there is no clear image. Only when you get just past 2f does your eye actually see a proper ( and inverted) image. In between those conditions, you can get clues about what you are looking at, depending on your powers of accommodation and the aperture of your pupil.

 

[A.T.]

With you and your eye at 'cc', rays are all incident back at your eye but there's no specific source. With you and your eye at 2f, there is an identifiable (inverted) image of each part of your face / eye formed at the eye.

By "cc" or "C" I mean the center of curvature, which is at 2f (2 * focal length) from the mirror. So "at cc" is the same as "at 2f". You seem to mean different things by this abbreviations?

 

[sophiecentaur]

By "cc" or "C" I mean the center of curvature, which is at 2f (2 * focal length) from the mirror. So "at cc" is the same as "at 2f". You seem to mean different things by this abbreviations?

Yes. Sloppy thinking of mine. 2f is from the equivalent lens treatment and is more familiar.

 

[A.T.]

I still don's see why you stress the optics of the eye in this.

I was just reacting to @hutchphd, who puts a focus on this. It determines how blurry the picture will be.

For the question, if the seen picture is inverted or not, it's not that important. You can simply assume a small aperture (pin-hole) for this.

 

[SHASHWAT PRATAP SING]

Sophiecentuar I just wanted to confirm that by saying r you mean the radius of curvature of the concave mirror...?

 

[hutchphd]

Thanks to @sophiecentaur and @A.T. My insistence that the entirety of the imaging lens needed a negative focal length in the "interim" region was not correct. For a fixed focus camera/eyeball only a corrective lens would need to be negative. Apologies for the oops. I think we agree.
If I can find a suitable mirror I may make a movie...I have a decent optical rail ...YOUTUBE watch out.

 

[SHASHWAT PRATAP SING]

Thank you sophiecentaur, A.T. and jbriggs444 for all you did for me...

 

[A.T.]

Thank you sophiecentaur, A.T. and jbriggs444 for all you did for me...

Thanks for your question. I learned something new myself.

 

[sophiecentaur]

Thanks for your question. I learned something new myself.

We were all looking at the subject from a new angle -literally.

 

[A.T.]

- For a distant camera the picture inversion happens when the object is at the mirror's focal point.
- For a camera at the object the picture inversion happens when the camera & object are at the mirror's center of curvature.

Just for completeness the remaining case:
- For a distant object the picture inversion happens when the camera is at the mirror's focal point.

 

[SecularSanity]

We'd have to turn around and face the real image, correct? Is there a difference between the image of the real image that we see in the mirror vs. on the screen?

Is the image that we see in the mirror just like a plane mirror image of the real image?

Is the image that we see in the mirror a true mirror image of the object?

see video

 

[A.T.]

We'd have to turn around and face the real image, correct?

Only if you put a screen where the real image is formed, and ensure appropriate lighting. Otherwise, if you turn away from the mirror you just see what is behind you.

 

[sophiecentaur]

Is there a difference between the image of the real image that we see in the mirror vs. on the screen?

Yes. Real images of that kind tend to 'hang there' and they move about as you move your head - relative to what's behind them (parallax effect) and that is unsettling for the brain. Because of the distances involved, the fact that there's 'nothing supposed to be there' and that you can also see things 'through' that real image, it doesn't look genuine. An image projected on a screen is a much more familiar thing and it behaves 'right'. These things are not indicated by a simple ray diagram. See https://www.amazon.com/dp/B089D83GXH/?tag=pfamazon01-20 that you can buy. It just looks wrong.

Is the image that we see in the mirror just like a plane mirror image of the real image?

Is the image that we see in the mirror a true mirror image of the object?

It is what it is. The point is more to do with how our brain deals with it - bearing in mind that the evolution of vision, over millions of years, didn't have to deal with high quality images in mirrors. We are still confused to some extent. Try cutting your own hair with the aid of two mirrors or drilling a tooth accurately (as a dentist does every day).

 

[A.T.]

Is the image that we see in the mirror just like a plane mirror image of the real image?

Is the image that we see in the mirror a true mirror image of the object?

An object is mirrored if an odd number of dimensions is inverted.

- Normal flat mirror inverts 1 : back&front -> you see a mirrored object

- Non-reversing-mirror inverts 2 : back&front, left&right (e.g.) -> you see a non-mirrored object

- Concave mirror with object & eye within radius of curvature: inverts 1 : back&front -> you see a mirrored object

- Concave mirror with object & eye beyond radius of curvature: inverts 3 : back&front, left&right, up&down -> you see a mirrored object

 

[SecularSanity]

An object is mirrored if an odd number of dimensions is inverted.

- Normal flat mirror inverts 1 : back&front -> you see a mirrored object

- Non-reversing-mirror inverts 2 : back&front, left&right (e.g.) -> you see a non-mirrored object

- Concave mirror with object & eye within radius of curvature: inverts 1 : back&front -> you see a mirrored object

- Concave mirror with object & eye beyond radius of curvature: inverts 3 : back&front, left&right, up&down -> you see a mirrored object

Let me see if I understand you correctly. When the image is anywhere between f and c, beyond c, or even at c, the image that we see in the mirror is only flipped vertically but it is a non-reversing image.

On the other hand, the image that we see on the screen is flipped vertically and horizontally.

Is this correct?

 

[A.T.]

Let me see if I understand you correctly. When the image is anywhere...

I didn't say anything about the location of "the image", just about the location of object & eye, and what the eye sees. Basically watching your own face in the mirror.

One reason why this thread is so long, is talking about "the image" in a scenario with multiple images.

 

[SecularSanity]

I didn't say anything about the location of "the image", just about the location of object & eye, and what the eye sees. Basically watching your own face in the mirror.

One reason why this thread is so long, is talking about "the image" in a scenario with multiple images.

Well, that’s where the confusion lies. The image formed on our eye when looking into the mirror is an inverted, non-reversing image. It’s as if we’re facing the inverted object. When we turn our head, and face the screen, as you can see, the image is an inverted mirror image of the object.

 

[sophiecentaur]

One reason why this thread is so long, is talking about "the image" in a scenario with multiple images.

Agreed.

As for the inversion business, if you are looking into mirrorworld, there will be lateral inversion always. (Clockwise goes anti-clockwise) Thereafter you can apply the rules of a lens which give no inversion when close up and (additional) complete inversion further out. (Writing will always be back to front) But looking (over your shoulder) at the distant projected image on a screen, writing will be 'legible' (clockwise goes clockwise) because you will have done another lateral inversion by looking at the 'back' of the image.

 

[SecularSanity]

Agreed.

As for the inversion business, if you are looking into mirrorworld, there will be lateral inversion always. (Clockwise goes anti-clockwise) Thereafter you can apply the rules of a lens which give no inversion when close up and (additional) complete inversion further out. (Writing will always be back to front) But looking (over your shoulder) at the distant projected image on a screen, writing will be 'legible' (clockwise goes clockwise) because you will have done another lateral inversion by looking at the 'back' of the image.

I don't think that's correct. If you take the image your eye sees in the mirror, and flip it vertically, where it's now upright, the writing would be legible. If you did the same with the image on the screen, and flipped it vertically, the image would also need to be flipped horizontally for the writing to be legible.

 

[sophiecentaur]

I don't think that's correct.

OK try this. The image in a plane mirror is laterally inverted. Reduce the radius of curvature 'a bit'. The image is still laterally inverted. That happens right in as far as 2F, after which the image flips both side to side to side and top to bottom. The lateral inversion you started with is there in addition anyway. So clockwise still goes anti-clockwise. If, as you claim, only one inversion occurred beyond 2F then which one would ti be? Would it be up down or side to side?
I think the problem is with the term 'lateral inversion' which implies side to side but it's really an inversion of handedness. Two people looking in the same mirror - one stands up and one lays down. How would you describe the difference in what the guy laying down sees, compared with the guy standing? Then rotate the sign they are reading. It doesn't help either of them to read it any easier, which is why the handedness is probably a better description of the inversion. Too late to change now.

I do a bit of astronomy and a refracting scope flips the image both ways but there is no change of handedness. (A camera at prime focus produces normal images). I have a 'star diagonal' prism which turns things ' the right way up'. That makes looking at terrestrial images much easier, for a start because up is up. But now the image is L/R flipped. That is easy to cope with but writing is wrong. This also happens with my Reflector (two mirrors in it, of course) and they produce unflipped images on a camera sensor. The implication is that the image without a secondary mirror would be laterally inverted.

 

[A.T.]

An object is mirrored if an odd number of dimensions is inverted.

- Normal flat mirror inverts 1 : back&front -> you see a mirrored object

- Non-reversing-mirror inverts 2 : back&front, left&right (e.g.) -> you see a non-mirrored object

- Concave mirror with object & eye within radius of curvature: inverts 1 : back&front -> you see a mirrored object

- Concave mirror with object & eye beyond radius of curvature: inverts 3 : back&front, left&right, up&down -> you see a mirrored object

Well, that’s where the confusion lies.

Okay, let me clarify what I mean by "mirrored" in the above post:

1) Do this with both hands:

2) Look at one hand directly, and at the other one in your mirror (or through whatever setup you have).

3) If you can rotate your hands such that both look identical (not symmetrical) to you, then your mirror/setup "mirrors" the object, in the sense I used the term. Otherwise it doesn't.

Note that stuff like text written on paper is not a good test object for this, because it is basically a 2D object. It's better to have 3 distinct axes on your object.

 

[SecularSanity]

Agreed.

As for the inversion business, if you are looking into mirrorworld, there will be lateral inversion always. (Clockwise goes anti-clockwise) Thereafter you can apply the rules of a lens which give no inversion when close up and (additional) complete inversion further out. (Writing will always be back to front) But looking (over your shoulder) at the distant projected image on a screen, writing will be 'legible' (clockwise goes clockwise) because you will have done another lateral inversion by looking at the 'back' of the image.

The reason that I think it’s incorrect is because the image that you see in the mirror when flipped vertically is non-reversing. Look at the first image in post #132. You can read the writing, but for the image on the screen, (see second image in #132) you have to turn and face it, which causes the perceived horizontal direction. When you look at the screen, it’s as if it were an inverted plane mirror image. You’re looking at the mirror image flipped vertically. It's a perfectly stamped (mirror) image.

 

[jbriggs444]

Put an imaginary frosted pane of glass at the image plane where the real image lies. Clearly it matters whether you look at the pane from the one side or the other.