Thick convex mirror or a thin one for the anti-theft mirror?

[heavystray]

the question in my exam goes like this:
should we use a thick convex mirror or a thin one for the anti-theft mirror?

the given answer:
thin, because a thin convex mirror does not form multiple images

can someone please explain to me why a thin spherical mirror does not form multiple images compared to a thick mirror?
i try to ask my teacher but I'm not satisfied with her explanation
thank you in advance

 

[Drakkith]

What was your teacher's explanation?

 

[heavystray]

What was your teacher's explanation?

she said that since the anti-theft mirror is used to look at a distant object, the focus length of the mirror should be longer, so thin mirror= long f. isn't the thickness of a mirror doesn't affect its focal length?

 

[jbriggs444]

she said that since the anti-theft mirror is used to look at a distant object, the focus length of the mirror should be longer, so thin mirror= long f. isn't the thickness of a mirror doesn't affect its focal length?

If I understand what is being referred to, the "thickness" of the mirror is a description of how much distance (in the direction toward the object) there is between the center of its reflective surface of the mirror and the edges. This means that the thickness or thinness of a mirror does not reflect its construction (i.e. the distance between the front side of your bathroom mirror and the silvered coating on its back) but does depend on its curvature.

Of course, the curvature of a mirror is very directly related to its focal length.

It is possible to construct a mirror with a short focal length, a high curvature and a thin front-to-back distance using the same concept as a Fresnel lens -- concentric rings in a sawtooth pattern. https://en.wikipedia.org/wiki/Fresnel_lens

 

[sophiecentaur]

she said that since the anti-theft mirror is used to look at a distant object, the focus length of the mirror should be longer, so thin mirror= long f. isn't the thickness of a mirror doesn't affect its focal length?

It's a pity she didn't explain it better. Clearly, it's the focal length of a lens of mirror that counts in where an image is formed. but there are other issues to be considered for a security mirror. You need a wide angle of view and the viewer needs to be able to operate the system over a range of positions. I guess she was implying that the back of a spoon (a 'deep reflector') wouldn't make a good security mirror but a larger 'flatter looking' mirror would do the job. However, a plane mirror would he totally flat but would not do the job.

 

[heavystray]

It's a pity she didn't explain it better. Clearly, it's the focal length of a lens of mirror that counts in where an image is formed. but there are other issues to be considered for a security mirror. You need a wide angle of view and the viewer needs to be able to operate the system over a range of positions. I guess she was implying that the back of a spoon (a 'deep reflector') wouldn't make a good security mirror but a larger 'flatter looking' mirror would do the job. However, a plane mirror would he totally flat but would not do the job.

what do you mean by focal length of a lens of mirror?

 

[heavystray]

It's a pity she didn't explain it better. Clearly, it's the focal length of a lens of mirror that counts in where an image is formed. but there are other issues to be considered for a security mirror. You need a wide angle of view and the viewer needs to be able to operate the system over a range of positions. I guess she was implying that the back of a spoon (a 'deep reflector') wouldn't make a good security mirror but a larger 'flatter looking' mirror would do the job. However, a plane mirror would he totally flat but would not do the job.

But a larger mirror doesn't necessarily mean it is flat, right? Sorry, i can't really understand what are u suggesting

 

[sophiecentaur]

what do you mean by focal length of a lens of mirror?

Focal length is the distance from the 'back' of a concave mirror at which parallel rays are brought to a focus. The focal point is where an image of a distant object will be formed by a concave lens. For a convex mirror, you get a 'virtual' image at a distance behind the mirror. The focal length is described as a negative value. The smaller the radius of curvature, the smaller the magnitude of the focal length. Look in the back of a spoon and you will see an image of the room which appears to be very close behind the spoon (and inconveniently tiny).
If you look at a security mirror (much longer focal length) the images appear distant (but closer than the source objects) and slightly reduced in size.

But a larger mirror doesn't necessarily mean it is flat, right? Sorry, i can't really understand what are u suggesting

If you have a mirror with the radius of curvature of a spoon, it can only be a few cm wide; the focal length is short. A security mirror will have a radius of curvature of, probably, a metre or two. That means it can be two metres wide.

Draw two circles on paper - one large and one small - to represent the side view of a reflector. The mirror with the largest radius can be made larger in area.
look at this and other links. (Search for convex mirror equation - or similar terms)

 

[heavystray]

Focal length is the distance from the 'back' of a concave mirror at which parallel rays are brought to a focus. The focal point is where an image of a distant object will be formed by a concave lens. For a convex mirror, you get a 'virtual' image at a distance behind the mirror. The focal length is described as a negative value. The smaller the radius of curvature, the smaller the magnitude of the focal length. Look in the back of a spoon and you will see an image of the room which appears to be very close behind the spoon (and inconveniently tiny).
If you look at a security mirror (much longer focal length) the images appear distant (but closer than the source objects) and slightly reduced in size.If you have a mirror with the radius of curvature of a spoon, it can only be a few cm wide; the focal length is short. A security mirror will have a radius of curvature of, probably, a metre or two. That means it can be two metres wide.

Draw two circles on paper - one large and one small - to represent the side view of a reflector. The mirror with the largest radius can be made larger in area.
look at this and other links. (Search for convex mirror equation - or similar terms)

1.i understand what's the meaning of focal length, what i don't is what do you mean by LENS OF MIRROR?

2.ok, so since it's a security mirror, you need to have a mirror with a longer focal length since a longer focal length mirror means a wider mirror? is it correct?

back to my original question:

the question in my exam goes like this:
should we use a thick convex mirror or a thin one for the anti-theft mirror?

the given answer:
thin, because a thin convex mirror does not form multiple images

can someone please explain to me why a thin spherical mirror does not form multiple images compared to a thick mirror?
i try to ask my teacher but I'm not satisfied with her explanation
thank you in advance

are you implying that a THIN mirror would have a wider view?
and how a thin mirror would avoid MULTIPLE IMAGES formed? ( that's the reason on why we should a thinner convex mirror- based on the scheme given)

 

[heavystray]

If I understand what is being referred to, the "thickness" of the mirror is a description of how much distance (in the direction toward the object) there is between the center of its reflective surface of the mirror and the edges. This means that the thickness or thinness of a mirror does not reflect its construction (i.e. the distance between the front side of your bathroom mirror and the silvered coating on its back) but does depend on its curvature.

Of course, the curvature of a mirror is very directly related to its focal length.

It is possible to construct a mirror with a short focal length, a high curvature and a thin front-to-back distance using the same concept as a Fresnel lens -- concentric rings in a sawtooth pattern. https://en.wikipedia.org/wiki/Fresnel_lens

so, the longer the distance between the pole of mirror and its edge, the thinner the mirror would be, right?
is this the thickness you're suggesting? or not

 

[jbriggs444]

so, the longer the distance between the pole of mirror and its edge, the thinner the mirror would be, right?
is this the thickness you're suggesting? or not

I was suggesting that the "thickness" is the horizontal distance from p to edge (referring to your drawing).

 

[jtbell]

1.i understand what's the meaning of focal length, what i don't is what do you mean by LENS OF MIRROR?

I'm 99.44% certain that this is a typographical error, and that sophiecentaur meant to write "lens or mirror."

 

[heavystray]

I was suggesting that the "thickness" is the horizontal distance from p to edge (referring to your drawing).

ok i got it. thank you very much

 

[heavystray]

I'm 99.44% certain that this is a typographical error, and that sophiecentaur meant to write "lens or mirror."

i know, i can't think of any other reasons

 

[sophiecentaur]

explain to me why a thin spherical mirror does not form multiple images compared to a thick mirror?

I just read this. What could you possibly mean by it?

 

[sophiecentaur]

so, the longer the distance between the pole of mirror and its edge, the thinner the mirror would be, right

Do you mean 'thinner' in terms of the ratio of the radius to the depth?
I think this calls for a diagram to explain your initial question. There are several different interpretations so far.

 

[heavystray]

Do you mean 'thinner' in terms of the ratio of the radius to the depth?
I think this calls for a diagram to explain your initial question. There are several different interpretations so far.

so, the question in my exam was to modify a convex mirror in some aspects ( including the thickness) so that it can be used as an anti-theft mirror efficiently.
to be honest, i don't know what 'thickness' the question was referring to, since my syllabus for physics is very basic, I'm assuming that the thickness refers to the distance of mirror's vertex and its back

so, i can't see why a thin mirror would do a better job (from the answer given)

so, i come here to ask if the 'thickness' of mirror refers to something else
i hope you understand my question :)

 

[sophiecentaur]

OK. That's a concrete question. I would say that the answer is that, for a given width, the thickness (focal length) should be chosen so that the field of view is the right width for the shop.
Assume that the viewer is situated on the axis of the mirror. Rays coming from all directions in the visual field have to be reflected back along the axis to the viewer. The laws of reflection will apply to all rays hitting the surface. The furthest off axis that objects could be seen would be about twice the angle subtended by the edge of the mirror from its centre of curvature. The [Edit: Smaller] the radius of curvature, the greater the possible range of angles that can be viewed.
There will be a lot of distortion of images near the edge if the radius is small and the mirror is nearly hemispherical.

Spend some time with compasses and a ruler and plot rays from various directions. You should get an idea of what I mean.

 

[Drakkith]

so, i come here to ask if the 'thickness' of mirror refers to something else

I've never heard or read of 'thickness' referring to anything but the literal thickness of the mirror itself. IE the distance from the front surface to the back surface. The focal length is always called the focal length and the curvature of the mirror is called the radius of curvature. Perhaps the question was referring to modifying the thickness so that it is thick enough to be sturdy, but thin enough to keep the weight down?

 

[sophiecentaur]

I've never heard or read of 'thickness' referring to anything but the literal thickness of the mirror itself. IE the distance from the front surface to the back surface. The focal length is always called the focal length and the curvature of the mirror is called the radius of curvature. Perhaps the question was referring to modifying the thickness so that it is thick enough to be sturdy, but thin enough to keep the weight down?

You could well be right. It seems to be one of those questions that teachers and examiners cook up without thinking it through. They then present it to students who cannot be expected to have a lot of practical knowledge on top of their formal Physics. Confusion reigns.
I wonder if the term "thickness" is an artefact of language translation.
PS many such mirrors are just shiny plastic that is very light weight and does an adequate job for a low price.

 

[heavystray]

You could well be right. It seems to be one of those questions that teachers and examiners cook up without thinking it through. They then present it to students who cannot be expected to have a lot of practical knowledge on top of their formal Physics. Confusion reigns.
I wonder if the term "thickness" is an artefact of language translation.
PS many such mirrors are just shiny plastic that is very light weight and does an adequate job for a low price.

yes, yes that's what i thought exactly. i can deal with it if the answer was thin so that the mirror can be moved easily or etc. but then the answer was thin because it would not form multiple images?!?

anyway, thanks for putting an effort to answer!

 

[sophiecentaur]

That "multiple images" answer is strange. How is it possible to see more than one image in a convex mirror? What was the question setter thinking about? You can get two different images in a concave mirror, depending where you put your head: virtual or real / upright or inverted but concave is used for 'shaving' mirrors, to be used close up and to give some magnification.
I can only suggest you challenge your teacher and see where the question was coming from. There may be some rational explanation - apart from lack of teacher knowledge.

 

[nasu]

Thickness may refer to the glass layer placed on top of the reflecting, metallic surface in the ordinary mirrors (not the front surface mirrors used in optics labs).
The only reference I found to such a thing (thick mirrors) was in some exam questions.

https://books.google.ca/books?id=Ir...ultiple images in thick convex mirror&f=false

They are discussing the multiple reflections at the two interfaces (air-glass and glass-metal).
It may be just one of these silly instances when the textbooks pick up some less relevant aspect and push it on the students before they understand the basics.
The OP poster has brought the same topic (thin and thick mirrors) in a previous post.
​

 

[sophiecentaur]

Sounds possible. But where would 'image quality' be relevant in that application? Perhaps the full text of the question would reveal something.

Thickness may refer to the glass layer placed on top of the reflecting, metallic surface in the ordinary mirrors (not the front surface mirrors used in optics labs).
The only reference I found to such a thing (thick mirrors) was in some exam questions.

https://books.google.ca/books?id=IryMtwHHngIC&pg=PA1102&lpg=PA1102&dq=multiple+images+in+thick+convex+mirror&source=bl&ots=sy_kcaMnaG&sig=cQqzfD5IB9rXGpYQSMlO-qcI17Y&hl=en&sa=X&ved=0CCgQ6AEwAWoVChMI8MOey7CqyAIVSyweCh0iRgtl#v=onepage&q=multiple images in thick convex mirror&f=false

They are discussing the multiple reflections at the two interfaces (air-glass and glass-metal).
It may be just one of these silly instances when the textbooks pick up some less relevant aspect and push it on the students before they understand the basics.
The OP poster has brought the same topic (thin and thick mirrors) in a previous post.
​

 

[_Anthony_]

This has nothing to do with focal length. Most everyday mirrors made of glass are coated on the back surface. A "thick" mirror's numerous internal reflections are generally quite visible, hence the answer given. The Newton ring interferometers I've built either use thin glass or half silvered glass for the same reason. It's hard to distinguish between the various reflections.

Anthony

 

[sophiecentaur]

If the exam question had been about an astronomical telescope with a back-silvered (concave, as it happens) mirror, the multiple reflections could have been relevant to the image quality. As it happens, the mirrors you see in supermarkets could well be surface silvered and plastic, in any case.

 

[_Anthony_]

With respect sophiecentur, astronomical mirrors are generally silvered on the front. There is a type of optical element that is silvered on back, it's called a mangin. Due to the color aberration introduced by refraction designs including mangins are uncommon. I've personally never seen an achromatic mangin just prescriptions that called for them. I have a cassegrain, [not of my making, I've only successfully made one (classical) cassegrain], with all spherical surfaces that uses a mangin for the convex secondary but the its first surface has an anti-reflection coating.

 

[nasu]

But the question was not about astronomical mirrors. The bathroom mirror is silvered on the back. And so are many cheap mirrors.
Anyway, the questions seem to be of little relevance to practical purposes. They made them up to support this concept of thick mirror which they like to introduce, for some reason.

 

[heavystray]

But the question was not about astronomical mirrors. The bathroom mirror is silvered on the back. And so are many cheap mirrors.
Anyway, the questions seem to be of little relevance to practical purposes. They made them up to support this concept of thick mirror which they like to introduce, for some reason.

Why does it matter if the question had been about astronomical mirrors? Sorry i don't really understand

 

[nasu]

Did you read the posts above?
The telescope mirror is silvered on the front so the thickness of glass is irrelevant for image construction. There are no reflections due to the glass.

 

[heavystray]

Did you read the posts above?
The telescope mirror is silvered on the front so the thickness of glass is irrelevant for image construction. There are no reflections due to the glass.

Yes, but i was actually referring to this post

If the exam question had been about an astronomical telescope with a back-silvered (concave, as it happens) mirror, the multiple reflections could have been relevant to the image quality. As it happens, the mirrors you see in supermarkets could well be surface silvered and plastic, in any case.

So, it's possible that the answer is thin bcs thin mirror would have less internal reflections?

 

[nasu]

Oh, but astronomical mirrors do not have silvered backs but fronts.

Yes, it may be that they refer to the multiple reflections produced by the glass, in the case of back silvered mirrors.
But I still think this is not an important point. The reflection from glass may be an order of magnitude weaker than the one from the metal.

 

[bubsir]

I can't say I read every comment so excuse me if I missed something. The terms "thick" and "thin" have special meaning when applied to lenses as there is an entire field of "thin lens" design techniques. But when it come to mirrors - to the best of my knowledge - there is only the physical thickness of a back side coated optic to consider. As just mentioned "The reflection from glass may be an order of magnitude weaker than the one from the metal." - in fact for a silver mirror it is about 4% vs 94% (~2% loss in the silver). However that is for normal incidence. At high angles (45 deg or so) the balance changes. By 60 degrees its more like 15% to 83% and get progressively worse. Most security/safety mirrors are front side (aluminum) coated polished metal or plastic.

 

[peterlonz]

It has taken many knowledgeable replies to determine that thickness means thickness.
The problem appears to be a very poorly worded exam question.
But it may not be so easily dismissed:
No student could be expected to answer on a logical basis, without more information particularly what is meant by a "security mirror".
So I would have expected any decent teacher to realize that many of the class could not adequately respond, & he or she should have prepared a full explanation, even to the point of providing a complete written answer.
Alas maybe the teacher was not at full strength on the subject.

 

[sophiecentaur]

With respect sophiecentur, astronomical mirrors are generally silvered on the front.

Yes. I know. And one good reason is to avoid multiple reflections. That was my point. Maybe I didn't write the comment well enough.