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

  1. Oct 1, 2015 #1
    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
     
  2. jcsd
  3. Oct 1, 2015 #2

    Drakkith

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    What was your teacher's explanation?
     
  4. Oct 1, 2015 #3
    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?
     
  5. Oct 1, 2015 #4

    jbriggs444

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    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
     
  6. Oct 1, 2015 #5

    sophiecentaur

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    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.
     
  7. Oct 2, 2015 #6
    what do you mean by focal length of a lens of mirror?
     
  8. Oct 2, 2015 #7
    But a larger mirror doesn't necessarily mean it is flat, right? Sorry, i can't really understand what are u suggesting
     
  9. Oct 2, 2015 #8

    sophiecentaur

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    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)
     
  10. Oct 2, 2015 #9
    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:

    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)
     
  11. Oct 2, 2015 #10
    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 Untitled.jpg
     
  12. Oct 2, 2015 #11

    jbriggs444

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    I was suggesting that the "thickness" is the horizontal distance from p to edge (referring to your drawing).
     
  13. Oct 2, 2015 #12

    jtbell

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    I'm 99.44% certain that this is a typographical error, and that sophiecentaur meant to write "lens or mirror."
     
  14. Oct 2, 2015 #13
    ok i got it. thank you very much
     
  15. Oct 2, 2015 #14
    i know, i can't think of any other reasons
     
  16. Oct 2, 2015 #15

    sophiecentaur

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    I just read this. What could you possibly mean by it?
     
  17. Oct 2, 2015 #16

    sophiecentaur

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    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.
     
  18. Oct 3, 2015 #17
    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 :)
     
  19. Oct 3, 2015 #18

    sophiecentaur

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    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.
     
  20. Oct 3, 2015 #19

    Drakkith

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    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?
     
  21. Oct 3, 2015 #20

    sophiecentaur

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    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.
     
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