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Homework Help: Number of images formed by 3 mutually perpendicular plane mirrors

  1. Jun 3, 2006 #1
    Sir/Madam,
    1)The 2 adjacent walls and the ceiling of a rectangular room are mirror surfaced.What is the number of images of himself does an observer sees?
    If it was the case of 2 mirrors I know it is 3. But here there are 3 mirrors which are mutually perpendicular. But if we take 2 mirrors at a time then the total number of images is 9. What do you say Sir/Madam?
    2)A convergent beam of light is incident on a convex mirror of radius of curvature 60 cm as shown in figure. What is the nature and position of the image formed by it?
    I solved it in the following way:
    Let u, v and f be the object distance, image distance and focal length of the convex mirror respectively.
    Here u = + 10 cm, f = +30 cm
    1/u + 1/v = 1/f
    v = (uf)/(u-f)
    = (10 x 30)/(10 – 30)
    = -15 cm
    Hence the image formed is virtual and 15 cm in front of the mirror. Is it right?
    3)A convex mirror of focal length f produces an image (1/n)th of the size of the object. What is the distance of the object from the mirror?
    I solved it in the following way:
    Magnification = 1/n = -(v/u)
    i.e. v = -(u/n)
    1/u + 1/v = 1/f
    1/u – (n/u) = 1/f
    By solving I get,
    u = (1-n)f
    Are my sign conventions right? Sometimes the diagram may not be clear. So I will try to describe the diagram. A convergent beam of light serves as a virtual object which appears to converge at a distance of 10 cm behind the mirror.
     

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    Last edited: Jun 3, 2006
  2. jcsd
  3. Jun 4, 2006 #2

    berkeman

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    Staff: Mentor

    On question -1-, I would guess that you get one additional image at the corner of the 3 planes. Since it is a cube corner, you should get a reflection from it back to you in the middle of the room. I don't know if it's a real image, though. Have to try it or else do some ray tracing sketching to figure that out. So you'd get the 3 reflections from the planes, the 2 reflections from the 2 edges, and the 1 from the corner. Is a total of 6 the correct answer for question -1-?
     
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