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Optics - Finding Angular Size and Image Location

  1. Jul 22, 2012 #1
    1. 1. The problem statement, all variables and given/known data
    (SEE PIC given BELOW) A pencil is standing upright in front of a mirror at a distance of 20 cm from the surface. A variety of mirrors can be placed where the dotted box is located. The mirror may be either concave, flat or convex, based upon the following questions. An observer's eye is directly in front of the pencil and the mirror and the observer can see both the object (pencil) and its image. The observer's eye is 20 cm from the pencil, and at a level equal to the midpoint of the pencil. You may also assume that for a curved mirror its vertex (the center of the mirror's surface) is located right at the tip of the leftmost arrow in the diagram.

    PIC: http://tinypic.com/r/14y06di/6 or see attached


    3) Where is the image located if the mirror is flat?
    4) Where could the image be located if the mirror is convex?
    multiple choice answers for Q3 and Q4
    a) 20 cm in front of the observer
    b) 40
    c) 60
    d) 80
    e) 100
    f) N/A


    2. Relevant equations


    (1/S1) + (1/S2) = (1/F)
    Angular Size (in radians) = diameter/Distance
    More?


    3. The attempt at a solution


    3 ) C, 60 cm, 20 to the pencil, 20 to mirror, 20 past mirror
    4 ) B, 40 cm. Not sure?
     

    Attached Files:

    Last edited: Jul 22, 2012
  2. jcsd
  3. Jul 22, 2012 #2

    Simon Bridge

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    1. you are making a small-angle approximation arn't you?
    2. the angular size does depend on the distance to the image though - the farther away the image the smaller the angular size.
    3. since no position axis are provided, you have to specify your origin explicitly ... some conventions would have the image at -20cm.
    4. what sort of image would you expect from a convex mirror? Can you describe where to expect that sort of image? How does the radius of curvature of the mirror affect this?
     
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