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Position of image of an immersed object

  1. May 20, 2010 #1
    Position of image of an immersed object.. Are books wrong?

    1. The problem statement, all variables and given/known data

    In almost every book I checked, the image of an immersed object is always vertically above the object. Is this always the case and is independent on the position you are looking from?

    2. Relevant equations

    n = sin i / sin r

    3. The attempt at a solution

    According to my drawings the image is only VERTICALLY above the object if you look directly from above. I used snell's law to find the angles i and r, and then located the image. I always used 2 rays emerging from the object and was extra careful to mark the angles accurately and pass through the right positions. I also tried to find some flash or java animation that could illustrate this but I couldn't find any. Are the books wrong?
     
    Last edited: May 21, 2010
  2. jcsd
  3. May 21, 2010 #2
    You are perfectly correct.
    Most books show the case where the image is viewed from vertically above. It's usually in connection with using apparent depth of water to measure the refractive index.
    The books should explain that this is the case, and only relates to a narrow bundle of rays moving vertically upwards.
    There is a diagram here from one of my old books which shows how the position of the image changes as you view from a point further to the right.
    The images are I1 I2 and I3 and lie on a curve called a "caustic". I1 is the standard case when viewed from vertically above.
    There are two caustics in the diagram. There is also the one on the left for the case when you view from the left.
    The diagram isn't perfectly clear but does show the point you have correctly brought up.
    apparent-depth.png
     
  4. May 21, 2010 #3
    Many thanks, I looked everywhere for this diagram but couldn't find it anywhere neither in books nor on the net.
     
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