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What angle is subtended when using this 270-diopter objective?

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data
    An anatomist is viewing heart muscle cells with a microscope that has two selectable objectives with refracting powers of 140 and 270 diopters. When she uses the 140-diopter objective, the image of a cell subtends an angle of 3.7 x 10-3 rad with the eye. What angle is subtended when she uses the 270-diopter objective?


    2. Relevant equations
    tan alpha=h/f


    3. The attempt at a solution
    h=tan(3.7x10^-3)(140) = 0.518
    tan beta = 0.518/270
    beta = 0.0019185 rad


    This is incorrect... I am not sure if I'm even going about this problem the right way. Thanks for any help you can give!!
     
  2. jcsd
  3. Mar 31, 2009 #2

    Redbelly98

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    Note the small angle involved (3.7 x 10^-3 rad), so the small angle approximation is valid
    θ ≈ sinθ ≈ tanθ​
    The image will simply be magnified in proportion to the power of the objective.
     
  4. Mar 31, 2009 #3
    I don't really understand what this means.. how are you saying I would go about solving this with that in mind?
     
  5. Mar 31, 2009 #4

    Redbelly98

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    The image originally subtended an angle of 3.7 x 10^-3 rad.

    Using a stronger objective, we expect the image to appear larger.

    Since the objective strength has been increased by a ratio of (270/140), the 3.7 x 10^-3 rad angle will get multiplied by that same factor.
     
  6. Mar 31, 2009 #5
    Ohh, I was making it harder than it should be. Thank you very much!
     
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