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Pinhole camera question with only two known variables?

  1. Jul 21, 2011 #1
    1. The problem statement, all variables and given/known data

    True or False: If a pinhole camera casts on the screen an image of 40.0cm in size of an object situated at a distance of 40.0m from the camera, then the size of the object is 10.0m.

    2. Relevant equations

    M = hi/ho = di/do

    3. The attempt at a solution

    hi = 40.0cm
    do = 40.0m
    ho = 10.0m (?)

    M = hi/ho = 0.04m
    di = dohi/ho = 0.16m
    M = di/do = 0.004m

    I'm guessing it is FALSE because the two values for M are different but I really have no idea how to go about a question like this. Any help would be greatly appreciated!! :D
     
  2. jcsd
  3. Jul 21, 2011 #2

    collinsmark

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    Hello ldesai149,

    Welcome to Physics Forums!
    There's a mistake above involving what's in red. But read below before reaching a final conclusion in your answer. You used ho = 10 m as part of your calculations, but you shouldn't use a specific number for ho, because you don't know for sure what the object height actually is yet.
    This is a true or false question. So at the time the statement is given, you don't really know what the object height ho is. Maybe it's 10 m if the statement is true. But maybe it's 12 m or 100 m, or some other height, if the statement is false. It's best not to use a specific value for ho unless you can derive that value first.

    Since you don't know what ho is, is there a way to calculate it knowing only that hi = 0.40 m, and do = 40 m? If, based only on that information, you can calculate ho to be 10 m (without using "10 m" as part of your calculations), then the statement is true. If you calculate some other number or if there is simply not enough information to derive the 10 m figure, then the statement is generally false. :wink:
     
    Last edited: Jul 21, 2011
  4. Jul 22, 2011 #3

    Redbelly98

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    Put another way, how many variables are in that equation? How many are given in the problem statement? Can this equation be solved with that information? (Hint: do not consider ho=10.0m as given; as collinsmark said, we do not know this.)
     
  5. Jul 25, 2011 #4
    Thank you! :D It was a question on an exam and I couldn't stop thinking about it..
     
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