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Geometric Optics question

  1. Apr 29, 2005 #1
    Hello! I'm having difficulty answering the following question:


    Camera A has a lens with an aperture diameter of 8.50 mm. It photographs an object using the correct exposure time of 3.33×10−2 s.

    What exposure time should be used with camera B in photographing the same object with the same film if this camera has a lens with an aperture diameter of 22.8 mm?



    I have no idea how to approach this problem. It's the only problem of the chapter that deals with time and aperture diamter - the only formula I can use is : f/D (focal lenght/aperture diameter). However I don't understand where time fits in there. I hope someone can help me start this problem. Thank you.
     
  2. jcsd
  3. Apr 29, 2005 #2

    OlderDan

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    Exposure time must be regulated to limit the amount of light energy captured by the camera and delivered to the film. If the rate of light energy is constant (it is), then the amount of energy captured depends on how big the aperture is, and how long it is left open. Think about how increasing the size of the aperture will affect the amount of light energy that gets into the camera.
     
  4. Apr 29, 2005 #3
    So what you are saying is if the aperture diameter increases, then less exposure time is needed since larger apertures allow more light to come in. However, I still don't understand how to approach this problem. =(
     
  5. Apr 29, 2005 #4

    OlderDan

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    You are on the right track. Light energy is spread uniformly over a surface. The energy of the light that you capture with a lens depends on the how much of that surface you capture. If you increase the aperture from 8.5mm to 22.8mm, you will be capturing a larger surface. How much larger? How much SURFACE is associated with each diameter? How much more surface does the larger lens have, or better yet, what is the ratio of the two surfaces? You have to shorten the exposure time of the large lens so that the same amount of energy gets captured by both lenses.
     
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