Image distance / focal length relation

  • Thread starter jmcgraw
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  • #1
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Let O be the object, L be the lense, I be the image, and S be a screen for projecting an image. The lens can be placed anywhere between O and S. Let f be the focal length of the lense. Prove that for an image to be clearly formed on screen S, OS > 4f must be true.

A figure of a "too short" OS distance (since the image would be past the screen) would look like this:

O-----L-----------S----I


I am having a very hard time proving that OS>4f must be true!! Any hints?
 

Answers and Replies

  • #2
andrevdh
Homework Helper
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For the image distance [itex]d_i[/itex] subs [itex]s-d_o[/itex] where s is the distance between object and screen. After a bit of work you should get to
[tex]s=\frac{{d^2}_o}{d_o-f}[/tex]
which gives you a quadratic equation in [itex]d_o[/itex]
By requiring that the determinant should be positve the result follows.
 

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