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Thread: If f is the focal length of a convex lens and an object is placed at a distance...

  1. #1
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    If f is the focal length of a convex lens and an object is placed at a distance...

    If f is the focal length of a convex lens and an object is placed at a distance...-shikaboom.pngBeen trying to relate this as f is constant, help?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: If f is the focal length of a convex lens and an object is placed at a distance..

    We are given:

    $\displaystyle \frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

    Treating $\displaystyle f$ as a constant, can you implicitly differentiate with respect to $\displaystyle u$?
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    Re: If f is the focal length of a convex lens and an object is placed at a distance..

    Write this as $\displaystyle f^{-1}= u^{-1}+ v^{-1}$ and differentiate with respect to u.

    $\displaystyle 0= -u^{-2}- v^{-2}\frac{dv}{du}$
    $\displaystyle v^{-2}\frac{dv}{du}= -u^{-2}$
    $\displaystyle \frac{dv}{du}= -u^{-2}v^2$
    $\displaystyle \frac{dv}{du}= -\frac{v^2}{u^2}$.
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