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  4. A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is

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Q. A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point $15\,cm$ from the lens on the opposite side. If the lens is removed the point where the rays meet will move $5\,cm$ closer to the lens. The focal length of the lens is

AIPMTAIPMT 2011Ray Optics and Optical Instruments

Solution:

Here, $v=+15\, cm , $
$u=+(15-5)=+10 \,cm$
According to lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f} $
$\Rightarrow \frac{1}{15}-\frac{1}{10}=\frac{1}{f}$
$\Rightarrow f=-30\, cm$