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  4. Two lenses of focal lengths 20 cm and -40 cm are held in contact. The image of an object at infinity will be formed by the combination at

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Q. Two lenses of focal lengths $20\, cm$ and $-40\, cm$ are held in contact. The image of an object at infinity will be formed by the combination at

Ray Optics and Optical Instruments

Solution:

Equivalent focal length is given by,
$\frac{1}{f} = \frac{1}{f_1}+\frac{1}{f_2}$
Here, $f_1 = 20\, cm$ and $f_2 = -40 \,cm$
$\therefore \frac{1}{f} = \frac{1}{20}-\frac{1}{40} =\frac{ 2-1}{40} $
$ \Rightarrow f = 40 \,cm$
$ \because\frac{1}{f} = \frac{1}{v}-\frac{1}{u}=\frac{1}{v}=\frac{1}{v}-\frac{1}{\infty} $
$\Rightarrow v = f =40 \,cm \left[\because u =\infty\right]$