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  4. The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used?

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Q. The graph shows how the magnification $m$ produced by a convex thin lens varies with image distance $v$. What was the focal length of the used?Physics Question Image

Ray Optics and Optical Instruments

Solution:

For a lens $m=\frac{f-v}{f}=-\frac{1}{f} v+1$
Comparing it with $y=m x+c$
Slope $=m=-\frac{1}{f}$
From graph, slope of the line $=\frac{b}{c}$
Hence $-\frac{1}{f}=\frac{b}{c} $
$\Rightarrow |f|=\frac{c}{b}$