At what distance from a convex lens of focal | vedclass

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(D) For a convex lens, the magnification $m$ is given by $m = \frac{v}{u}$.Given that the image size is $1/2$ of the object size, the magnification $m

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(D) For a convex lens, the magnification $m$ is given by $m = \frac{v}{u}$.Given that the image size is $1/2$ of the object size, the magnification $m$ can be $\pm 1/2$.Case $1$: For a real image, $m = -1/2$.Using the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ and $m = \frac{v}{u}$, we have $v = mu = -u/2$.Substituting into the lens formula: $\frac{1}{30} = \frac{1}{-u/2} - \frac{1}{u} = -\frac{2}{u} - \frac{1}{u} = -\frac{3}{u}$.Thus, $u = -3 	imes 30 = -90 \ cm$.The distance is $90 \ cm$.Case $2$: For a virtual image, $m = +1/2$.$\frac{1}{30} = \frac{1}{u/2} - \frac{1}{u} = \frac{2}{u} - \frac{1}{u} = \frac{1}{u}$.Thus, $u = 30 \ cm$.Since $90 \ cm$ is the provided option, the correct answer is $90 \ cm$.

At what distance from a convex lens of focal length $30 \ cm$, an object should be placed so that the size of the image is $1/2$ of the object (in $cm$)?

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