A point object is placed at a distance of 10 | vedclass

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(A) For a concave mirror,the mirror formula is $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.Given $u = -10 \ cm$ and $v = -20 \ cm$,we find the focal len

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$0.4 \ cm$ away from the mirror

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(A) For a concave mirror,the mirror formula is $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.Given $u = -10 \ cm$ and $v = -20 \ cm$,we find the focal length $f$:$\frac{1}{f} = \frac{1}{-20} + \frac{1}{-10} = \frac{-1-2}{20} = -\frac{3}{20} \implies f = -\frac{20}{3} \ cm$.Differentiating the mirror formula with respect to $v$ and $u$:$-\frac{1}{v^2} dv - \frac{1}{u^2} du = 0 \implies \frac{dv}{du} = -\frac{v^2}{u^2}$.Here,$du = -0.1 \ cm$ (as the object moves towards the mirror).Substituting the values:$dv = -\left(\frac{-20}{-10}ight)^2 	imes (-0.1) = -(2)^2 	imes (-0.1) = -4 	imes (-0.1) = 0.4 \ cm$.The positive sign indicates that the image shifts away from the mirror.

$A$ point object is placed at a distance of $10 \ cm$ and its real image is formed at a distance of $20 \ cm$ from a concave mirror. If the object is moved by $0.1 \ cm$ towards the mirror,the image will shift by about:

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