The focal length of a concave mirror is f and | vedclass

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Question

(A) For a concave mirror,the focal length is taken as $-f$.The distance of the object from the principal focus is $x$. Since the object is placed in f

Vedclass · Accepted Answer

$\frac{f}{x}$

Vedclass · Answer

(A) For a concave mirror,the focal length is taken as $-f$.The distance of the object from the principal focus is $x$. Since the object is placed in front of the mirror,the object distance $u = -(f + x)$.Using the mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f_{mirror}}$$\frac{1}{v} + \frac{1}{-(f+x)} = \frac{1}{-f}$$\frac{1}{v} = \frac{1}{f+x} - \frac{1}{f} = \frac{f - (f+x)}{f(f+x)} = \frac{-x}{f(f+x)}$$v = -\frac{f(f+x)}{x}$Magnification $m = -\frac{v}{u} = -\left( \frac{-\frac{f(f+x)}{x}}{-(f+x)} \right) = -\frac{f}{x}$The magnitude of magnification is $|m| = \frac{f}{x}$.

The focal length of a concave mirror is $f$ and the distance from the object to the principal focus is $x$. The magnification will be:

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