The focal length of a convex lens is f. An ob | vedclass

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(C) The focal length of the convex lens is given as $f$. The object is placed at a distance $x$ from the first focal point. Since the first focal poin

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$\frac{f}{x}$

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(C) The focal length of the convex lens is given as $f$. The object is placed at a distance $x$ from the first focal point. Since the first focal point is at a distance $f$ from the optical center,the total object distance $u$ from the optical center is $u = -(f + x)$. Using the lens formula,$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$. Substituting $u = -(f + x)$,we get $\frac{1}{v} - \frac{1}{-(f + x)} = \frac{1}{f}$. $\frac{1}{v} = \frac{1}{f} - \frac{1}{f + x} = \frac{f + x - f}{f(f + x)} = \frac{x}{f(f + x)}$. Thus,$v = \frac{f(f + x)}{x}$. The magnification $m$ is given by $m = \frac{v}{u}$. $m = \frac{\frac{f(f + x)}{x}}{-(f + x)} = -\frac{f}{x}$. The ratio of the size of the real image to the object is the magnitude of magnification,which is $|m| = \frac{f}{x}$.

The focal length of a convex lens is $f$. An object is placed at a distance $x$ from its first focal point. The ratio of the size of the real image to that of the object is

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