The distance of a real object from the focus | vedclass

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(D) For a convex mirror,the focal length $f = +\frac{a}{2}$.The object is placed at a distance $b$ from the focus. Since the object is real,it is plac

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none of these

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(D) For a convex mirror,the focal length $f = +\frac{a}{2}$.The object is placed at a distance $b$ from the focus. Since the object is real,it is placed in front of the mirror. The distance of the object from the pole is $u = -(b + \frac{a}{2})$.Using the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$:$\frac{1}{v} + \frac{1}{-(b + a/2)} = \frac{1}{a/2}$$\frac{1}{v} = \frac{2}{a} + \frac{1}{b + a/2} = \frac{2}{a} + \frac{2}{2b + a}$$\frac{1}{v} = \frac{2(2b + a) + 2a}{a(2b + a)} = \frac{4b + 4a}{a(2b + a)}$$v = \frac{a(2b + a)}{4(b + a)}$The distance of the image from the focus is $|v - f|$:$|v - f| = |\frac{2ab + a^2}{4(b + a)} - \frac{a}{2}| = |\frac{2ab + a^2 - 2a(b + a)}{4(b + a)}|$$= |\frac{2ab + a^2 - 2ab - 2a^2}{4(b + a)}| = |\frac{-a^2}{4(b + a)}| = \frac{a^2}{4(b + a)}$Since this result is not among the options,the correct answer is $D$.

The distance of a real object from the focus of a convex mirror of radius of curvature $a$ is $b$. Then the distance of the image from the focus is

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