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(B) For a convex mirror,the mirror formula is $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Given the reflecting surface is towards the negative $x-$ axis

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(B) For a convex mirror,the mirror formula is $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Given the reflecting surface is towards the negative $x-$ axis,the focal length is positive,so $f = +f_0$ (where $f_0 > 0$).For real objects,the object distance $u$ is negative,so let $u = -x$ where $x > 0$.The mirror formula becomes $\frac{1}{v} + \frac{1}{-x} = \frac{1}{f_0} \Rightarrow \frac{1}{v} = \frac{1}{f_0} + \frac{1}{x} = \frac{x + f_0}{x f_0}$.Thus,$v = \frac{x f_0}{x + f_0}$.As $x 	o 0$,$v 	o 0$.As $x 	o \infty$,$v 	o f_0$.Since $v$ is always positive and less than $f_0$,the graph represents a curve starting from the origin $(0,0)$ and asymptotically approaching $v = f_0$ as $u$ becomes more negative. This corresponds to the curve shown in option $B$.

$A$ convex mirror of focal length $f$ is placed at the origin with its reflecting surface towards the negative $x-$ axis. Choose the correct graph between $v$ and $u$ for $u < 0$.

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