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(A) For a concave mirror,the mirror formula is given by: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Using sign convention,$f = -|f|$. Thus,$\frac{1}{v}

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(A) For a concave mirror,the mirror formula is given by: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Using sign convention,$f = -|f|$. Thus,$\frac{1}{v} = -\frac{1}{|f|} - \frac{1}{u}$.$1$. When $u = 0$,$\frac{1}{v} = -\infty$,so $v = 0$.$2$. When $u = |f|$,$\frac{1}{v} = -\frac{1}{|f|} + \frac{1}{|f|} = 0$,so $v = \infty$.$3$. When $u = \infty$,$\frac{1}{v} = -\frac{1}{|f|}$,so $v = -|f|$.As $u$ increases from $0$ to $|f|$,$v$ changes from $0$ to $-\infty$. As $u$ increases from $|f|$ to $\infty$,$v$ changes from $+\infty$ to $-|f|$.Comparing these characteristics with the given graphs,option $A$ correctly represents this behavior.

As the position of an object $(u)$ reflected from a concave mirror is varied,the position of the image $(v)$ also varies. By letting the $u$ change from $0$ to $+\infty$,the graph between $v$ versus $u$ will be:

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