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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 $u < 0$.

Similar Questions

What is the nature of the image formed for an object placed on the principal axis of a concave mirror between the pole and the focus?

$A$ spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror,what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)

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Reason $(R):$ The laws of reflection are strictly valid for plane surfaces but not for large spherical surfaces.

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