Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

From mirror formula, we know that

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

For $u<0$, the objects are real in nature.

Image distance is given by $v=\frac{uf}{u-f}$

In case of a convex mirror, for a real object, image formed is virtual in nature. So, $v>0$.

$\therefore$ Graph lies in $2^{nd}$ Quadrant.

As the object is moved towards pole, the magnification increases and tends to unity at the poles.

$\Rightarrow$ The slope of the graph of $v$ vs $u$ in $2^{nd}$ Quadrant should increase negatively.

So, when $u=0$, then ${}^{\prime }{v}^{\prime }$ will also be zero.

Hence, option (c) is the correct answer.