Question

For a plane mirror oriented as shown in the figure, the relation between object distance $\left(u\right)$ and image distance $\left(v\right)$ from the mirror, can be best represented by which graph?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

We know that by sign convention, the direction of the incident ray is taken as positive and its opposite is considered negative.
Thus, object distance $\left(u\right)$ is negative and image distance $\left(v\right)$ is positive.
Also, object distance $\left(u\right)$ $=$ image distance $\left(v\right)$, for a plane mirror.

So,
$v=-u$ .............$\left(1\right)$
On comparing $\left(1\right)$ with the equation of straight line $y=mx+c$, we get,
$\Rightarrow \text{slope}=m=-1$
$\Rightarrow \tan \theta =-1$
$\Rightarrow \theta =-{45}^{\circ }$ or ${135}^{\circ }$
with $+x$ - axis.
So, the graph will be as shown below.

Hence, $\left(A\right)$ is the correct answer.