Question

The figure shows a spherical concave mirror of radius of curvature $R=10\text{cm}$, with its pole at $(0,0)$ and principal axis along $x-$axis. There is a point object $O$ at $(-40\text{cm},1\text{cm})$. The position of the image is :

• A. $(\frac{-40}{7}\text{cm},\frac{-1}{7}\text{cm})$
• B. $(\frac{+40}{7}\text{cm},\frac{+1}{7}\text{cm})$
• C. $(\frac{-20}{7}\text{cm},\frac{-1}{7}\text{cm})$
• D. $(\frac{+20}{7}\text{cm},\frac{+1}{7}\text{cm})$

Answer 1

The correct option is A $(\frac{-40}{7}\text{cm},\frac{-1}{7}\text{cm})$

Here, $u=-40\text{cm}$
$f=\frac{-10}{2}=-5\text{cm}$
$[$as per sign convention$]$
So, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{40}=\frac{-1}{5}$
$\Rightarrow \frac{1}{v}=\frac{-7}{40}$
$\Rightarrow v=\frac{-40}{7}\text{cm}$
Also, magnification,
$m=\frac{-v}{u}=\frac{\frac{40}{7}}{-40}=\frac{-1}{7}$
So, $\frac{h_i}{h_o}=\frac{-1}{7}$
$\Rightarrow h_i=\frac{-1}{7}\times h_o=\frac{-1}{7}\times 1=\frac{-1}{7}\text{cm}$