Question

The co-ordinates of the image of point object $P$ formed by a concave mirror of radius of curvature $20\text{cm}$ (consider paraxial rays only) as shown in the figure is.

• A. $(-13.33\text{cm};-1\text{cm})$
• B. $(13.33\text{cm};+1\text{cm})$
• C. $(-13.33\text{cm};+1\text{cm})$
• D. $(13.33\text{cm};-1\text{cm})$

Answer 1

The correct option is D $(13.33\text{cm};-1\text{cm})$

Radius of curvature $R=20=2f$
$f=\frac{20}{2}=10\text{cm}$
Mirror formula
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\frac{1}{-10}=\frac{1}{v}-\frac{1}{40}\Rightarrow \frac{-1}{10}+\frac{1}{40}=\frac{1}{v}\Rightarrow v=-\frac{40}{3}\text{cm}$
$v=-13.33\text{cm}$

Magnification $m=\frac{-v}{u}=\frac{hi}{ho}\Rightarrow h_i=\frac{-\left(\frac{-40}{3}\right)}{-40}{h}_o=\frac{-1}{3}\times 3$
$h_i=-1\text{cm}$
Hence the coordinates of image $(13.33\text{cm},-1\text{cm})$