Question

A magnified, inverted image is located a distance of 32.0 cm from a concave mirror with a focal length of 12.0 cm. Determine the object distance and tell whether the image is real or virtual.

Answer 1

Given,

Image distance, $v=32cm$

Focal length, $f=12cm$

From mirror formula,

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

$\Rightarrow \frac{1}{-12}=\frac{1}{-32}+\frac{1}{u}$

$\Rightarrow \frac{1}{u}=\frac{1}{32}-\frac{1}{12}$

$=\frac{12-32}{32\times 12}=-\frac{20}{32\times 12}=\frac{-5}{96}$

$u=\frac{-96}{5}=-19.2cm$