Question

A man holds a spherical shaving mirror of radius of curvature 60 cm, and focal length 30 cm, at a distance of 15 cm, from his nose. Find the position of image, and calculate the magnification.

Answer 1

Distance of the object, i.e. nose, from the mirror (u) = -15 cm
The focal length of the concave mirror (f) = -30 cm

We have to find the distance of the image (v).

Using the mirror formula, we get
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{-30}=\frac{1}{v}-\frac{1}{15}$

$$\begin{gathered} \mathrm{or}\frac{1}{v}=\frac{1}{15}-\frac{1}{30} \\ \mathrm{or}\frac{1}{v}=\frac{2-1}{30} \\ \mathrm{or}\frac{1}{v}=\frac{1}{30} \\ \mathrm{v}=30\mathrm{cm} \end{gathered}$$

Thus, the position of the image is 30 cm behind the mirror.

Now, using the magnification formula, we get

$m=\frac{-\mathrm{v}}{\mathrm{u}}$

$m=\frac{-30}{-15}=2$

Therefore, the image is 2 times magnified than the object.