A spherical mirror produces an image of magnification -1.0 on a screen placed at a distance of 20 cm from the pole of the mirror.
(i) Write the type of mirror in this case.
(ii) What is the focal length of the mirror ?
(iii) What is the nature of the image formed?

Dear Student,
Given,
Magnification, M = -1.0
image distance, v = 20 cm

(i). ​​​​​Since, the magnification is negative, the image must be inverted which is the case for real images only. Concave mirrors provide real images. Hence,  the mirror must be a concave mirror.

(ii)
 $$\begin{gathered} M=\frac{height of the image}{\mathrm{si}ze of the object}=-\frac{image dis\tan ce \left(v\right)}{object dis\tan ce \left(u\right)}=-1 \\ Hence, \\ u=v \end{gathered}$$
This is the case when the object is placed at at the centre of curvature, i.e., when the image distance = Radius of curvature of the mirror (R).
u = R = 2f
where, f is the focal length of the mirror.
So,
2f = 20 cm
Hence,
f = 10 cm

(iii) The image formed is real, inverted and is of the same size as that of the object.

Regards