An object placed 20 cm in front of a mirror is found to have an image 15 cm (a) in front of it, (b) behind the mirror. Find the focal length of the mirror and the kind of mirror in each case.
(a) u = -20 cm, f = 12 cm, v = ?
We know that
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{-15}\) + \(\frac{1}{-20}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{f}\) = -\(\frac{1}{15}\) - \(\frac{1}{20}\)
= \(\frac{-4 - 3}{60}\)
= -\(\frac{7}{60}\)cm
∴ f = -\(\frac{60}{7}\) cm
The mirror is a concave mirror.
(b) u = -20 cm, v = 15 cm
We know that
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{15}\) + \(\frac{1}{-20}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{f}\) =\(\frac{1}{15}\) - \(\frac{1}{20}\)
= \(\frac{4 - 3}{60}\)
= \(\frac{1}{60}\)
∴ f = 60 cm
The mirror is a convex mirror.