An object is placed (a) 20 cm, (b) 4 cm, in front of a concave mirror of focal length 12 cm. Find the nature and position of the image formed in each case.
(a) u = -20 cm, f = -12 cm
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{v}\) + \(\frac{1}{-20}\) = \(\frac{1}{-12}\)
\(\frac{1}{v}\) = \(\frac{-1}{12}\) + \(\frac{1}{20}\)
= \(\frac{-20 + 12}{240}\) = \(\frac{-8}{240}\)
v = -30 cm
The image is formed at a distance of 30 cm in front of the mirror.
The image is real and inverted.
(b) u = -4 cm, f = -12 cm
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{v}\) + \(\frac{1}{-4}\) = \(\frac{1}{-12}\)
\(\frac{1}{v}\) = \(\frac{-1}{12}\) + \(\frac{1}{4}\)
\(\frac{-1 + 3}{12}\) = \(\frac{2}{12}\)
v = 6 cm
The image is formed at a distance of 6 cm behind the mirror.
The image is virtual and erect.