The image formed by a convex mirror is only one-third of the size of t

1.	The image formed by a convex mirror is only one-third of the size of the object. If the focal length of the mirror is 12 cm, the image formed will beA. 8 cm behind the mirrorB. 10 cm behind the mirrorC. 8 cm in front of the mirrorD. 10 cm in front of the mirror
Answer» Given Height of image(h_i) = \(\frac{height\,of\,object (h_o)}{3}\) focal length of mirror (f) = 12 cm m = \(\frac{h_i}{h_o}\,=\,\frac{-v}{u}\,=\,\frac{1}{3}\,\implies\) u = - 3v Using Mirror formula, \(\implies\,\frac{1}{v}\,+\frac{1}{u}\,=\,\frac{1}{f}\) \(\implies\,\frac{1}{v}\,+\,\frac{1}{-3v}\,=\,\frac{1}{12}\) \(\implies\,\frac{2}{3v}\,=\,\frac{1}{12}\) \(\implies\)v = 8 cm As v is positive, so image is formed at 8 cm behind the mirror

The image formed by a convex mirror is only one-third of the size of the object. If the focal length of the mirror is 12 cm, the image formed will beA. 8 cm behind the mirrorB. 10 cm behind the mirrorC. 8 cm in front of the mirrorD. 10 cm in front of the mirror

Answer»

Given

Height of image(h_i) = \(\frac{height\,of\,object (h_o)}{3}\) focal length of mirror (f) = 12 cm

m = \(\frac{h_i}{h_o}\,=\,\frac{-v}{u}\,=\,\frac{1}{3}\,\implies\) u = - 3v

Using Mirror formula, \(\implies\,\frac{1}{v}\,+\frac{1}{u}\,=\,\frac{1}{f}\)

\(\implies\,\frac{1}{v}\,+\,\frac{1}{-3v}\,=\,\frac{1}{12}\)

\(\implies\,\frac{2}{3v}\,=\,\frac{1}{12}\)

\(\implies\)v = 8 cm

As v is positive, so image is formed at 8 cm behind the mirror