Question

At what distance should an object be placed from a concave mirror of focal length 10 cm, so that a real image 5 times larger is formed? Also, find the position of the image.

Hint:

A real and inverted image means the image distance is negative.

Answer 1

Let the object distance be \( u \) and the image distance be \( v \). Given that the magnification \( m \) is -5 for a real and inverted image, we use: \[ m = \frac{-v}{u} \] \[ v = -5u \] Using the mirror formula: \[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \] Substituting \( f = -10 \) cm and \( v = -5u \): \[ \frac{1}{-10} = \frac{1}{u} + \frac{1}{-5u} \] Solving, we get \( u = -12 \) cm and \( v = -60 \) cm.