Question

The focal length of a convex lens is 50 cm. State the position of the image of an object placed at a distance of 25 cm, perpendicularly on its axis. Also, determine the magnification of the image.

Hint:

A negative image distance in convex lenses indicates a virtual image.

Answer 1

Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Given \( f = 50 \) cm and \( u = -25 \) cm: \[ \frac{1}{50} = \frac{1}{v} - \frac{1}{-25} \] \[ \frac{1}{v} = \frac{1}{50} - \frac{1}{25} = \frac{1}{50} - \frac{2}{50} = \frac{-1}{50} \] \[ v = -50 \text{ cm} \] The image is formed at -50 cm, meaning it is virtual and on the same side as the object.
Magnification is given by: \[ m = \frac{v}{u} = \frac{-50}{-25} = 2 \] Thus, the image is magnified and erect.