Question

An object is placed at a distance of 24 cm from a convex mirror. Its image is formed behind the mirror at a distance of 6 cm. The focal length of convex mirror is

Answer 1

-8 cm

Answer 2

We use the mirror formula:

$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$

For a convex mirror, the image is virtual so its distance is taken as negative (using the sign convention where the object distance $u$ is positive):

• $u = 24 \text{ cm}$
• $v = -6 \text{ cm}$

Plugging in the values:

$$\frac{1}{f} = \frac{1}{24} + \left(-\frac{1}{6}\right) = \frac{1}{24} - \frac{4}{24} = -\frac{3}{24} = -\frac{1}{8}$$

Thus,

$$f = -8 \text{ cm}$$

The negative sign indicates the focal length for a convex mirror (according to the sign convention).