Question

A concave mirror produces three times enlarged image of an object placed at 10 cm in front of it. Calculate the focal length of the mirror. Show the formation of the image with the help of a ray diagram when object is place at 6 cm away from the pole of a convex mirror.

Answer 1

A. The focal length of the mirror is 15cm

B. See the attached image below for the ray diagram.

How to determine the focal length of the mirror?

Given:

Magnification,
`\(m = 3\)`

Object distance,
`\(u = 10 \, \text{cm}\)`

We know:

`\[ m = (v)/(u) = (-v)/(-10) = 3 \]`

This implies:
`\(v = 30 \, \text{cm}\)`

Using the mirror formula:

`\[ (1)/(f) = (1)/(v) + (1)/(u) = (1)/(30) + (1)/(10) \]`

`\[ (1)/(f) = (10 - 30)/(30 * 10) = (-20)/(300) \]`

`\[ f = 15 \, \text{cm} \]`

Hence, the focal length of the mirror is
`\(15 \, \text{cm}\)`.

Focal length refers to a fundamental characteristic of optical systems, such as lenses and mirrors. It is the distance between the optical center (or principal point) of the lens or mirror and its focal point