Question

In a concave mirror, the image is formed at a distance 'b' from the focus when an object is placed at a distance 'a' from the focus. What will be focal length of the mirror?
1. ab
2. a + b
3. √ab
4. \(a+b \over 2\)

Answer 1

Correct Answer - Option 3 : √ab

CONCEPT:

• Concave mirror: The mirror in which the rays converge after falling on it is known as the concave mirror.
  • Concave mirrors are also known as a converging mirror.
  • The focal length of a concave mirror is negative according to the sign convention.
• Mirror Formula: The following formula is known as the mirror formula:

\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

where f is focal length v is the distance of the image from the mirror, and u is the distance of the object from the mirror.

EXPLANATION:

Let the focal length of the mirror is f.

Given that u = - (a + f) and v = - (b + f)

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

\(-\frac{1}{f}=-\frac{1}{a +f}-\frac{1}{b+f}\)        (since focal length of a concave mirror is negative)

\(\frac{1}{f}=\frac{(a +f)+(b +f)}{(a +f)(b +f)}\)

It will be a quadratic equation. On solving it

f² = ab

f = √ab 

So the correct answer is option 3.