Question

If the distances of the object and its real image from the principal focus of a concave mirror are 16 cm and 9 cm respectively, then the focal length of the mirror is

• A. 30 cm
• B. 12 cm
• C. 18 cm
• D. 24 cm

Hint:

Newton's formula, \(f^2 = x_1 x_2\), is a powerful shortcut for problems where distances are given relative to the focus, not the pole. It is much faster than using the standard mirror formula \(1/f = 1/v + 1/u\) in these specific cases.

Answer 1

The Correct Option is B

This problem can be solved using Newton's formula for mirrors.
Newton's formula states that \( f^2 = x_1 x_2 \), where f is the focal length, \(x_1\) is the distance of the object from the principal focus, and \(x_2\) is the distance of the image from the principal focus.
We are given:
Distance of the object from the focus, \( x_1 = 16 \) cm.
Distance of the real image from the focus, \( x_2 = 9 \) cm.
Substitute these values into Newton's formula:
\( f^2 = 16 \times 9 = 144 \).
Taking the square root to find the focal length:
\( f = \sqrt{144} = 12 \) cm.
The focal length of the concave mirror is 12 cm.