Question

A concave mirror is used to form an image of an object. The object distance (u) is 30 cm and the image distance (v) is 15 cm. Calculate the focal length (f) of the mirror.

• A. -10 cm
• B. -30 cm
• C. 10 cm
• D. 30 cm

Hint:

Always remember the sign convention: for mirrors, real objects and real images are formed in front of the mirror, meaning their distances (\(u\) and \(v\)) are negative. Concave mirrors have a negative focal length.

Answer 1

The Correct Option is A

To find the focal length of the concave mirror, we will use the mirror formula:

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

Where:

• \(f\) is the focal length of the mirror,
• \(v\) is the image distance, and
• \(u\) is the object distance.
• In concave mirrors, the focal length is negative, and distances are measured with respect to the mirror's pole.

 

Given:

• Object distance, \(u = -30 \, \text{cm}\)
• Image distance, \(v = -15 \, \text{cm}\)

We follow the sign conventions for mirrors (distances measured in the direction of incident light are positive; otherwise, they are negative).

Substitute the given values into the mirror formula:

\(\frac{1}{f} = \frac{1}{-15} + \frac{1}{-30}\)

Calculate the right-hand side:

\(\frac{1}{f} = -\frac{1}{15} - \frac{1}{30}\)

Find a common denominator:

\(\frac{1}{f} = -\frac{2}{30} - \frac{1}{30} = -\frac{3}{30}\)

Therefore:

\(\frac{1}{f} = -\frac{1}{10}\)

This gives us the focal length:

\(f = -10 \, \text{cm}\)

Thus, the correct answer is -10 cm, which matches the given correct answer option.