Question

The power of a lens is $ 4 \, D $. Its focal length is

• A. \( 0.25 \, cm \)
• B. \( 2.5 \, cm \)
• C. \( 25 \, cm \)
• D. \( 0.025 \, cm \)

Hint:

Remember that the formula \( P = \frac{1}{f} \) requires the focal length to be in meters. Don't forget to convert the units if the answer is required in centimeters or other units.

Answer 1

The Correct Option is C

Step 1: Recall the relationship between the power of a lens and its focal length.
The power \( P \) of a lens in diopters (D) is the reciprocal of its focal length \( f \) in meters (m): \[ P = \frac{1}{f} \]
Step 2: Convert the given power to find the focal length in meters.
Given power \( P = 4 \, D \), we can find the focal length \( f \): \[ 4 = \frac{1}{f} \] \[ f = \frac{1}{4} \, m \] \[ f = 0.25 \, m \]
Step 3: Convert the focal length from meters to centimeters.
Since \( 1 \, m = 100 \, cm \), we can convert the focal length: \[ f = 0.25 \, m \times \frac{100 \, cm}{1 \, m} \] \[ f = 25 \, cm \] The focal length of the lens is \( 25 \, cm \).