Question

If the focal length of the lens is f and power is P then

• A. \(f + P = 0.5\)
• B. \(f \times P = 1\)
• C. \(P + f = 1\)
• D. \(P + f = 2\)

Hint:

Always remember the unit convention for the power of a lens formula. If the focal length is given in centimeters (cm), you must convert it to meters before calculating the power in diopters. The formula becomes \( P(D) = \frac{100}{f(cm)} \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The power (P) of a lens is a measure of its ability to converge or diverge light. It is defined as the reciprocal of its focal length (f).

Step 2: Key Formula or Approach:
The formula relating the power of a lens and its focal length is:
\[ P = \frac{1}{f} \] A crucial condition for this formula is that the focal length \(f\) must be measured in meters (m) for the power \(P\) to be in diopters (D).

Step 3: Detailed Explanation:
Starting with the formula \( P = \frac{1}{f} \).
If we multiply both sides of the equation by \(f\), we get:
\[ P \times f = \frac{1}{f} \times f \] \[ P \times f = 1 \] This relationship holds true as long as the units are consistent (focal length in meters and power in diopters).

Step 4: Final Answer:
Therefore, the correct relationship between the focal length \(f\) and power \(P\) of a lens is \(f \times P = 1\).