The power of a lens in diopters is

Analysis

The question asks for the mathematical definition of the power of a lens, specifically when measured in diopters.

Concept

In optics, the power of a lens ($P$) is a measure of its ability to converge or diverge light rays. It is defined as the reciprocal of the focal length ($f$) of the lens, provided that the focal length is measured in meters.

The unit of power is the diopter (D), where $1 \text{ diopter} = 1 \text{ m}^{-1}$.

The formula is expressed as:

Solution

1. Identify the relationship: The power of a lens is inversely proportional to its focal length.
2. Apply the unit constraint: For the power to be expressed in diopters, the focal length $f$ must be in meters.
3. Formulate the equation: $P = \frac{1}{f}$.
4. Compare with the given options: • Option A: $3f$ (Incorrect) • Option B: $\frac{1}{f}$ (Correct) • Option C: $2f$ (Incorrect) • Option D: $f$ (Incorrect)

Exam Tip

Always check the units! If a JAMB question gives you the focal length in centimeters (cm), you must convert it to meters (m) by dividing by 100 before using the formula $P = \frac{1}{f}$. For example, if $f = 20\text{ cm}$, convert it to $0.2\text{ m}$, then $P = \frac{1}{0.2} = 5\text{ diopters}$.