Determine the focal length of a thin converging lens if the power is 5.0 dioptres

Analysis

The question asks for the focal length of a converging lens given its power in dioptres. This is a standard optics problem involving the relationship between the power of a lens and its focal length.

Concept

The power ($P$) of a lens is defined as the reciprocal of its focal length ($f$) when the focal length is measured in metres. The formula is:

Where:

• $P$ is the power measured in dioptres ($D$).
• $f$ is the focal length measured in metres ($m$).

Solution

1. Identify the given information: • Power ($P$) = $5.0\text{ D}$

2. Rearrange the formula to solve for $f$: $$f = \frac{1}{P}$$

3. Substitute the values into the formula: $$f = \frac{1}{5.0}$$

4. Calculate the result: $$f = 0.2\text{ m}$$

The focal length of the lens is $0.2\text{ metres}$.

Conclusion

Comparing our result to the given options: A. 0.1 m B. 0.2 m C. 2.0 m D. 2.5 m

The correct option is B.

Exam Tip

Always remember that the unit for focal length must be in metres when using the power formula. If the question gives you the focal length in centimetres (e.g., $20\text{ cm}$), you must convert it to metres ($0.2\text{ m}$) before calculating the power, or use the formula $P = \frac{100}{f(\text{in cm})}$. This simple check prevents common calculation errors in JAMB Physics!