Calculating Lens Power for Concave Lens

This solution explains how to determine the power of a concave lens using its given focal length.

Understanding Lens Power

The power of an optical lens quantifies its ability to refract, or bend, light. It is mathematically defined as the inverse of the focal length when the focal length is measured in meters.

The formula relating power (\(P\)) and focal length (\(f\)) is:

\(P = \frac{1}{f}\)

Here:

• \(P\) represents the lens power, measured in Diopters (D).
• \(f\) denotes the focal length of the lens, measured in meters (m).

Sign Convention for Concave Lenses

A fundamental rule in optics is the sign convention. For a concave lens, the focal length is always negative (\(f < 0\)). This is because a concave lens diverges light rays, and its principal focus is considered virtual.

Applying the Formula to the Given Problem

We are provided with the following information:

• The focal length (\(f\)) of the concave lens is \(0.5\) m.
• According to the sign convention, since it is a concave lens, we must use \(f = -0.5\) m for calculations.

Step-by-Step Calculation

1. Identify Given Value: The focal length is stated as \(0.5\) m.
2. Apply Sign Convention: As it is a concave lens, the focal length \(f = -0.5\) m.
3. Use the Power Formula: Recall the formula \(P = \frac{1}{f}\).
4. Substitute the Value: Insert the effective focal length into the formula: \(P = \frac{1}{-0.5 \text{ m}}\)
5. Calculate the Result: Performing the division gives the power: \(P = -2.0 \text{ D}\)

Conclusion

Therefore, the power of the concave lens with a focal length of \(0.5\) m is \(-2.0\) Diopters.