Understanding Lens Power and Focal Length

The question asks us to identify the type of lens and its focal length given its power. Lens power is a measure of how much a lens converges or diverges light. It is related to the focal length of the lens.

Relationship Between Power and Focal Length

The power of a lens (P) is defined as the reciprocal of its focal length (f), provided the focal length is measured in meters. The unit of power is Diopter (D).

The formula is:

P = \frac{1}{f} (where f is in meters)

Calculating Focal Length from Power

We are given the power of the lens, P = -2.5 D.

We can rearrange the formula to find the focal length:

f = \frac{1}{P}

Substituting the given power value:

f = \frac{1}{-2.5 \text{ D}}

To calculate this, we can write -2.5 as a fraction:

-2.5 = -\frac{25}{10} = -\frac{5}{2}

So, the focal length is:

f = \frac{1}{-\frac{5}{2}} = -\frac{2}{5} \text{ meters}

Converting the fraction to a decimal:

-\frac{2}{5} = -0.4

Therefore, the focal length is -0.40 \text{ m}.

Determining the Type of Lens

The sign of the lens power indicates the type of lens:

• A positive power (and thus a positive focal length) corresponds to a converging lens, which is typically a convex lens.
• A negative power (and thus a negative focal length) corresponds to a diverging lens, which is typically a concave lens.

In this problem, the power is given as P = -2.5 D, which is a negative value. This indicates that the lens is a diverging lens.

A diverging lens is a concave lens.

The focal length we calculated is -0.40 \text{ m}, which is also negative, confirming it is a diverging or concave lens.

Summary

Based on the given power -2.5 \text{ D}:

• The negative sign of the power tells us the lens is a concave lens.
• The focal length is calculated as f = \frac{1}{P} = \frac{1}{-2.5} = -0.40 \text{ m}.

So, the type of lens is Concave, and its focal length is -0.40 m.

Revision Table: Lens Types and Properties

Additional Information: Importance of Lens Power

Lens power is a very practical concept, especially in ophthalmology. Spectacle prescriptions are given in terms of lens power (in Diopters). This allows opticians to easily determine the correct lenses needed to correct vision problems like myopia (nearsightedness, corrected with concave lenses of negative power) or hyperopia (farsightedness, corrected with convex lenses of positive power).

The unit Diopter is defined as the reciprocal of the focal length in meters. So, a lens with a focal length of 1 meter has a power of 1 Diopter. A stronger lens (one that converges or diverges light more strongly) has a shorter focal length and thus a higher absolute power value.