A doctor has prescribed a corrective lens of power \(+1.5 \mathrm{D}\). Find the focal length of the lens. Is the prescribed lens diverging or converging?

The lens formula is a simple yet powerful tool in optics.
It is defined as the relationship between the power of a lens (P) and its focal length (f).
The formula is as follows: \[ P = \frac{1}{f} \]
Here, 

• P stands for the power of the lens, measured in diopters (D).
• f is the focal length of the lens, measured in meters (m).

This equation helps in calculating either the power or focal length of a lens if one of the values is known.
It is especially useful in applications such as eye prescriptions, magnifying glasses, and other optical devices.
In our example, the given power is \(+1.5 D\). By rearranging the lens formula, we can solve for the focal length: \[ f = \frac{1}{P} \] This rearranged formula allows easy calculation of the focal length.
Simply plug the power into the formula to find the focal length.

Focal length is the distance between the center of a lens and its focus point.
It is crucial for understanding how lenses bend light.
In our specific problem, the power of the lens is given as \( +1.5 D \).
We can determine the focal length using the lens formula rearranged: \[ f = \frac{1}{P} \].
Substituting the given power: \[ f = \frac{1}{1.5} \]
Simplifying this: \( f = \frac{10}{15} = 0.67 \text{ meters}\).
Thus, the focal length of this lens is 0.67 meters or 67 centimeters.
Understanding this value helps in knowing how much the light will bend through the lens, which is crucial for applications like correcting vision.

Lenses can either be converging or diverging.
This distinction plays a significant role in how they affect light.

A converging lens (also known as a convex lens) has positive power.
It bends light rays towards a focal point.

• They are thicker in the middle and thinner at the edges.
• Commonly used in applications like magnifying glasses and corrective lenses for hyperopia (farsightedness).

In contrast, a diverging lens (also known as a concave lens) has negative power.
It spreads light rays away from a focal point.

• They are thinner in the middle and thicker at the edges.
• These lenses are used in applications like correcting myopia (nearsightedness).

In our example, the given prescription is \( +1.5 D\), indicating a positive power.
Thus, the lens is converging.
Understanding the type of lens helps in knowing how it will affect vision and other optical outcomes.