Find the focal length of a lens of power \(-2.0 \mathrm{D}\). What type of lens is this?

The power of a lens is a fundamental concept in optics. It tells how strongly a lens converges or diverges light. The power (P) of a lens is measured in diopters (D), and it is related to the focal length (f) using the simple formula: \[ P = \frac{1}{f} \] Here, \( P \) is in diopters, which is the reciprocal of the focal length in meters. So, if you have a lens with a power of -2.0 D, you can find its focal length by rearranging the formula as such: \[ f = \frac{1}{P} \] By substituting \( P = -2.0 \) into the equation, you’ll get: \[ f = \frac{1}{-2.0} = -0.5 \] The negative focal length indicates that the lens has specific properties that we will explore further in the next sections.

A diverging lens is a lens used to spread out light rays that are initially traveling parallel to its principal axis. These lenses are typically thinner in the middle and thicker at the edges, making them look as if they are bent inward. When parallel light rays pass through a diverging lens, they are refracted outward, causing the rays to diverge away from a common point. This point is known as the focal point, and it lies on the same side of the lens as the incoming light rays. Because the rays don't actually converge on this point, it’s called a virtual focal point.
If the calculated focal length is negative, it means we are dealing with a diverging lens. This fits our exercise since we found a focal length of -0.5 meters when given a lens power of -2.0 D. Therefore, this lens causes light rays to spread out and is classified as a diverging lens.

A concave lens is another term for a diverging lens. It is named for its shape: concave, which means curving inward. This curve causes light rays to diverge as they pass through the lens. Concave lenses are commonly used in a variety of optical devices such as glasses to correct for short-sightedness (myopia), cameras, and laser beams.
These lenses have unique characteristics:

• They spread light rays apart.
• They produce virtual images that are upright and smaller compared to the object.
• They have negative focal lengths.

In our exercise, the lens had a power of -2.0 D, leading to a negative focal length of -0.5 meters. Thus, this negative focal length signifies a concave lens, making it clear that the lens in the problem is used to diverge light rays.