Modern Physics

# Divergent lens: characteristics, elements, types, applications

The divergent lenses are those that are thinner in its central part and thicker at the edges. As a consequence, they separate (differ) the light rays that hit them parallel to the main axis. Its extensions end up converging into the focus of the image to the left of the lens.

Divergent or negative lenses, as they are also known, form what we call virtual images of objects. They have multiple applications. In particular, ophthalmology is used to correct myopia and some types of astigmatism.

So if you suffer from nearsightedness and wear glasses, you have a perfect example of a divergent lens in your hand.

## Divergent lens characteristics

As explained above, diverging lenses are narrower at the center than at the edges. Furthermore, in this type of lens, one of its surfaces is always concave. This gives this type of lens several features.

For a start, the extent of the rays that affect them results in virtual images that cannot be collected on any type of screen. This is because the rays passing through the lens do not converge at any time, as they diverge in all directions. Also, depending on the curvature of the lens, the rays will open to a greater or lesser degree.

Another important feature of this type of lens is that the focus is to the left of the lens, so that it is between the lens and the subject.

Furthermore, with divergent lenses, the images are smaller than the object and are between the object and focus.

## Divergent lens elements

In studying them, it is essential to know which elements make up lenses in general and divergent lenses in particular.

The optical center of a lens is called the point through which the rays are not deflected. The main axis, however, is the line that joins the aforementioned point and the main focus, the latter being represented by the letter F.

The point at which all rays that strike the lens parallel to the main axis are called the main focus.

In this way, the distance between the optical center and the focus is called the focal length.

The centers of curvature are defined as the centers of the spheres that create the lens; In this way, the radii of curvature are the radii of the spheres that give rise to the lens. Y ya, finally, is called the optical plane to the central plane of the lens.

## Imaging

To graphically determine the formation of an image on a thin lens, it is only necessary to know the direction that two of the three rays whose trajectory is known will follo

One is the one that affects the lens parallel to the optical axis of the lens. Once refracted into the lens, this passes through the focus of the image. The second of the rays whose trajectory is known is the one that passes through the optical center. This will not change your trajectory.

The third and last is the one that passes through the object’s focus (or its extension crosses the object’s focus) which, after refraction, will follow a direction parallel to the optical axis of the lens.

In this way, in general, one type of image or another will be formed on the lens depending on the position of the object or body in relation to the lens.

However, in the particular case of diverging lenses, regardless of the position of the body in front of the lens, the image that will be formed will have certain characteristics. And is that in divergent lenses the image will always be virtual, smaller than the body and straight.

## applications

The fact that they can separate the light passing through them gives divergent lenses interesting qualities in the field of optics. This way they can correct myopia and some specific types of astigmatism.

Divergent ophthalmic lenses separate the light rays so that when they reach the human eye, they are further apart. Thus, when they go through the cornea and the lens, they go further and can reach the retina, executing the vision problems of people with myopia.

## Types

As we’ve already mentioned, converging lenses have at least one concave surface. For this reason, there are three types of divergent lenses: biconcave, plano-concave and convex-concave.

The biconcave divergent lenses are formed by two concave surfaces, the concave planes have a concave and flat surface, while in the convex-concave or divergent meniscus one surface is slightly convex and the other is concave.

## Differences with converging lenses

In converging lenses, unlike what happens in diverging lenses, the thickness decreases from the center to the edges. Thus, in this type of lens, light rays that strike parallel to the main axis are concentrated or converge on a single point (in focus). In this way they always create real images of objects.

In optics, converging or positive lenses are mainly used to correct nearsightedness, presbyopia and some types of astigmatism.

## Gaussian Equation of Lenses and Magnification of a Lens

The type of lens that is most commonly studied are called thin lenses. This defines all lenses whose thickness is very small compared to the radius of curvature of the surfaces that limit them.

The study of this type of lens can be carried out mainly through two equations: the Gauss equation and the equation that allows you to determine the magnification of the lens.

### Gaussian Equation

The importance of the thin-lens Gaussian equation lies in the large number of basic optical problems that can be solved. Its expression is as follows:

1 / f = 1 / p + 1 / q

Where 1 / f is the lens power and f is the focal length or distance from the optical center to the focus F. The unit of measurement of a lens power is the diopter (D), with the value 1 D = 1 m -1 . On the other hand, pyq are, respectively, the distance at which an object is located and the distance at which its image is observed.

## Exercise solved

A body is placed 40cm from a divergent lens of -40cm focal length. Calculate the height of the image if the object’s height is 5 cm. Also determine if the image is correct or inverted.

We have the following data: h = 5 cm; p = 40 cm; f = -40 cm.

These values ​​are substituted into the Gaussian thin lens equation:

1 / f = 1 / p + 1 / q

And you get:

1 / -40 = 1/40 + 1 / q

Where q = – 20 cm

Then we replace the result obtained earlier in the equation for magnifying a lens:

M = – q / p = – -20 / 40 = 0.5

Getting the value of the increase is:

M = h ‘ / h = 0.5

Deleting from this equation h ‘, which is the height value of the image, you get:

h’ = h / 2 = 2.5 cm.

The height of the image is 2.5 cm. Also, the image is correct since M> 0 and has decreased since the absolute value of M is less than 1.