Modern Physics

# Convergent lens: characteristics, types and solved exercise

The converging lenses are those that are thicker in its central part and thinner at the ends. As a result, they concentrate (converge) in a single point the light rays that strike them parallel to the main axis. This point is called the focus, or image focus, and is represented by the letter F. Converging or positive lenses form the which is called real images of objects.

A typical example of a converging lens is a magnifying glass. However, it is common to find this type of lens in much more complex devices such as microscopes or telescopes. In fact, a basic composite microscope consists of two converging lenses that have a short focal length. These lenses are called objective and eyepieces.

Magnifying glass, a converging lens.

Convergent lenses are used in optics for different applications, although perhaps the best known is to correct vision defects. Thus, they are indicated to treat farsightedness, presbyopia and also some types of astigmatism, such as farsightedness astigmatism.

## Characteristics

Converging lenses have several defining characteristics. In any case, perhaps the most important thing is what we have already advanced in defining it. Thus, converging lenses are characterized by deflecting through the focus any ray that strikes them in a direction parallel to the main axis.

Also, conversely, any incident beam passing through the focus is refracted parallel to the optical axis of the lens.

## Converging lens elements

For your study, it is important to know which elements constitute the lenses in general and the convergent lenses in particular.

In general, the optical center of a lens is called the point at which all rays passing through it are not deflected.

The main axis is the line joining the optical center and the main focus, which we already mentioned is represented by the letter F.

The main focus is called the point where all rays that strike the lens parallel to the main axis meet.

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; being, on the other hand, the radii of curvature of the radii of the spheres that give rise to the lens.

And finally, the center plane of the lens is called the optical plane.

## Image formation in converging lenses

For the formation of images in converging lenses, a series of basic rules explained below must be taken into account.

If the beam hits the lens parallel to the axis, the emerging beam will converge to the image focus. On the other hand, if an incident beam crosses the target’s focus, the beam emerges in a direction parallel to the axis. Finally, the rays that cross the optical center are refracted without suffering any kind of deviation.

As a consequence, the following situations can occur in a converging lens:

– That the object is located in relation to the optical plane at a distance greater than twice the focal length. In this case, the image produced is real, inverted and smaller than the object.

– That the object is located at a distance from the optical plane equal to twice the focal length. When this happens, the image obtained is a real image, inverted and the same size as the object.

– That the object is at a distance from the optical plane between one and two times the focal length. Then a produced image is real, inverted and larger than the original object.

– That the object is located at a distance from the optical plane less than the focal length. In this case, the image will be virtual, direct and larger than the object.

## Types of Converging Lenses

There are three different types of converging lenses: biconvex lenses, flat convex lenses, and concave convex lenses.

Biconvex lenses, as the name implies, consist of two convex surfaces. Meanwhile, convex planes have a flat, convex surface. And finally, concave-convex lenses consist of a slightly concave and convex surface.

## Difference with divergent lenses

Divergent lenses, on the other hand, differ from converging lenses in that the thickness decreases from the edges towards the center. Thus, unlike what happened with the convergents, in this type of lens the light rays that reach parallel to the main axis are separated. In this way they form what are called virtual images of objects.

In optics, divergent or negative lenses, as they are also known, are used primarily to correct nearsightedness.

## Gaussian Equations for Thin Lens and Magnifying a Lens

In general, the type of lens studied is the thin lens type. They are defined as those that have a small thickness compared to the radius of curvature of the surfaces that limit them.

This type of lens can be studied with the Gaussian equation and with the equation that allows you to determine the magnification of a lens.

### Gaussian Equation

The thin-lens Gaussian equation serves to solve many basic optical problems. Hence its great importance. Its expression is as follows:

1 / f = 1 / p + 1 / q

Where 1 / f is what is called the power of a lens and f is the focal length or distance from the optical center to the focus F. The unit of measurement for the power of a lens is the diopter (D), where 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.

### Magnifying a lens

The lateral magnification of a thin lens is obtained with the following expression:

M = – q / p

Where M is the increase. From the amount of the increase, a series of consequences can be deduced:

Yes | M | > 1, the image size is larger than the object

Yes | M | <1, the image size is smaller than the object

If M> 0, the image is correct and on the same side of the lens as the object (virtual image)

If M <0, the image is inverted and on the side opposite the object (real image)

## Exercise solved

A body is located one meter away from a converging lens, which has a focal length of 0.5 meters. What will the body image look like? How far will it be?

We have the following data: p = 1 m; f = 0.5 m.

We substitute these values ​​into the Gaussian thin lens equation:

1 / f = 1 / p + 1 / q

And the following remains:

1 / 0.5 = 1 + 1 / q; 2 = 1 + 1 / q

We clean 1 / q

1 / q = 1

To clean and get:

q = 1

Therefore, we substitute in the magnification equation for a lens:

M = – q / p = -1 / 1 = -1

Therefore, the image is real since q> 0, inverted because M<0 is of equal size, since the absolute value of M is 1. Finally, the image is one meter away from the focus.