CONVERGING LENS: CHARACTERISTICS, TYPES AND SOLVED EXERCISE - PHYSICAL - 2025

The converging lenses are those thinner at the edges that are thicker in its central part. As a consequence, they concentrate (converge) the rays of light that fall on them parallel to the main axis at a single point. This point is called the focus, or image focus, and is represented by the letter F. Converging or positive lenses form what are 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 compound microscope is one made up of two converging lenses that have a small focal length. These lenses are called objective and ocular.

Magnifying glass, a converging lens.

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

characteristics

Converging lens. Chetvorno

Converging lenses have a number of characteristics that define them. In any case, perhaps the most important is the one that we have already advanced in its definition. Thus, convergent lenses are characterized by deflecting through the focus any ray that falls on them in a direction parallel to the main axis.

Furthermore, reciprocally, any incident ray that passes the focus is refracted parallel to the optical axis of the lens.

Converging lens elements

For its study, it is important to know what elements make up lenses in general and converging lenses in particular.

In general, it is called the optical center of a lens to the point where every ray that passes through it does not experience any deflection.

The main axis is the line that joins the optical center and the main focus, which we have already commented, is represented by the letter F.

The main focus is the point where all the rays that hit the lens are parallel to the main axis.

The focal length is the distance between the optical center and the focus.

The centers of curvature are defined as the centers of the spheres that create the lens; The radii of curvature being the radii of the spheres that give rise to the lens.

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

Image formation in converging lenses

In order to form the images in converging lenses, a series of basic rules must be taken into account, which are explained below.

If the beam strikes the lens parallel to the axis, the emerging beam converges on the image focus. Conversely, if an incident ray passes through the object focus, the ray emerges in a direction parallel to the axis. Finally, the rays that pass through the optical center are refracted without experiencing any kind of deflection.

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

- That the object is located with respect to the optical plane at a distance greater than twice the focal length. In that case, the image that is 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 that is 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 once and twice the focal length. Then an image is produced that is real, inverted and larger than the original object.

- That the object is located at a distance from the optical plane that is less than the focal length. In that 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, plano-convex lenses, and concave-convex lenses.

Biconvex lenses, as the name suggests, are made up of two convex surfaces. The plano-convex, meanwhile, have a flat and a convex surface. And finally, concave convex lenses are made up of a slightly concave and a convex surface.

Difference with divergent lenses

Converging lens. Fir0002 (talk) (Uploads)

Divergent lenses, on the other hand, differ from convergent lenses in that the thickness decreases from the edges towards the center. Thus, contrary to what happened with convergent lenses, in this type of lens the light rays that strike 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 myopia.

Gaussian equations of thin lenses and magnification of a lens

In general, the type of lenses that are studied are what are called as thin lenses. These are defined as those that have a small thickness compared to the radii 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 determining the magnification of a lens.

Gauss equation

The Gaussian equation for thin lenses is used to solve a multitude of basic optical problems. Hence its great importance. Its expression is the following:

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 of the power of a lens is the diopter (D), where 1 D = 1 m ^-1. For their part, p and q are respectively the distance at which an object is located and the distance at which its image is observed.

Magnification of a lens

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

M = - q / p

Where M is the magnification. From the value of the increase, a number of consequences can be deduced:

If -M-> 1, the image size is larger than the object

If -M- <1, the image size is smaller than the object size

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

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

Exercise resolved

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 away will it be?

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

We plug these values ​​into the Gaussian equation for thin lenses:

1 / f = 1 / p + 1 / q

And the following remains:

1 / 0.5 = 1 + 1 / q; 2 = 1 + 1 / q

We isolate 1 / q

1 / q = 1

To then clear q and get:

q = 1

Hence, we substitute in the equation for the magnification of a lens:

M = - q / p = -1 / 1 = -1

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

References

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2. Lekner, John (1987). Theory of Reflection, of Electromagnetic and Particle Waves. Springer.
3. Light (nd). In Wikipedia. Retrieved on March 20, 2019, from en.wikipedia.org.
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6. Hecht, Eugene (2002). Optics (4th ed.). Addison Wesley.
7. Tipler, Paul Allen (1994). Physical. 3rd Edition. Barcelona: I reversed.