The converging lenses They are those that are thicker in the central part and thinner at the edges. 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.
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.
Article index
Converging lenses have a number of defining characteristics. In any case, perhaps the most important is the one that we have already advanced in its definition. Thus, converging 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..
For its study, it is important to know what elements constitute lenses in general and converging lenses in particular..
In general, the optical center of a lens is called the point through which every ray that passes through it does not experience any deviation..
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..
With regard to the formation of images in converging lenses, a series of basic rules must be taken into account, which are explained below..
If the ray hits the lens parallel to the axis, the emerging ray 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 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 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 this case, the image will be virtual, direct and larger than the object.
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. Convex planes, meanwhile, have a flat and a convex surface. And finally, concave convex lenses are made up of a slightly concave and a convex surface..
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 is called virtual images of objects.
In optics, divergent or negative lenses, as they are also known, are mainly used to correct myopia.
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.
The Gaussian equation for thin lenses can be used to solve a multitude of problems in basic optics. 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. On the other hand, p and q are respectively the distance at which an object is located and the distance at which its image is observed.
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:
Yes | M | > 1, the size of the image is larger than that of the object
Yes | M | < 1, el tamaño de la imagen es menor que el del objeto
If M> 0, the image is right and on the same side of the lens as the object (virtual image)
Yes M < 0, la imagen está invertida y en el lado contrario que el objeto (imagen real)
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 you be?
We have the following data: p = 1 m; f = 0.5 m.
We substitute 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 solve for q and obtain:
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 y de igual tamaño dado que el valor absoluto de M es 1. Por último, la imagen se encuentra a un metro de distancia del foco.
Yet No Comments