DIVERGING LENS: CHARACTERISTICS, ELEMENTS, TYPES, APPLICATIONS - PHYSICAL - 2025

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

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

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So if you are nearsighted and wear glasses, you have a perfect example of a divergent lens on hand.

Diverging Lens Features

As explained previously, divergent lenses are narrower in their central part than at the edges. Furthermore, in this type of lens one of its surfaces is always concave. This gives this type of lens a series of characteristics.

To begin with, the prolongation of the rays that strike them results in virtual images that cannot be collected on any type of screen. This is so, because the rays passing through the lens do not converge at any point, since they diverge in all directions. In addition, depending on the curvature of the lens, the rays will open to a greater or lesser extent.

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

In addition, in divergent lenses the images are smaller than the object and are between it and the focus.

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Diverging lens elements

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

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

The name main focus is the point at which all the rays that hit the lens are found parallel to the main axis.

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 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.

Imaging

To graphically determine the formation of an image in a thin lens, it is only necessary to know the direction that two of the three rays

whose trajectory is known will follow.

One of them is the one that hits the lens parallel to the optical axis of the lens. This, once refracted in the lens, will pass through the image focus. The second of the rays whose path is known is the one through the optical center. This will not change its trajectory.

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

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

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

Applications

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

Diverging ophthalmic lenses separate light rays so that when they reach the human eye they are further apart. Thus, when they cross the cornea and the lens, they go further and can reach the retina, causing vision problems in people with myopia.

Types

As we have already discussed, converging lenses have at least one concave surface. Because of this, there are three types of divergent lenses: biconcave, plano-concave, and convex-concave.

Divergent biconcave lenses are made up of two concave surfaces; plano-concave lenses have a concave and a flat surface, while in convex-concave or divergent meniscus one surface is slightly convex and the other is concave.

Differences with converging lenses

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

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

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Gaussian equation of lenses and magnification of a lens

The type of lenses that are most commonly studied are known as thin lenses. This defines all lenses whose thickness is very low compared to the radii of curvature of the surfaces that limit them.

The study of this type of lens can be carried out mainly through two equations: the Gaussian equation and the equation that allows determining the magnification of the lens.

Gauss equation

The importance of the Gaussian equation for thin lenses lies in the large number of basic optical problems it can solve. Its expression is the following:

1 / f = 1 / p + 1 / q

Where 1 / f is the power of the 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), the value being 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.

Exercise resolved

A body is placed 40 centimeters from a diverging lens of -40 centimeters focal length. Calculate the height of the image if the height of the object is 5 cm. Also determine if the image is straight or reversed.

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

These values ​​are substituted into the Gaussian equation for thin lenses:

1 / f = 1 / p + 1 / q

And you get:

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

From where q = - 20 cm

Next, we substitute the result obtained previously in the equation for the magnification of a lens:

M = - q / p = - -20 / 40 = 0.5

Obtaining that the value of the increase is:

M = h '/ h = 0.5

Solving from this equation h ', which is the value of the height of the image, we get:

h '= h / 2 = 2.5 cm.

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

References

1. Light (nd). On Wikipedia. Retrieved on April 11, 2019, from es.wikipedia.org.
2. Lekner, John (1987). Theory of Reflection, of Electromagnetic and Particle Waves. Springer.
3. Light (nd). In Wikipedia. Retrieved on April 11, 2019, from en.wikipedia.org.
4. Lens (nd). On Wikipedia. Retrieved on April 11, 2019, from es.wikipedia.org.
5. Lens (optics). In Wikipedia. Retrieved on April 11, 2019, from en.wikipedia.org.
6. Hecht, Eugene (2002). Optics (4th ed.). Addison Wesley.
7. Tipler, Paul Allen (1994). Physical. 3rd Edition. Barcelona: I reversed.