Convergence of a spherical lens

Convergence is the ability of spherical lenses to deflect the path of light rays that pass through them, causing them to converge or diverge after they pass.

The great convergence of the lens used in the loupes allows them to focus the light rays.
Convergence or vergence is the ability of spherical lenses to converge or diverge the light rays that pass through them. Convergence can be calculated as the inverse of the focal length, measured in meters. Furthermore, the convergence of a lens can be positive if it is converging , or negative if it is diverging.

The equation used to calculate the vergence of a spherical lens is shown below, note:

C — convergence (m -1 or di)

f — focal length (m)

The convergence of a lens is measured in the unit of m-1. However, we usually call this unit a diopter, its symbol is di . The greater the diopter of a lens, the greater its ability to change the direction of light rays falling on it.


Determine the convergence of a concave lens of focus equal to +0.5 m.

Analyzing the calculation performed, we can say that this lens has a convergence of 2 diopters , which is equivalent to a 2 degree lens, like those prescribed for the correction of visual defects.

Focus of a lens

The focus of a lens is the region where the rays of light refracted by it meet , or even the region where the extensions of refracted rays meet. We say that when the focus of the lens is crossed by rays of light, its focus is real and positive, on the contrary, when crossed by extensions, it is virtual and negative:

Converging and diverging lens

What determines whether a lens is converging or diverging is the relationship between the refractive indices of the lens and the medium in which it is located, as well as the radii of curvature of its faces. This relationship is called the Halley equation, also known as the lens maker’s equation .

2 — lens refractive index

1 — refractive index of the medium

1 and R 2 — radii of curvature of lens faces (m)

Let’s analyze the previous formula. First, if the index of refraction of the medium (n 1 ) is greater than the index of refraction of the lens (n ​​2 ), the lens will have the sign of its focal length changed , that is, if this lens was converging, it will start to behave itself as a diverging lens and vice versa. If one of the faces of the lens is parallel, its radius of curvature will be infinite and therefore the ratio 1/R will be zero.

The following figure, as a diverging lens, inserted into a medium of lower refractive index, refracts the light that passes through it:

The diverging lens has negative foci.

Now configure a figure that shows how a converging lens refracts light rays that fall on its surface:

When passing through the converging lens, parallel light rays intersect at the focal point.

In summary: if the convergence of a lens is positive, that lens is converging, otherwise, it will be divergent.

spherical lens

Spherical lenses are transparent media arranged in curved shapes and varying thicknesses along their length. These lenses have the ability to refract light rays, converging them to a point in front of them (focal point) or diverging them.

Spherical lenses are those that have some radius of curvature on at least one of their faces. They are usually made of transparent materials, such as glass or acrylic, and are usually very thin (thin).

There are basically two categories of spherical lenses : concave lenses and convex lenses .

  • Concave lenses: When immersed in air, or in a medium with a lower refractive index, concave lenses are diverging. Concave lenses are thicker at their edges than at their center.

    Convex lenses: These lenses are able to converge light into a focal point when immersed in some medium of lower refractive index. Convex lenses always have thin edges.

→ Juxtaposition of spherical lenses

The juxtaposition of spherical lenses consists of pairing two or more lenses so that we obtain new modules of convergence, that is, by combining lenses, it is possible to obtain different paths for the light that falls on them. In addition, the juxtaposition of lenses helps to correct a phenomenon that occurs a lot with spherical lenses: chromatic aberration .

Chromatic aberration arises due to refraction and the time that light remains inside the spherical lens. As spherical lenses have a variable thickness, some light rays tend to stay inside them for a longer time, and this makes these components of light emerge from the lens surface with small lag angles in relation to lenses that traveled longer paths . short. The effect of this phenomenon causes distorted images , in which it is possible to observe the colors of an object slightly shifted from each other.

In order to perform the juxtaposition between lenses, it is necessary that no physical medium is between the surfaces of the lenses. In juxtaposition, the vergence of the set of juxtaposed lenses is determined by the sum of the vergence of each lens:

C — vergence of lens juxtaposition

1 — Lens Vergence 1

2 — Lens Vergence 2

  • example of juxtaposition

Two thin spherical lenses, with diopters equal to -3 di and +4 di, are juxtaposed. What should be the diopter of the association of these lenses?


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