# What is the sign convention for lenses? ## Lens Builder’s Formula

The most widely used optical systems today are lenses. They are part of eyeglasses, cameras, binoculars and a long etcetera. In this section we are going to study them in the light of geometrical optics. To do this we will see:

Observe how convergent lenses are thicker in their central part and divergent lenses are thicker at their ends. On the other hand, meniscus-convex and meniscus-concave lenses are also called meniscus-convergent and meniscus-divergent respectively. The signs of the indicated radii correspond to the DIN criterion.

The convergent or divergent behavior of a lens actually depends on the ratio between the refractive index of the medium surrounding the lens,n , and that of the lens itself, n’. When we say in general that a lens is converging or diverging, we do so assuming that n’>n , and more specifically, that the lens is in air ( n=1 ).

To obtain the above formula, we start from the particular case of the biconvex lens in the previous image. Since it is a thin lens, we can disregard its thickness and place the origin of the optical system at the center of the lens itself. In this way, the rays coming from point P, which is at a distance s from the origin are first refracted on the surface of radius R1 and form an image at point P1, at a distance s1 from the origin. The fundamental equation of the diopter gives us the following relationship:

## How are thin lenses classified?

Types. We can classify lenses according to different criteria: … From now on we will focus on thin lenses. Behavior: We say that there are converging lenses (also called convex or positive) and diverging lenses (also called concave or negative).

## What is sys in lenses?

The distances of the object and the image to the optical vertex are denoted s and s’ respectively. The heights of the object and image are denoted by y and y’. The focal lengths are denoted by f and f’.

### Convergent lens

When we work in optics, especially when we try to obtain the FUNDAMENTAL ECUATION OF THE SPHERICAL DIOPTRIUM, we use the following sign convention, proposed by the DIN standards, that although sometimes it is complicated, it is more than necessary to take them into account:

2.- Horizontal distances are positive if from the OPTICAL VERTEX (point where the optical axis intercepts with the optical system under study), we move to the right; and negative if from the optical vertex we move to the right.

### What do diverging lenses look like?

Diverging lenses are transparent bodies made of organic or mineral material that can refract light and form an image. Light incident perpendicularly on a diverging lens is refracted from the focal plane (in the case of converging lenses it is refracted towards the focal plane).

### How do light rays behave as they pass through the lens?

An optical lens has the ability to refract light and form an image. Light incident perpendicularly on a lens is refracted toward the focal plane, in the case of converging lenses, or from the focal plane, in the case of diverging lenses.

### Divergent lens

In geometrical optics there are different standards and conventions that you can use to analyze problems. We recommend that you follow the DIN standard (initials of Deutsches Institut for Normung or German Institute for Standardization) also called European standard. However, at the end of this section we will present you, as a reference, another sign criterion that is also widely used.

Rays form positive angles to the principal axis or to any other axis when the ray is brought to the axis by the shortest path in a counterclockwise direction. Rays form negative angles with the main axis or with any other axis when taking the ray to the axis by the shortest path we turn in the same direction as clockwise.

If you find it difficult to remember the above criterion, remember that, in paraxial approximation, α≃tanα=opposite cathetuscontiguous cathetus , so you can deduce the sign from the sign of the distances corresponding to the opposite cathetus and contiguous cathetus.

### How is the focal length of a diverging lens measured?

Designating by s the object-mirror distance, s’ the image-mirror distance, the relation linking both magnitudes to the radius of curvature of the mirror R is: The focal length of the mirror is given by: f’ = R/2.

### What does Afocal lens mean?

The afocal method consists of placing a camera or webcam directly over the eyepiece of a telescope. The method is often used in astrophotography. An alternative to the afocal method is to place the camera in prime focus.

### What is an ideal optical system?

An ideal optical system is one that allows each point of the object to be represented at a specific point in the image (9). Based on the lens as an image-forming element, the following optical systems can be mentioned: Human eye. Photographic camera.

### Physical Lenses

Diverging lenses are bounded by two surfaces, at least one of which is concave. Thanks to this specific shape, diverging lenses are able to separate the light rays incident on them or, in other words, to make them “diverge”. Diverging lenses are used in optics-optometry to compensate for refractive errors or defects such as myopia and some types of astigmatism. We explain how they do it.