# Analytical study on spherical lenses

The magnifying glass is an optical magnifying instrument

Like spherical mirrors, lenses also provide an image of a linear, transverse object. Thus, the positions and heights of objects placed in front of a spherical lens are determined through the same equations studied in spherical mirrors. This equality is also valid for the rules of signs, therefore, analyzing the focal lengths, we have to make the following use:

*– f > 0: the spherical lens is of the converging type;
– f < 0: the spherical lens is of the diverging type.*

To determine the focal length of a spherical lens, we use the Gauss equation which is as follows:

On what:

** f –** is the focal length of the lens,

**– is the distance from the object to the lens and**

*p***– is the distance from the image to the spherical lens. In the above equation, we realize that not only can we determine the focal length of a spherical lens, but we can also determine any of the unknowns, provided the others are provided.**

*p’*In the above equation, we have:

– ** i** is the image size and

**is the object size.**

*o*__Let’s look at an example:__

Suppose an object is placed 60 cm from a spherical converging lens. Such a lens has a focal length of 20 cm. Calculate the distance from the image to the lens.

**Resolution** :

As the lens is converging type, we have that the distance from the object to the lens and the focal length are positive, *p =* + 60 cm and *f =* + 20 cm. To calculate the distance from the image to the lens, we have:

Applying the linear increase equation, we have: