# What is the focal point of a lens in a geometrical optics problem?

• Marioweee
In summary, the conversation discusses a problem related to geometric optics and determining the focal point of a lens. The problem is solved by treating the first surface of the lens as a mirror and using the Lensmarker's equation to determine the focal length of the system.
Marioweee
Homework Statement
We have a divergent lens on which a beam of parallel rays strikes from left to right. Part of the light reflects off the first face and the reflected rays converge at the point indicated by the arrow, which is - 25.5 cm from the vertex of the first lens surface. Assuming that the lens is symmetrical, that is, that "R1= -R2 &, which is thin, and whose refractive index is 1.5, state the value of the focal point of the lens with its sign.
Relevant Equations
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I have recently started with geometric optics and I do not quite understand what this problem asks of me. According to the statement, the focal point of the lens would be -25.5cm, right? That is, it is only a problem of concepts where it is not necessary to take into account the radii of the lenses or the refractive index, right?
Maybe I am very wrong that is why I ask for some help.
This is the picture of the problem that I have done.

Marioweee said:
According to the statement, the focal point of the lens would be -25.5cm, right?
Why would you think that? Hint: Solve the problem in two steps. Step one: Treat the first surface of the lens as a mirror. What can you then deduce?

If the first surface is treated as a spherical mirror then f=R/2. From this equation we can determine the value of R1. Then, from the Lensmarker's equation I could determine the focal length of the system, right?

Marioweee said:
If the first surface is treated as a spherical mirror then f=R/2. From this equation we can determine the value of R1. Then, from the Lensmarker's equation I could determine the focal length of the system, right?
Right!

Thank you very much for your help

## 1. What is the difference between geometrical optics and physical optics?

Geometrical optics deals with the behavior of light as it travels in a straight line and interacts with objects, while physical optics takes into account the wave nature of light and its interactions with matter.

## 2. How do you determine the path of light in a geometrical optics problem?

In geometrical optics, the path of light can be determined using the principles of reflection and refraction, which follow the laws of reflection and Snell's law respectively.

## 3. What is the importance of the focal length in geometrical optics?

The focal length is a crucial parameter in geometrical optics as it determines the position and size of the image formed by a lens or mirror. It is also used to calculate the magnification of an image.

## 4. How do you calculate the refractive index of a material in a geometrical optics problem?

The refractive index of a material can be calculated using Snell's law, which relates the angle of incidence and refraction to the refractive indices of the two materials involved.

## 5. Can geometrical optics be applied to all types of light, including visible light and other forms of electromagnetic radiation?

Yes, geometrical optics can be applied to all types of light, as long as the wavelength is much smaller than the size of the objects being considered. This includes visible light, as well as other forms of electromagnetic radiation such as radio waves and X-rays.

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