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

AI Thread Summary
The discussion focuses on understanding the focal point of a lens in geometric optics. The initial assumption is that the focal point is -25.5 cm, but clarification is sought regarding the relevance of lens radii and refractive index. A suggested approach involves treating the lens's first surface as a mirror to deduce the focal length using the formula f=R/2. This method allows for the calculation of the radius of curvature and ultimately the system's focal length. The conversation concludes with acknowledgment of the guidance provided.
Marioweee
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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.
WhatsApp Image 2021-10-03 at 20.02.34.jpeg
 
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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
 

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