What is the mathematical explanation for Fresnel lenses?

[Lucas Olivio]

Homework Statement: what is the mathematical explanation for fresnel lenses
Homework Equations: No equations were provided

I'm going to post a link to one article I found that I think has the answer, but I couldn't understand because of my lack of knowledge in physics and math.

https://www.hindawi.com/journals/mpe/2018/4654795/

 

[Klystron]

If you have difficulty understanding the math in the link you posted, perhaps reading about Fresnel lens applications will help your understanding. This wikipedia article describes the design and history of visible light lenses.

Similar lens antennas guide microwaves in the radio frequency (RF) section of the electromagnetic spectrum. Notice the similar geometries of lighthouse lenses and microwave antennas, suggesting the underlying mathematics.

 

[berkeman]

(Note -- thread moved from the Homework Help forums, since it does not seem to be a homework-type question)

 

[berkeman]

Welcome to the PF, Lucas!

I'm going to post a link to one article I found that I think has the answer, but I couldn't understand because of my lack of knowledge in physics and math.

https://www.hindawi.com/journals/mpe/2018/4654795/

Can you say a bit more about your physics and math background? Have you had algebra? How about trigonometry? And have you learned about Snell's Law yet?

https://en.wikipedia.org/wiki/Snell's_law

 

[Lucas Olivio]

If you have difficulty understanding the math in the link you posted, perhaps reading about Fresnel lens applications will help your understanding. This wikipedia article describes the design and history of visible light lenses.

Similar lens antennas guide microwaves in the radio frequency (RF) section of the electromagnetic spectrum. Notice the similar geometries of lighthouse lenses and microwave antennas, suggesting the underlying mathematics.

Thanks Klystron! I'll give these links a try. If more doubts come I'll make sure to post here again.

 

[Lucas Olivio]

Welcome to the PF, Lucas!

Can you say a bit more about your physics and math background? Have you had algebra? How about trigonometry? And have you learned about Snell's Law yet?

https://en.wikipedia.org/wiki/Snell's_law

Thanks berkeman!
My Knowledge in these areas is moderate, my university course don't have much focus on these subjects so I end up forgetting about things. The Senll's Law I actually studied just to try solve the question, still didn't understood how the article came up with that 5 first equations only from the snell law...
In the moment I'm currently taking an online course in optical physics to be able to resolve this question, but I feel like I'm still missing something...