How do you use Fermat's principle of least time to explain various concepts in geometrical optics?
You can use Fermat's principle to derive the laws on which geometrical optics is based: The laws of reflection and refraction.
For example, do a Google search for "law of refraction fermat principle" and you'll find many web pages and even a video which try to explain how the law of refraction can be derived from Fermat's principle. If you don't understand one of those derivations, post a link to it and ask questions about the specific things that you're stuck on.
Okay thank you,,
So when we talk about optic geometry, we just explain the reflection and refraction, isn't it ??
then what if the answer to the question "how do you use Fermat's principle to explain the need for forms of mirrors and lenses"?
Yes. That is the basis of geometrical optics.
I don't quite understand the question. Use Fermat to derive the laws of optics, then use those laws to design mirrors and lenses to do what you would like (form images, for example).
Yeah i mean, how we use fermat principle to explain the required shapes of lenses and mirrors ?
Usually, the need for designing certain shapes of the mirrors and lenses is for aberration correction purpose. Aberration comes in various forms, all of them have adverse effect on the formed image, so suppressing them by designing certain shapes and/or material of the mirrors and lenses is demanded.
So, the design of mirror and lens just for certain purpose, is'n it?
Then, we derived the fermat principle that can we use to design the mirror and lens for certain purpose, is'n it
Are you asking about correcting for abberations? Or just asking about the basic shapes of lenses and mirrors?
The (practical) purpose for which lenses or mirrors with certain shapes needs to be produced usually comes first, then one applies the theories either through Fermat's principle or merely ray tracing to analyse the optical elements.
I asking about basic shapes of lenses or mirror and also another shapes of lenses or mirror,
So, we need the purpose first,
then we can use many theories to analyse it, isn't it ?
It should be that way, you don't normally use your design software to design optics as a plaything as weird as you want (except for learning purpose). There must be a specific purpose for certain optics design.
Okay, thak your for the explanation
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