MadSci Network: Physics

Subject: Fermat's principle in optics

Date: Wed Jul 16 08:57:24 2003
Posted by Ericsson
Grade level: nonaligned School: No school entered.
City: No city entered. State/Province: No state entered. Country: No country entered.
Area of science: Physics
ID: 1058363844.Ph

I've asked a similar question before which i may not have stated what do i mean 
in a more appropriate way. Fermat stated that light will take the path which 
requires the shortest path. So using this we can derive a value of n(refractive 
index) of a medium. However in the same medium the path with the shortest time 
is actually the shortest path. So using the same principle, a paraboloidal 
mirror can be used to reflect light to a focal point. So by using the same 
principle, one can derive the expression for the curvature of the mirror? (i.e 
the expression for the parabola) It is stated that by having one general plane 
which the parallel beams of light passes through at the same time, from the 
plane to the point on the mirror, it will be reflect in such a way that the 
light will travel the same distance from the point on the mirror to the focal 
point. It is stated that using this method, the expression of the curvature can 
be derived. To be more clear in what i mean, this principle is used to design 
mirrors which focus light from distant source(light almost become parallel) to 
a point or this application of the principle can also be seen in making the 
satellite dish. So i wonder if anyone can provide me with a way to derive the 
curvature of the mirror. Thanks in advance.

Re: Fermat's principle in optics

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