MadSci Network: Physics Query:

### 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
Message:

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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