- #1

fluidistic

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## Homework Statement

Assume that the surface S which delimits the 2 mediums is a revolution surface around the z-axis. Light rays start at point [tex]F_1[/tex] and all the rays going through the surface reach the plane [tex]\Sigma[/tex] in a same amount of time.

Show that S is the result of rotating an ellipse with eccentricity [tex]\frac{n_2}{n_1}[/tex].

## Homework Equations

None given.

## The Attempt at a Solution

[tex]t=\frac{d}{v}[/tex].

[tex]t_0=\frac{l_0 n_2}{c}[/tex], [tex]t_1=\frac{l_1 n_1}{c}[/tex].

Hence the time taken for any ray to go from [tex]F_1[/tex] to [tex]\Sigma[/tex] is [tex]t=\frac{1}{c} (l_0 n_2 +l_1n_1)=K[/tex].

Therefore [tex]\frac{l_0}{n_1}+\frac{l_1}{n_2}=\frac{Kc}{n_1n_2}[/tex].

I know that the eccentricity is defined as [tex]e=\sqrt {1-\frac{b^2}{a^2}[/tex]. The problem I'm facing is that I don't have the equation of an ellipse yet.

Have I to find K?

I'll try something.