Optical polarization concept

[bluesky]

In the context of elliptical polarization,every book writes out this formula:

 

(E_y/E_0y)^2 + (E_x/E_0x)^2 -2(E_y/E_0y)(E_x/E_0x) cos ε= (sinε)^2

 

where ε is the initial phase difference.

 

After that they write this is the equation of an ellipse making an angle α with the E_x-E_y co-ordinate system such that

 

tan 2α=[[2E_0x*E_0y]cos ε]/[(E_0x)^2 - (E_0y)^2]

 

This is NOt a homework problem;but I want to clarify how does the 2nd relation concering tan 2α comes.

 

I tried to understand by expanding tan 2α and by dividing RHS by (E_0x)^2 throught.

But the factor cos ε is annoying.

 

Can anyone please tell how the relation comes?

[Qfwfq]

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