Geometrical problem related to thin film interference

[khaos89]

Look at the picture below, I have to prove that the optical path length difference is

$\Delta=n(BC+CD)-BE=2nd\cos(r)$

[PLAIN]http://img200.imageshack.us/img200/2271/schermata082455775alle1.th.png

The problem is just how to get $2nd\cos(r)$

I actually don't have any idea :\

I have tried to work with trigonometry but no luck yet...

(I am posting it here because it's not related to course work, i am just trying to understand how it works when we don't have perpendicular incidence)

 

[khaos89]

Sorry, here we go with the pic:

[PLAIN]http://img193.imageshack.us/img193/2271/schermata082455775alle1.png

 

[GenePeer]

http://en.wikipedia.org/wiki/Thin-film_interference

Can't believe I'd forgotten it already! Half a year doing nothing is bad.

 

[khaos89]

Thanks a lot :)