Michelson morley exp and rotating 90 degrees

[LBloom]

Homework Statement

Ok, I was able to figure out the difference in time for the michelson morley experiment and hence the fringe shift is B^2*L/wavelength. What i can't understand is why after shifting the experiment 90 degrees the fringe shift is supposed to be different. the one perpindicular to the ether wind is now parallel, and vice versa so wouldn't they just exchange values for time in terms of how long it takes for the light to travel. Why should a 90 degree rotation affect that or lead to a different fringe?

Homework Equations

The Attempt at a Solution

 

[LBloom]

actually i think i got it (in british accent)