Michelson Morley Exp. Phase Difference Question

[bphili]

Homework Statement

The problem I am misunderstanding begins with a reference to a previous problem and example. Let me begin to ask my question by showing my work for the previous problem and describe the example in reference.

(reference problem) - Ch.1, #13.

Consider a reference frame moving with uniform velocity V through the ether. Show that according to the Galilean addition law, in this reference frame a light signal traveling at an angle θ' with the direction of V has a speed of

c'=√(c2-V2sin2θ')-Vcosθ'

Verify that this gives the expected result for a parallel light signal (θ'=0 deg.) and for a perpendicular light signal (θ'=90 deg.)

ANSWER:

(Vsinθ')2+(Vsin(π/2-θ')+c')2=c2

(Vsinθ')2+(Vcosθ'+c')2=c2

(Vcosθ'+c')2=c2-(Vsinθ')2

Vcosθ'+c'=√(c2-(Vsinθ'))

c'=√(c2-Vsinθ')-Vcosθ'

when that θ'=0 when c'=c-v', when θ'=90 c'=√(c^2-V^2)

My Problem:

Ch.1, #18)

In section 1.6 we calcualted the phase difference between the two beams of light in the Michelson-Morley interferometer on the assumption that one arm was parallel to the ether wind and the other was perpendicular. Repeat the calculation of the phase difference if one of the arms makes an angle 90 deg. with the ether wind and the other an angle 90 deg. + θ, as in fig.1.20.(Hint: use the result of problem 13, and assume V<<c.)

Thanks and I'm online because it hard to explain this without the book...

Homework Equations

The Attempt at a Solution

 

[NateD]

I'm not sure how to solve this problem, I have read and re-read the section and problem 13, trying to gain an understanding but I don't think I understand it enough to answer this question.