What is the correct equation for finding path difference in CD diffraction?

[unscientific]

Homework Statement

White light was shone vertically down on a cd tilted 5°, with adjacent tracks d = 720 nm. An observer some distance away observes a color of light. Determine that wavelength of light observed. (Refer to picture attachment)

Homework Equations

finding path difference

The Attempt at a Solution

I understand that finding the path difference is key to solving this problem. So, i found the path difference to be simply:

d cos (90+ 5 - ∅) = (1)(λ)


But the answer wrote path difference =
d cos (90 + 5 - ∅) - d cos (90 - 5)


Using the provided answer, it didnt make sense to me for the additional term of ' d cos (90 - 5)' to be there?

 

[Spinnor]

I think there will be path length differences from the 5 degree tilt of the cd and from the angle of the viewer, see sketch below,

 

[unscientific]

hmm i still don't seem to be able to grasp the answer..

 

[Spinnor]

Look at the sketch and follow the two paths. Calculate the path length difference from the first dashed line to the second dashed line. I think you will find the required answer.

 

[unscientific]

Look at the sketch and follow the two paths. Calculate the path length difference from the first dashed line to the second dashed line. I think you will find the required answer.

OH i get it! the tilting causes path difference before and after diffration at surface!

the right beam has to go down more while the left beam has to travel more!