Two glass plates - next dark fringe?

[lizzyb]

Question
Two glass plates 10.0 cm long are in contact at one end and separated at the other end by a thread 0.0500 mm in diameter. Light containing the two wavelengths 400 nm and 600 nm is incident perpendicularly. At what distance from the contact point is the next dark fringe?

Relevant Formulas
2 n t = m \lambda (1)
2 n t = (m + {{1}\over {2}}) \lambda (2)

Work So Far
This one is weird since the light contains two wavelengths plus I don't see how the size of the thread plays into this since we're to find the "next dark fringe" away from the contact point.

Now, the light coming through the plate on the top does not have a phase shift, but the one reflecting off the top of the bottom plate does phase shift 180 degrees. So it seems to me that equation (1) should be used.

How do I fit the distance between spots in this one?

 

[hage567]

The size of the thread is important because it tells you how the thickness (t) of the air film between the two pieces of glass changes.