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
[tex]2 n t = m \lambda[/tex] (1)
[tex]2 n t = (m + {{1}\over {2}}) \lambda[/tex] (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.

 

[m2003]

I would approach this problem by first understanding the phenomenon of interference. When light waves from different sources or different parts of the same source overlap, they can either constructively or destructively interfere with each other. In the case of two glass plates, the light waves that pass through the plates can interfere with each other, resulting in bright and dark fringes.

The formula (1) mentioned in the problem is known as the "path difference" formula, where n is the index of refraction of the medium, t is the thickness of the medium, m is the order of the fringe, and λ is the wavelength of the light. This formula is used when the path difference between the two waves is an integer multiple of the wavelength, resulting in constructive interference and a bright fringe.

In this problem, we are asked to find the distance from the contact point where the next dark fringe occurs. This means that the path difference between the two waves will be half of a wavelength, resulting in destructive interference and a dark fringe. This is where the formula (2) comes into play, where the path difference is equal to half of the wavelength.

Now, to incorporate the size of the thread into the problem, we must consider the fact that the light waves passing through the thread will also interfere with each other. This will result in a smaller path difference, which we can calculate using the diameter of the thread. This smaller path difference must be added to the path difference between the glass plates to find the total path difference.

Once we have the total path difference, we can use formula (2) to find the distance from the contact point where the next dark fringe occurs. This will give us the distance from the contact point to the first dark fringe. To find the distance to the next dark fringe, we must add the wavelength of the light to this distance.

In conclusion, as a scientist, I would use the principles of interference and the relevant formulas to solve this problem. I would also take into consideration the size of the thread to find the total path difference and ultimately the distance to the next dark fringe.