Interference in Air Wedges exercise

[Supergabson]

I have this question for my physics assignment.

Homework Statement

Two plane glass plates 10.0 cm long, touching at one end , are separated at the other end by strip of paper 1.5x10$^{-3}$ mm thick. When the plates are illuminated by monochromatic light, the avreage distance between constructive dark fringes is 0.20 cm calculate the wave length of the light.

I used the equation 2t=$\frac{λ}{2}$ but it gives me the wavelength of light in glass and I am looking for wavelength in air. please help

My physics book doesn't say how to do this type of question :(

Homework Equations

how to solve this question?

 

[technician]

The interference occurs as a result of the path in the air wedge so you are correct... you need the λ of the light in air.
One other consideration is that a phase shift of ∏ occurs at the reflection from the air/glass surface.

 

[technician]

Just realized !
The question wants you to calculate the wavelength of light !
You have information about the separation of dark fringes, the dimensions of the glass and the separation of the glass plates

 

[Supergabson]

What formula should I use that has the dimensions of the glass? I have no idea how the dimensions of the glass can lead me to the right answer

 

[ehild]

You need the dimension of the glass to get the thickness at distance d from the edge. The interference happens between the wave reflected from the front air wedge-glass interface and the one reflected from the back interface: the blue and green rays in the figure. "t " means the thickness at the spot of a dark strip along the wedge. As the green wave changes phase at the back air-glass interface, destructive interference occurs when 2t n(air) = mλ. The thickness varies with the distance d from the edge, how? For the consecutive dark strips, separated by 0.2 cm,
the order m differs by 1. What is the difference of the thickness between those spots?

ehild