Calculating Bright Fringes in Reflected Light from Two Flat Plates at an Angle

[JSapit]

Homework Statement

Two optically flat plates of glass are separated at one end by a wire of diameter 0.250 mm; at the other end they touch. Thus, the air gap between the plates has a thickness ranging from 0 to 0.250 mm. The plates are 15.0 cm long and are illuminated from above with light of wavelength 550.0 nm. How many bright fringes are seen in the reflected light?

Homework Equations

t=m(lambda)

The Attempt at a Solution

I know that there is two phase changes, so with this apparatus, there has to be a (1/2) added to create constructive interference. I also know that the ray has to travel through the thickness once, and then again, so the distance would be 2t. I tried solving for t via the equation 2t=(m+1/2)(lambda) and solving for t. That gives me the distance, but I'm not sure what to do from there. Am I on the right track?

 

[Delphi51]

I'm sure it can be done that way, and it will be a beautiful piece of work, but wouldn't it be easier just to find the distance between bright fringes? That is, how much width is needed to change 2t by one wavelength?

 

[JSapit]

So you mean just set up the equation as 2t=(1+1/2)(550nm)

Like that?

Since that give me the distance, how would I solve for just the bright fringes?

 

[Delphi51]

The thickness must CHANGE by 550 nm as you go from crest to crest.
Have to have a formula relating change in t and change in x.

 

[JSapit]

I figured it out. Thanks for your help!