Calculating (t1-t2): Three Bright Fringes on Inclined Glass Plates

[Eats Dirt]

Homework Statement

One glass plate sits flat and another is above it inclined on an angle(shown on diagram provided). monochromatic λ light shines on it. The fringes are spaced p apart, and the bottom plate is length d.
Between t1 and t2 there are three bright fringes.

What is (t1-t2) ?

Homework Equations

m\lambda_o=2n_f t\cos\theta_t+\frac{\lambda_o}{2}

The Attempt at a Solution

I'm not sure if what I did is valid because when I modeled it I did not take into account the glass plate on the bottom moving up to where I modeled it. Also this does not take into account the given distance between the fringes, p, explicitly which is another reason to why I think my solution may be incorrect.

m\lambda_o=2n_f t\cos\theta_t+\frac{\lambda_o}{2}
plug in 3 for the m fringes, also use t=t1-t2 for the heights of the plates. approximate theta as 0

3\lambda_o=2n_f (t_1-t_2)+\frac{\lambda_o}{2}\\<br /> <br /> \frac{1}{2n_f}[3\lambda_o-\frac{\lambda_o}{2}]= (t_1-t_2)

I'm pretty sure this is incorrect but do not know how else to attack the problem.

Any help would be much appreciated.

 

[haruspex]

Between t1 and t2 there are three bright fringes.

That's not a very precise definition of t1 and t2. Are those the positions of the outer two of the three bright fringes, or of the centres of the dark bands beyond them?

 

[Eats Dirt]

That's not a very precise definition of t1 and t2. Are those the positions of the outer two of the three bright fringes, or of the centres of the dark bands beyond them?

the question says "three fringes apart".

 

[haruspex]

the question says "three fringes apart".

It says what are three fringes apart? t1 and t2 are two points three fringes apart? Two fringes? Two dark bands? Please provide the whole text, as is.

 

[mmmendon]

Assuming that t1 and t2 are the air gap thicknesses at the two points that are 3 fringes apart, the correct answer is 3λ/2

 

[Eats Dirt]

Assuming that t1 and t2 are the air gap thicknesses at the two points that are 3 fringes apart, the correct answer is 3λ/2

Do you mind elaborating on the method you used?

 

[haruspex]

Assuming that t1 and t2 are the air gap thicknesses at the two points that are 3 fringes apart, the correct answer is 3λ/2

Please read the Forum guidelines. The idea is to nudge students, as gently as practicable, towards finding the answers for themselves.
Anyway, I'm still not sure what is meant by "two points that are 3 fringes apart". Do you mean, e.g., that there is a fringe at each and two more fringes between them? Eats Dirt, please post the exact and complete wording.

 

[Eats Dirt]

Anyway, I'm still not sure what is meant by "two points that are 3 fringes apart" ... Eats Dirt, please post the exact and complete wording.

It literally says the space between the two points is "3 fringes apart from top view" ... It is very ambiguous...

Perhaps, until I can clarify, just assume that the two points are 2p apart to allow three fringes, one at 0 one at p and one at 2p.

 

[haruspex]

It literally says the space between the two points is "3 fringes apart from top view" ... It is very ambiguous...

Perhaps, until I can clarify, just assume that the two points are 2p apart to allow three fringes, one at 0 one at p and one at 2p.

OK.
Where there is a bright fringe, what can you say about the separation of the two plates at that point in terms of λ?

 

[Eats Dirt]

OK.
Where there is a bright fringe, what can you say about the separation of the two plates at that point in terms of λ?

You can say that there is a maxima, so it corresponds to to a point of 2d=mλ, where m is the fringe number and d is the separation between the two plates?

 

[Eats Dirt]

If my above statement is correct then it would follow that <br /> 2d=m\lambda\\<br /> 2t_2=m\lambda\\<br /> 2t_1=(m+2)\lambda\\<br /> 2(t_1-t_2)=(m+2)\lambda-m\lambda\\<br /> (t_1-t_2)=\lambda<br />

 

[haruspex]

If my above statement is correct then it would follow that <br /> 2d=m\lambda\\<br /> 2t_2=m\lambda\\<br /> 2t_1=(m+2)\lambda\\<br /> 2(t_1-t_2)=(m+2)\lambda-m\lambda\\<br /> (t_1-t_2)=\lambda<br />

Yes, and that's consistent with mmmendon's answer since that was based on two intervening fringes instead of one