# Three bright fringes

1. Feb 22, 2014

### Eats Dirt

1. The problem statement, all variables and given/known data
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) ?

2. Relevant equations

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

3. 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

$$3\lambda_o=2n_f (t_1-t_2)+\frac{\lambda_o}{2}\\ \frac{1}{2n_f}[3\lambda_o-\frac{\lambda_o}{2}]= (t_1-t_2)$$

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

Any help would be much appreciated.

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Last edited: Feb 22, 2014
2. Feb 22, 2014

### haruspex

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?

3. Feb 23, 2014

### Eats Dirt

the question says "three fringes apart".

4. Feb 23, 2014

### haruspex

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.

5. Feb 23, 2014

### 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

6. Feb 23, 2014

### Eats Dirt

Do you mind elaborating on the method you used?

7. Feb 23, 2014

### haruspex

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.

8. Feb 23, 2014

### Eats Dirt

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.

9. Feb 24, 2014

### haruspex

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?

10. Feb 24, 2014

### Eats Dirt

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?

11. Feb 24, 2014

### Eats Dirt

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

12. Feb 24, 2014

### haruspex

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