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

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In summary: Yes, and that's consistent with mmmendon's answer since that was based on two intervening fringes instead of one.
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Eats Dirt
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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



[tex] m\lambda_o=2n_f t\cos\theta_t+\frac{\lambda_o}{2}[/tex]

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.

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

[tex]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) [/tex]

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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  • #2
Eats Dirt said:
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?
 
  • #3
haruspex said:
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".
 
  • #4
Eats Dirt said:
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.
 
  • #5
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
mmmendon said:
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?
 
  • #7
mmmendon said:
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.
 
  • #8
haruspex said:
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.
 
  • #9
Eats Dirt said:
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?
 
  • #10
haruspex said:
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?
 
  • #11
If my above statement is correct then it would follow that [tex]
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
[/tex]
 
  • #12
Eats Dirt said:
If my above statement is correct then it would follow that [tex]
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
[/tex]
Yes, and that's consistent with mmmendon's answer since that was based on two intervening fringes instead of one
 
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1. What are "three bright fringes" in the context of science?

Three bright fringes refer to the three central bright spots that are produced when light passes through a narrow slit or is diffracted by an object. These fringes are a result of constructive interference, where the waves from the light source combine to form a brighter spot.

2. How are three bright fringes related to the phenomenon of interference?

Three bright fringes are a direct result of interference, which is the interaction of two or more waves. When light waves interfere with each other, they can either cancel each other out (destructive interference) or combine to form a brighter spot (constructive interference). In the case of three bright fringes, constructive interference occurs, resulting in three bright spots.

3. What is the significance of studying three bright fringes in scientific research?

The study of three bright fringes is important in the field of optics and wave mechanics. It helps us understand the principles of interference and diffraction, which can be applied in various fields such as imaging, spectroscopy, and particle physics. The phenomenon of three bright fringes also has practical applications, such as in the development of diffraction gratings and interferometers.

4. How can we observe three bright fringes in a laboratory setting?

To observe three bright fringes, we need a coherent light source, such as a laser, and a narrow slit through which the light can pass. The light will then be diffracted, and the resulting interference pattern can be observed on a screen placed behind the slit. Three bright fringes will appear as three bright spots in the center of the pattern.

5. Can three bright fringes appear in other forms of waves besides light?

Yes, the phenomenon of three bright fringes can occur with any type of wave, such as sound waves, water waves, and even electromagnetic waves. As long as there is a coherent source and an obstruction or slit for the wave to pass through, three bright fringes can be observed. This allows for the study of interference and diffraction in various fields of science and engineering.

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