Understanding Young's Double Slit Experiment: Why 4.5 Fringes Shift?

In summary, the central bright fringe in Young's double slit experiment shifts 4.5 fringes when a piece of plastic is placed in front of one of the slits. This is because the thicker the plastic, the more it will shift the central maximum. The central maximum is where the phase difference is zero and adding the plastic adds 4.5 wavelengths to any path from that slit to the screen, resulting in the central maximum moving 4.5 wavelengths farther away from the other slit.
  • #1
Oerg
352
0
I have a problem on Young's double slits which says that the central bright fringe shifts 4.5? fringes after a piece of plastic is placed in front one of the slits.

My question is: Why is the central bright fringe shifted for 4.5 fringes? Shouldn't it be 0.5 fringe instead since maximum interference is already achieved then? (Because 4 wavelengths of optical path difference is the same as none at all [no considering the coherence length])
 
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  • #2
You are quite right is saying that 4 wavelengths are the same as none at all, but we are not talking about the phase change here. A thicker piece of plastic will shift the central maximum more than a thinner piece, i.e. the shift depends on how many wavelengths you can fit within a particular thickness of plastic.
 
  • #3
well, since there is an optical path difference then there is a phase change and the condition becomes [tex] a\sin{\theta}=OPD-\frac{OPD}{\lambda}+m\lambda [/tex]. Shouldn't this be the case?
 
  • #4
Consider what happens to the point where the central maximum was initially. With insertion of the plastic, this point is occupied by what used to be the minimum between fringes 4 and 5. Therefore, displacing air of thickness d with plastic of thickness d and index of refraction n adds 4.5 wavelengths to the central path, i.e.

[tex]\frac{d}{\lambda/n}=\frac{d}{\lambda}+4.5[/tex]
 
  • #5
but isn't the central fringe supposed to be the fringe where [tex] \theta [/tex] gives a maximum interference for the lowest [tex] \theta [/tex]? Because the sin function has a decreasing gradient, the size of the the central fringe is the largest so the central fringe can't possibly move more than a fringe. Is there anything wrong with my reasoning?
 
  • #6
Oerg said:
but isn't the central fringe supposed to be the fringe where [tex] \theta [/tex] gives a maximum interference for the lowest [tex] \theta [/tex]? Because the sin function has a decreasing gradient, the size of the the central fringe is the largest so the central fringe can't possibly move more than a fringe. Is there anything wrong with my reasoning?
The central fringe appears where the phase difference is zero (or path length difference is zero wavelengths). Fringe 4 appears where the phase difference is 4*2π (or path length difference is 4 wavelengths).

When you add the plastic to one slit, you are essentially adding 4.5λ to any path from that slit to the screen. The central maximum correspondingly moves to a point on the screen that is 4.5λ farther away from the other slit in order to preserve the criterion that the difference between the two paths is zero wavelengths.
 

1. What is Young's Double Slit Experiment?

Young's Double Slit Experiment is a classic physics experiment conducted by Thomas Young in the early 1800s to demonstrate the wave-like nature of light. It involves passing a beam of light through two parallel slits and observing the interference pattern formed on a screen placed behind the slits.

2. Why does the experiment result in a pattern of fringes?

This experiment results in a pattern of fringes because when light passes through the two slits, it diffracts and creates two new wavefronts. These wavefronts interfere with each other, creating areas of constructive and destructive interference, resulting in a pattern of bright and dark fringes on the screen.

3. What causes the fringes to shift in Young's Double Slit Experiment?

The fringes in Young's Double Slit Experiment can shift due to a change in the wavelength of the light source, a change in the distance between the slits, or a change in the distance between the slits and the screen. These changes affect the path length of the light waves, causing the interference pattern to shift.

4. Why is the shift in fringes approximately 4.5?

The shift in fringes in Young's Double Slit Experiment is approximately 4.5 because it is the result of the wavelength of the light source being much smaller than the distance between the slits and the screen. This causes the interference pattern to spread out and the fringes to shift by a fraction of the wavelength, which is approximately 4.5.

5. How does Young's Double Slit Experiment support the wave theory of light?

Young's Double Slit Experiment supports the wave theory of light by demonstrating that light exhibits properties of waves, such as interference and diffraction. The experiment also shows that light behaves as a wave, spreading out and creating a pattern of fringes, rather than just a straight beam of light. This supports the idea that light is a wave rather than a particle, as predicted by the wave theory of light.

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