Double Slit Experiment glass thickness

[y_chen]

A double-slit experiment is set up using a helium-neon laser (lambda =633nm) . Then a very thin piece of glass ( n=1.50 ) is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the m = 15.0 dark fringe. How thick is the glass?

I really need help on this question. I understand that for the double-slit experiment, destructive interference occurs when d sin theta= (m-0.5)lambda. However, I do not understand how to incorporate the information about the central point being occupied by what had been the m=15.0 dark fringe. Also, how does the piece of glass play a role in the question? Thanks so much for all your help!

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[cesiumfrog]

You have a http://groups.google.com/group/Gmail-ABCs/browse_thread/thread/1e89d941615e3d35"

As for how the glass plays a role, instead of just using some formula you will need to understand conceptually how that formula is derived (so that you can derive an appropriately modified version). Recall that the wavelength depends on the refractive index.

 

[ogb p]

I understand your confusion and am happy to help you understand this concept better. In the double-slit experiment, light passes through two slits and creates an interference pattern on a screen. The distance between the slits, d, and the wavelength of the light, lambda, determine the location of the bright and dark fringes on the screen.

In this scenario, the thickness of the glass (n=1.50) plays a role in altering the path of the light passing through it. This means that the light passing through the glass will have a different wavelength, and therefore, the interference pattern on the screen will also be affected.

The central point on the screen being occupied by the m=15.0 dark fringe means that the light passing through the glass has created destructive interference at that point. Using the equation d sin theta= (m-0.5)lambda, we can calculate the thickness of the glass by substituting the values we know:

d sin theta = (m-0.5)lambda

d * sin 90° = (15-0.5)*(633nm)

d = (14.5)*(633nm)/sin 90°

d = 9160.5nm

Therefore, the thickness of the glass is approximately 9.16 micrometers.

I hope this explanation helps you understand the concept better. Remember, as a scientist, it is important to always question and seek understanding in order to further our knowledge and discoveries. Best of luck in your studies!