Path length difference and Diffraction

[fogvajarash]

Homework Statement

A double slit experiment is set up using a helium-neon laser (wavelength 633 nm). Suppose we add a small piece of glass (n = 1.50) over one of the slits. Then, the central point on the screen is occupied by what had been the m = 10 dark fringe. Determine the thickness t of the glass.

Homework Equations

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The Attempt at a Solution

I'm trying to figure out how to understand the solution to this problem. Basically the solution shows as a reference the diagram attached. However, what I don't understand is why would adding the glass shift the rays like that? Is there any known explanation for that? How do we know that the interference that produces the central fringe is shifted?

Then, the solution stated finding the number of the wavelengths in both the glass and the "no glass interface". The equations are m₁ = t/λ and m₂ = (nt)/λ. Then, it states that the path length has increased by Δm wavelengths. Why is this the case? I thought that the path length was the "extra distance" that one of the rays had traveled with respect with the other. Is there a way to say in this case that the path length will be "Δm"?

I am sorry if I am not clear, but the topic is very confusing for me right now (especially understanding how does glass shift the fringe patterns and the meaning of the path length difference). Thanks for your patience.

Image link: http://imgur.com/aTBc067

 

[SammyS]

Homework Statement

A double slit experiment is set up using a helium-neon laser (wavelength 633 nm). Suppose we add a small piece of glass (n = 1.50) over one of the slits. Then, the central point on the screen is occupied by what had been the m = 10 dark fringe. Determine the thickness t of the glass.

Homework Equations

-

The Attempt at a Solution

I'm trying to figure out how to understand the solution to this problem. Basically the solution shows as a reference the diagram attached. However, what I don't understand is why would adding the glass shift the rays like that? Is there any known explanation for that? How do we know that the interference that produces the central fringe is shifted?

Then, the solution stated finding the number of the wavelengths in both the glass and the "no glass interface". The equations are m₁ = t/λ and m₂ = (nt)/λ. Then, it states that the path length has increased by Δm wavelengths. Why is this the case? I thought that the path length was the "extra distance" that one of the rays had traveled with respect with the other. Is there a way to say in this case that the path length will be "Δm"?

I am sorry if I am not clear, but the topic is very confusing for me right now (especially understanding how does glass shift the fringe patterns and the meaning of the path length difference). Thanks for your patience.

Image link: http://imgur.com/aTBc067

The wavelength is reduced in the glass relative to what it is in a vacuum . There are more waves in the glass than there would be with the glass removed. So it is as if there is added path length for light traveling through the glass.

 

[fogvajarash]

The wavelength is reduced in the glass relative to what it is in a vacuum . There are more waves in the glass than there would be with the glass removed. So it is as if there is added path length for light traveling through the glass.

Thanks, that's helpful. I understand that there are less waves in the vacuum medium, but how does this relate to the path length? Does the "extra number of wavelengths" mean path length? And as well, I still don't understand why having the glass would deflect the light rays in that way (both in the vacuum slit and in the slit with glass) to produce the central maximum. Why is this?

Thank you for your answer.