Question about a double-slit experiment

[Nivlac2425]

Homework Statement

A sheet of plastic, n=1.6, covers the entrance of one slit of a double-slit. When the double-slit is illuminated by monochromatic light with wavelength = 586 nm, the center of the screen on the other side of the double-slit appears dark rather than light. What is the minimum thickness of this sheet of plastic?

Homework Equations

The Attempt at a Solution

I know that in order for the bright area on the screen to be dark instead of light, destructive interference must be occurring.
I can also find the velocity, v, of the light in the plastic with the equation n=c/v

 

[drolex]

You can also find the phase difference in the light between the two slits. You need equations. Maybe read the section in your book about the "Double Slit Experiment".

 

[Nivlac2425]

To have destructive interference, the light would have to have a 180degree phase difference right? But how does the thickness of the plastic affect the phase difference of the light in respect to the unaffected light?

Thanks

 

[Doc Al]

But how does the thickness of the plastic affect the phase difference of the light in respect to the unaffected light?

Compare the phase shift of light going through a thickness of plastic versus light going through the same thickness of air (or vacuum). Hint: Consider how the wavelength changes in the plastic.

 

[Nivlac2425]

The wavelength is decreased in the plastic, but by how much? Thickness probably affects that, but what else, the index of refraction? It would need a net phase change of 180 degrees to cause destructive interference.

Thanks

 

[Doc Al]

The wavelength of light in a material depends on the material's index of refraction. The phase change in passing through the material depends on the material's thickness and the wavelength of light in the material.