# Question about a double-slit experiment

1. Jan 2, 2009

### Nivlac2425

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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 occuring.
I can also find the velocity, v, of the light in the plastic with the equation n=c/v

2. Jan 2, 2009

### 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".

3. Jan 2, 2009

### 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

4. Jan 3, 2009

### Staff: Mentor

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.

5. Jan 3, 2009

### 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

6. Jan 4, 2009

### Staff: Mentor

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.