How Does a Thin Glass Affect the Double Slit Interference Pattern?

[G01]

Light of wavelength 600nm passes through two slits separated by .2mm and is observed on a screen 1.0m behind the slits. The location of the central max is marked on the screen and labeled [tex]y_0[/tex]

A) at what distance are the m = 1 bright fringes. I got this part. the answer is .003m or 3mm.

B) A very thin piece of glass is placed over one hole, causing the light in that hole to move slower. The light is delayed by 5.0 X 10^-16s. What fraction of the wave period is this. It is 1/4 of the wave period. I got this as well.

C) The phase difference? The one wave is delayed by 1/4 of a period, so the phase difference is pi/2.

D) Which way does the central max move and how far. I know it moves toward the glass covered hole, but I can't figure out how far. Can anyone help me to figure out how to proceed with this part. Even a small hint will help. Thank you.

 

[Nate810]

The central max moves toward the glass covered hole, but the exact distance it moves depends on the wavelength of the light. Using the equation d = (mλ)/(2d_s), where m is the order of the max (in this case, 0), λ is the wavelength of the light (600 nm), and d_s is the slit separation (0.2mm), you can calculate the distance the central max moves. This gives a displacement of 0.003 mm, or 3 microns.

 

[kyle8921]

The central max will move towards the glass covered hole because the light passing through it is slowed down, causing a phase difference between the two waves. To calculate how far the central max will move, you can use the formula y = λD/d, where y is the distance from the central max to the glass covered hole, λ is the wavelength, D is the distance from the slits to the screen, and d is the distance between the slits. In this case, the wavelength remains the same at 600nm and the distance from the slits to the screen is 1.0m. However, the distance between the slits changes to 0.2mm + 5.0 x 10^-16s, which is essentially the original distance plus a very small amount. This means that the central max will move a very small distance towards the glass covered hole, but the exact amount will depend on the value of the added delay.