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 y_0

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.

 

[member 553083]

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.