Double slit problem with glass block

[Sarah Hallsway]

Homework Statement

Light of wavelength 600 nm passes through two slits separated by 0.20 mm and is observed on a screen 1.0 m behind the slits. The location of the central maximum is marked on the screen and labeled y=0.

(I only need help on the last 2 parts, but I will list all of them in case information from them is needed to complete the last parts.)

a. At what distance, on either side of y=0, are the m=1 bright fringes?

b. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0x10^-16 s in comparison to the wave going through the other slit.
What fraction of the period of the light wave is this delay?

c. With the glass in place, what is the phase difference, [delta phi][/0], between the two waves as they leave the slits?

d. The glass causes the interference fringe pattern on the screen to shift sideways. Which way does the central maximum move (toward or away from the slit with the glass) and by how far?

Homework Equations

lambda=yd/mL
where
y= place on y-axis of screen
d= distance between two slits
m=diffraction order
L= distance of slits from screen

and
period=1/frequency

lambda=v/f

The Attempt at a Solution

For the first problem, I plugged in the known values into the first equation I provided, and got an answer of 3.0 mm. For the second problem, I manipulated some variables in the bottom two equations to get a fraction of a period.

I am not stuck on the last two. For c, I started by dividing 1.0m/600E-9m to get how many wavelengths ahead one light beam is from the other. That value was 1.6E6. I took this to mean that without the glass, this value represented how far ahead the wave is from the other. However, without being given the thickness of the glass, I do not know how to take it into account.

For d, I am having a similar problem, since the thickness of the glass is unknown. Logically, I would imagine that the fringes would move away from the slit with the glass, since the glass has a higher n value than air does. To solve this problem, I drew a triangle from the two slits to the fringes, but could not find enough known values to calculate y.

Any help is appreciated. Thank you!

 

[haruspex]

For c, I started by dividing 1.0m/600E-9m

You are asked about the phase difference caused by the glass. Why would the distance from there to the screen be relevant?

 

[J Hann]

What is the distance the "unencumbered" wave has traveled from the slit when
the wave that was delayed by 5 * 10 E-16 sec emerges from its slit?
What fraction of a wavelength is this?
How does this affect the geometry at the slits?