Multiple Slit Interference - 3rd Slit Added Between 2 Slits

[SMA777]

Homework Statement

Suppose a third slit of the same width were added halfway between the original two slits.
(the original two slits were a distance d apart). When there were just 2 slits, the point C was the center (a principal max), point Z was the first maximum after C, point Y was the second maximum after C, and point X was the minimum after Y (or the 3rd minimum after C).

a. Would point Z be a principal maximum, a minimum, or neither? Explain
b. Would point Y be a principal maximum, a minimum, or neither? Explain
c. Would point X be a principal maximum, a minimum, or neither? Explain

Homework Equations

ΔD = dsinθ where ΔD is the path length difference between slits, and d is the distance between slits

The Attempt at a Solution

I really don't know where to begin. If we say ΔD1 was the path length difference between the two slits, then ΔD2 = 2 ΔD1 where ΔD2 is the path length difference between slit 1 and 3. (by my labeling original slits were slit 1 and 3, and slit 2 was added in the middle, a distance d/2 from each original slit)

I know C would still be a maximum because it is the center. Other than that, I'm not sure where to begin. Any tips are appreciated.

 

[Spinnor]

This might help,

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html#c3

https://www.google.com/search?hl=en...&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi