# Multiple Slit Interference - 3rd Slit Added Between 2 Slits

1. Nov 13, 2012

### SMA777

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

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

2. Relevant equations

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

3. 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.

2. Nov 13, 2012