(Solved): Light ( = 600 nm) is incident on a setup with six slits. The width of each slit is a = 1.5 mm, and ...

Light (? = 600 nm) is incident on a setup with six slits. The width of each slit is a = 1.5 mm, and the
separation between each successive slit is d = 8 mm. The light passing through the slits creates a pattern
on a screen that is L = 1.25 m away.

a) For the first few parts of this problem, you can ignore the effects of the diffraction envelope, and consider
the interference pattern only.
How far above the central bright spot is the first order principal maximum? (In the figure, what is the
value y for this maximum?)
(b) Between principal maxima, there are also secondary maxima with minima between them.
How many minima are there between the m=0 and m=1 principal maxima? What phase differences
(?) between rays from successive slits cause these dark spots? For each phase difference, draw the
associated phasor diagrams that add the six rays to show that they result in no light.
(c) Now we’ll add in the effects of diffraction from the width of the slits.
In part (a), you found the location of the first order principal maximum. Assuming that the central
maximum has intensity I0, what is the intensity of the first order maximum?
(d) How many bright fringes (principal maxima) are observed within the central diffraction envelope?
(e) Let’s say you want to be able to resolve fringes from two wavelengths, ?1 = 600.0 nm and ?2 = 600.5
nm with at the fourth order maximum. What is the minimum number of slits to resolve these fringes?
Can it be done with this setup?