Young's double slit and interference maximums

[DWill]

Homework Statement

In a Young's double slit experiment the width of each slit is a, the distance between the centers
of the slits is d, and the 10th interference maximum to the right of the central maximum is the first
missing maximum. a) Find the ratio of the slit separation distance to the width, d
a
b) Find the number of interference maximums across the central diffraction maximum.
c) Find the ratio of the intensity of the 5th interference maximum relative to intensity of the
central maximum.

Homework Equations

phi = (2pi / lambda) * d * sin(theta)
beta = (2pi / lambda) * a * sin(theta)

The Attempt at a Solution

(a) I see that the ratio d/a is phi/beta, but how do I determine the value of phi and beta? All I can think of is that the 1st minimum occurs at beta = 2pi, but I'm not sure how that would relate here.
(b) No idea on this one
(c) There's a long equation for I that relates it to I_o. It also includes cos^2 (phi/2) and also sin(beta/2), and is too long and I'm not sure how to write it here. I can figure this out I think if I know the value of either phi or beta, and then use the d/a ratio from part (a) to find the other value. Once I have those 2 I can use the equation to relate the 5th interference maximum intensity to I_o (central max intensity).

Some explanations will also be greatly appreciated!

 

[Redbelly98]

Your textbook should have an equation for the intensity of a single-slit diffraction pattern. You will need that.

There should also be an equation for the interference maximums.