Interference of light Intensity

[mbnMecha]

An Interference pattern is produced by light of wavelength 490nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of d=0.630mm.
a) If the slits were very narrow what would be the angular position theta1 and theta2 of the first and second lateral interference maxima?
b)Let the slits have width a=0.42 mm. In terms of the intensity I0 at the center of the central maximum, what is the intensity at each of the angular positions theta1 and theta2

Homework Equations

Intensity of light during diffraction:
I=Im (sinx/x)^2 where I am is the max intensity and x=phase difference/2 = (pi*a*sin(theta))/wavelength
Intensity of light during interference
I=4I0cos^2(z) where z = phasedifference/2 = (pi*d*sin(theta))/wavelength

Intensity of light during double slit diffraction
I=Imcos^2(z)*(sinx/x)^2)

The Attempt at a Solution

I have solved for theta1 and theta2 and got:
theta1=7.78 x 10^(-4) rd
theta2= 1.55 x 10^(-3) rdWhat I can't seem to understand is how to find part the intensities in part b. the question does not mention whether we should take the Effects of diffraction into consideration and I don't know what formula to use. what should I do?

 

[mfb]

What I can't seem to understand is how to find part the intensities in part b. the question does not mention whether we should take the Effects of diffraction into consideration

You have to take them into account, otherwise there won't be an intensity change. This diffraction is an interference effect as well, by the way.

and I don't know what formula to use.

The one you have posted.

 

[mbnMecha]

You have to take them into account, otherwise there won't be an intensity change. This diffraction is an interference effect as well, by the way.The one you have posted.

I have posted 3 equations.. does that mean I have to consider the equation with both the interference and the diffraction factors? thanks in advance.

 

[mfb]

Well, you know the result of the "interference formula" already: you are calculating the intensity of a maximum.