Intensity of Diffraction Pattern

[Stendhal]

Homework Statement

An interference pattern is produced by light with a wavelength 580 nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of 0.480 mm .

Let the slits have a width 0.320 mm . In terms of the intensity I_0 at the center of the central maximum, what is the intensity at the angular position of θ_1?

Edit: Apologies in advance for the messy equation below. I'm not quite sure how to use the toolbar above for subscripts and exponents.

Homework Equations

I_1 = I_0 * cos^2((π*d*sin(θ_1) / λ)*((sin(π*a*sin(θ_1)/λ)/(π*a*sin(θ_1)/λ))^2

θ_1 = 1.21*10^-3 rad

d = .480*10^-3 m

a = .320*10^-3 m

λ = 580*10^-9 m

The Attempt at a Solution

The equation is just multiplying the interference pattern by the diffraction pattern. Mostly just plugging in the variables and then solving from there.

The answer I got was .23[/0], but that was wrong. My question is, since the original problem is stating that the distance is being measured from center, would I subtract the width a from the separation d, so that I find the actual separation between the two slits?

 

[gneill]

The distance between the slits is measured center-to-center, so you don't need to subtract the slit width.

Your formula is tricky to parse, but I think that the parentheses are unbalanced. It can be tough to keep them straight when rendering them in ascii.

Here's a screen capture of the formula in question:

When I plug in your given values I don't get the same result that you did. (I get a smaller value).

Try breaking your calculation up into smaller steps and present the intermediate results. Perhaps we can spot where our versions diverge.

 

[Stendhal]

Alright so I first calculated π*a*sin(θ)/λ, which I got equal to 2.097

Then I took sin(ANS)/ANS = .4122

.4122^2 = .1699

Since the interference pattern for this problem comes out to approximately 1, the final answer is:

I = .17I_0

Is that what you got?

 

[gneill]

Yes. That's what I got.

 

[Stendhal]

Alright, I guess there was some sort of calculator error that messed me up. Thank you for your help!