A beam of yellow laser light (590 nm) passes through a circular aperture of diameter 5.0 mm. What is the angular width of the central diffraction maximum formed on a screen?

Question

I can't seem to get this answer right. I don't think I am finding the first part of the problem correctly, so could someone please correct me?

asintheta = .087lamda
so .087 as the first minimum

sintheta = (.087)(590e-9m) / (5.0e-3m) = 1.02e-5
sin-1 (1.02e-5) = 5.88e-4 degrees
(5.88e-4) - (.087) = 8.64e-2 degrees for angular width.

Where did i go wrong and how do I fix i

Answer 1

http://en.wikipedia.org/wiki/Angular_resolution

a sinTheta= 1.22 lambda

1.22 comes from a Bessel function, indicating the distance to the first min.

Answer 2

I just tried the problem with 1.22 and i got -1.21 as my final angular width. However, this is also incorrect.
any ideas where I am going wrong?

Answer 3

I have also tried using the positive of the angular width. But that is wrong, too. I used the same equation as i did above but with the 1.22