Question

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?

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 = 1.22lamda

sintheta = (1,22)(590e-9m) / (5.0e-3m) = 0.00014396
sin-1 (1.43e-4) = .00824
(.0082) - (1.227) = -1.21

Where did i go wrong and how do I fix it?

Answer 1

I agree with your formula for sin theta.

sin theta = 1.44*10^-4

theta = 0.0082 degrees

I don't understand why you subtracted 1.22 in the last step. You can't have a negative spread angle. You are subtracting a dimensionless number (1.22) from a number with dimensions of degrees. That is a no-no.

Answer 2

Well, that was a step my teacher did so I just followed it. However, .00082 degrees is not the correct answer either (or the variant of 8.2e-4). So I am just totally lost on this one. :/