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?

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.

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. :/

To find the angular width of the central diffraction maximum, you're on the right track using the formula asin(theta) = 1.22 * lambda, where theta is the angular width in radians and lambda is the wavelength of the light.

However, there are a couple of errors in your calculation:

1. First, let's convert the diameter of the circular aperture from millimeters to meters correctly. You have the diameter as 5.0 mm, so it should be written as 5.0e-3 m, not 5.0e-6 m.

2. Secondly, when you calculate sin(theta), you used the incorrect value of 1.22 as a coefficient. The correct value is indeed 1.22, but you should use sin(theta) = (1.22 * lambda) / (d), where d is the diameter of the circular aperture.

Let's correct the calculation step by step:

d = 5.0e-3 m
lambda = 590e-9 m

sin(theta) = (1.22 * lambda) / d
*sin(theta) = (1.22 * 590e-9 m) / (5.0e-3 m)
*sin(theta) = 0.143256
theta = sin^(-1)(0.143256)
theta ≈ 8.25 degrees

So, the correct angular width of the central diffraction maximum formed on the screen is approximately 8.25 degrees.