How Is the Angular Width of a Central Diffraction Maximum Calculated?

[msk172]

Homework Statement

A beam of yellow laser light (580 nm) passes through a circular aperture of diameter 4 mm. What is the angular width of the central diffraction maximum formed on a screen? (Define the angular width as the full angle from one minimum of the central diffraction maximum to the diametrically opposite minimum.)

Homework Equations

sinθ=1.22(λ/d)

θ = angle to first minimum
λ = wavelength
d = diameter of aperture

The Attempt at a Solution

This problem seems to be fairly straightforward, but I'm not coming up with the correct answer. Convert λ to mm to get .00058, divide by 4, and then multiply by 1.22. This value is equal to sinθ, so simply take sin-1 of that number to get θ. Computer does not like this answer. Help, anyone? Thanks in advance!

 

[msk172]

LOL. Disregard. Realized correct answer moments after posting. Thanks anyways!

 

[nlightner]

Your approach is correct, but there may be some rounding errors in your calculations. The angular width of the central diffraction maximum can be calculated using the formula θ = sin^-1(1.22(λ/d)), where λ is the wavelength in meters and d is the diameter of the aperture in meters. In this case, λ = 580 nm = 0.00058 m and d = 4 mm = 0.004 m. Plugging these values into the formula, we get θ = 0.00058/0.004 = 0.145 radians. To convert to degrees, simply multiply by 180/π, which gives an angular width of 8.32 degrees.