I have one more problem left of my homework and I seemed to be stumped. I don't even know where to begin with this problem, which comes from the section of my book labeled Single-Slit Diffraction. Anyways, here is how the problem reads:
You need to use your cell phone, which broadcasts an 800 MHz signal, but you're behind two massive, radio-wave-absorbing buildings that have only a 15 m space between them.
What is the angular width, in degrees, of the electromagnetic wave after it emerges from between the buildings?
I calculated the wavelength at 800mhz = .381m
a= 15m (distance of the slit OR distance between two buildings.
The Attempt at a Solution
Due to the slit being so large, I am not sure how to approach the problem. I assume that we cannot use a small-angle approximation due to how large the slit and wavelengths are.
I think the equation to use would be the following
delta r= a/2 *sin(theta) = wavelength/2
However, I am not sure how to rearrange to get theta.
I tried rearrangeing to get aSin(theta) = wavelength => theta = sin-1(wavelength/a) and got 1.43 degrees. Would this be correct or did I just hammer the problem?
If anyway can give me a hand (or somewhere to start) I would really appreciate it.