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## Homework Statement

Hello everyone,

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:

Problem 22.18

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.

## Homework Equations

## 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.

Thanks,

Randy