Question

You need to use your cell phone, which broadcasts an 833 MHz signal, but you're in an alley between 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?

Answer 1

Let,

•        : be the space between buildings.
•        : be the frequency of the broadcast signal.

Given:-

• 
• 
• 

This is the problem of diffraction where electromagnetic wave encounters the obstacle. By single slit diffraction we have,

Where, is the angle for first diffraction minimum.

    is the wavelength of the electromagnetic wave and is given by,

Where, c is the speed of light. Therefore,

This is the angle between central maximum and first minimum for diffraction.

The angular width is twice of this angle thus,

This is the angular width of the electromagnetic wave after it emerges from between the buildings.