Detecting the smoke

Classical Mechanics Level pending

Let's make a new way of detecting smoke in a room. There are two pipes of the same length \(l\) that pass maser emissions and that meet at one end. Normally, both of them are filled with air and when the maser rays meet, the detected intensity is the sum of the two ray intensities. However, if smoke enters one pipe, it changes the refractive index inside the pipe, and the maser rays may interfere constructively or destructively when they meet. If we want to observe the first order minimum when the smoke fills one of the pipes, what should be the length of the pipes \(l\) in mm?

Details and assumptions

  • Smoky air has a refractive index of 1.53.
  • A maser is like a laser, it just emits microwaves.
  • The maser has the wavelength \(1000 mm\)

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