Grade 12 2-D Wave Interference

[012anonymousx]

Hello and thank you!

I am having trouble understanding Mr. Thomas Young's equations for the double-slit apparatus with the bands etc.

Specifically, for constructive interference:
Length = PS1-PS2 = n(lamda)

What I understand is that this n value is the phase shift in their wavelength. (i.e. one whole wavelength, a half a wavelength, etc.)

But for destructive interference, the formula is:
Length = PS1-PS2 = (n-0.5)(lamda)

Why is 0.5 being subtracted? I do not understand conceptually.

 

[Valerie Park]

The 0.5 is subtracted in order to account for the difference in phase between two waves arriving at a point. When two waves have a phase difference of 180 degrees, they cancel each other out and produce destructive interference. Subtracting 0.5 from the phase shift (n) represents this 180 degree phase difference.