THIN FILM INTERFERENCE
Constructive: 2t = (m +
1/2)(λ/n) in one special case!
Destructive: 2t = m (λ/n)
in one special case!
Here m is any positive
integer.
These equations are for the
case that nfilm is greater than nair.
Instead of “remembering a formula,” which will be inappropriate
half the time, it is vital to work out the path and phase
differences from scratch in each individual example.
THE INTERFEROMETER
LIGO, the gravitational
radiation observatories.
NEXT
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)
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