Answer
(a) destructive interference
(b) constructive interference
(c) constructive interference
Work Step by Step
(a) We know that the phase difference between the waves is given as
$\Delta \phi=\frac{2d}{\lambda}+\frac{1}{2}$
We plug in the known values to obtain:
$\Delta \phi=\frac{2(0.60\times 10^{-6}m)}{600\times 10^{-9}m}+\frac{1}{2}$
$\Delta \phi=2.5$
Thus, in the given scenario, the interference is destructive.
(b) We know that
$\Delta \phi=\frac{2d}{\lambda}+\frac{1}{2}$
We plug in the known values to obtain:
$\Delta \phi=\frac{2(0.60\times 10^{-6}m)}{800\times 10^{-9}m}+\frac{1}{2}=2.0$
Thus, the given case is constructive interference.
(c) We know that
$\Delta \phi=\frac{2(0.60\times 10^{-6}m)}{343\times 10^{-9}m}+\frac{1}{2}$
$\Delta \phi=3.5+0.5=4.0$
Thus, the given case is constructive interference.
