what does it mean by path difference and phase difference plz explain me in detail - Physics - Wave Optics

Question

what does it mean by path difference and phase difference plz
explain me in detail

A K Daya Sir · Accepted Answer

Path difference and phase difference is meaningful for waves of
same frequency and it is used to determine constructuve and
destructive interference in waves
Path difference (measured in terms of wavelength) is the actual
measurable difference in distance that two waves travel from a
source to a common point In my diagram the path difference between
the red and blue wave is lambda / 4 (For this measure the distance
between any two consecutive crests or trough in terms of
wavelength)
Phase difference (measured in radians) is the difference in the
phases of the two sinusoidal waves of same frequency In my diagram
the blue wave leads the red wave by a phase difference of pi/2 (or
90 degrees) It is denoted in the equation of the wave in the
argument of sine
(Wt - pi/2) is the phase at any time, while -pi/2 is the phase
difference
-
At time t = 0, the blue wave has displacement equal to 0, while
that of red wave has negative displacement (-A)
-
At pi/2, the blue wave has maximum positive displacement(+A),
while that of red wave is zero Hence Blue wave is leading by a
phase difference of pi/2 and path difference of lambda /4
There is a relation between path difference and phase difference
You know that one oscillation is completed in 2pi radian which is
equivalent to wavelength (lambda)
So path difference of one wavelength is equal to phase
difference of 2pi radian
Path difference of one unit is equal to phase difference of 2*pi
/ lambda
And path difference of x is equal to phase difference of (2*pi /
lambda) x = kx
The term [k = 2*pi / lambda] is a constant called wave
number
<img src="http://oi40%20tinypic%20com/2niuxpj%20jpg">
For constructive interference, the waves should differ by a path
difference of integral multiple of wavelength, lambda, 2 lambda, 3
lambda, so on
This is equal to phase difference of 0, 2pi, 4pi, 6pi even
multiple of pi
For destructive interference, the path difference should be odd
integral multiple of half-lambda
( lambda /2,
3 lambda /2,
5 lambda / 2
This is equal to phase difference of (pi, 3pi, 5pi, 7pi, odd
multiple of pi