Two waves, from the same source, may arrive at a point by different paths. Path Difference can be:

1.    Geometrical Path Difference:    If there is a physical difference in the routes travelled:

2.    Optical Path Difference: This difference arises when one of the waves undergoes refraction, through another                   medium, causing a change in its wavelength. When the two waves arrive at the destination they have travelled a            different number of wavelengths. The optical path difference (OPD) is thus quoted in terms of wavelength.

    The diagram shows two rays of light travelling along paths of equal geometric length. One travels through the air and       the second passes through a block of glass of length LThe wavelength of the light in glass decreases due to refraction      and it exits the glass out of phase with wave 1. It can be shown that a length L, in a medium of refractive index n,           is equivalent to the length nl in air.

The geometric path length in the glass     =    L

The optical path length in the glass          =    nglass L

So, the optical path difference (OPD)       =    nglass L    -     nair L

Thus,                                         OPD        =    nglass L    -     L            (as  nair = 1.0)

Path Difference and Interference:

Path difference contributes to interference. If waves are out of phase they will interfere destructively. If they are in phase then they interfere constructively...

S1 and S2 are two coherent sources of waves in air:

The path difference is (S2Q - S1Q).

For constructive interference to take place at Q the waves must be in phase so this difference must be a whole number of wavelengths (m):

PD    =    (S2Q - S1Q) = λ                where m = 0,1,2,3...

For destructive interference to occur the waves must be out of phase at Q, which means a PD of  λ/2, so:

PD    =    (S2Q - S1Q) = (m + 1/2 ) λ    where m = 0,1,2,3...

NB: Whether the path difference is geometrical or optical these rules apply.

The phase difference at Q is related to the optical path difference by:

where λ is the wavelength in vacuum.

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