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 **L**. The 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 = **n**_{glass} **L**

So, the optical path difference (OPD) = **n**_{glass} **L** - **n**_{air} **L**

Thus, **OPD** = **n**_{glass} **L** - **L ** (as **n**_{air} = 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*...

S_{1} and S_{2} are two coherent sources of waves **in air**:

The path difference is (S_{2}Q - S_{1}Q).

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** = (S_{2}Q - S_{1}Q) = **m ****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** = (S_{2}Q - S_{1}Q) = (**m + **^{1}/_{2} ) **λ **where **m** = 0,1,2,3...

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

**Q**is related to the optical path difference by:

**λ**is the wavelength in vacuum.