When light travels from a denser medium to a rarer medium, such as from water to air or from glass to air, the path difference arises due to the change in the refractive index of the media. The refractive index, denoted by the symbol "n," is a measure of how much light is bent or refracted as it passes through a medium.
The path difference is the extra distance that light travels in the denser medium compared to the rarer medium. It can be calculated using the following formula:
Path Difference = (n1 - n2) * d
Where:
- n1 is the refractive index of the denser medium,
- n2 is the refractive index of the rarer medium, and
- d is the thickness of the medium the light is passing through.
The refractive index of a medium is a dimensionless quantity that determines how much the speed of light is reduced when it enters that medium compared to its speed in a vacuum. Since the speed of light in a vacuum is constant, the refractive index directly relates to the change in the speed of light.
The path difference accounts for the change in the speed of light and results in a phase shift between the light waves passing through the two different media. This phase shift can lead to phenomena such as refraction, reflection, or interference, depending on the specific conditions and geometries involved.