When light travels from a rarer (less optically dense) medium to a denser (more optically dense) medium, such as from air to water or from air to glass, a phenomenon called refraction occurs. Refraction is the bending of light as it passes from one medium to another with a different optical density.
The path difference refers to the difference in the path lengths traveled by two rays of light that are initially parallel but undergo refraction at an interface between two media. The path difference arises due to the difference in the speed of light in the two media.
The path difference can be calculated using the formula:
Δx = t × (n₂ - n₁),
where Δx is the path difference, t is the thickness or distance traveled in the denser medium, n₁ is the refractive index of the rarer medium, and n₂ is the refractive index of the denser medium.
It's important to note that the path difference only arises when there is a non-zero angle of incidence between the incident ray and the normal to the interface. If the incident ray is perpendicular to the interface, there will be no path difference.
The phenomenon of refraction and the associated path difference have important implications in various optical phenomena, such as the bending of light in lenses, the formation of rainbows, and the apparent displacement of objects when viewed through transparent media.