When light travels from a rarer (less dense) medium to a denser medium, such as from air to water or air to glass, the path difference arises due to the change in the speed of light.
The path difference refers to the difference in the optical path length traveled by two rays of light that take different paths. Optical path length is defined as the product of the physical distance traveled by light and the refractive index of the medium through which it travels.
When light enters a denser medium, its speed decreases, and as a result, the wavelength of the light decreases while the frequency remains constant. This change in speed causes the light rays to bend towards the normal (the line perpendicular to the surface) at the interface between the two media.
The path difference occurs because the light ray traveling through the denser medium travels a shorter distance compared to the light ray in the rarer medium. The shorter path length in the denser medium leads to a phase difference between the two rays.
This phase difference is responsible for various phenomena, such as refraction, reflection, and interference. For example, in the case of refraction, the path difference causes the light ray to change direction as it enters the denser medium. In the case of interference, the path difference between two or more light rays can result in constructive or destructive interference, producing interference patterns.
To calculate the exact path difference, you need to know the refractive indices of the two media and the angles at which the light rays are incident on the interface. The path difference can be determined using the appropriate equations derived from Snell's law and the principles of wave optics.
In summary, when light travels from a rarer to a denser medium, the path difference arises due to the change in the speed of light. This path difference causes the light rays to bend and is responsible for various optical phenomena.