Wave Optics

In our discussion of lenses, mirrors and optical instruments we use the model of geometric optics in which we represent light as rays which are straight lines that are bent at a reflecting or refracting surface. Many aspects of the behavior of light can’t be understood on the basis of propagation of rays. Light is fundamentally a wave and in some situations we have to consider its wave properties explicitly.

If two or more light waves of the same frequency overlap at a point, the total effect depends on the phases of the waves as well as their amplitude. The resulting patterns are as a result of the wave nature of light and can’t be understood on the basis of rays.

Two monochromatic sources of the same frequency and with any definite, constant phase relation (not necessarily same phase) are said to be coherent.

The phase difference between two waves at a point will depend upon :

(i) the difference in path lengths of the two waves from their respective sources.

(ii) the refractive index of the medium

(iii) initial phase difference, between the sources, if any.

(iv) Reflections, if any, in the path followed by waves.

In the case of light waves,

The phase difference on account of path difference

Phase difference \displaystyle = \frac{Optical \, Path \, difference}{\lambda}\times 2\pi

Phase difference \displaystyle = \frac{ \mu (Geometrical \, Path \, difference )}{\lambda}\times 2\pi

where λ is the wavelength in free space.

In the case of reflection, the reflected disturbance differs in phase by π with respect to the incident one if the wave is incident on a denser medium from a rarer medium.

No such change of phase occurs when the wave is reflected in going from a denser medium to a rarer medium

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