The interference effect at any point is to be observed by the eye. Due to persistence of vision eye cannot detect rapid changes in intensity. To observe interference, we want the effect at any point to remains same at all times. This will be so if δT does not depend on time. For a given set up; for a particular point P; δ is time independent; therefore δT will not depend on time if δi remains same at all times. Any two sources of light having same phase difference at all times are known as coherent sources. To observe interference with light we must have coherent sources.
Independent; idential sources of light are not coherent sources. Their phase difference changes 108 times in one second. With such sources the interference pattern changes 108 times in one second. The eye cannot follow such rapids changes. The interference produced is, therefore, not observed. To observe interference with light we have to produce coherent sources from an incohorent source. This can be achieved by using
(i) reflection
(ii) refraction
(iii) multiple reflection and refraction of light