Ray geometry of Young’s experiment
In Fig. 26.13 all light waves leave Sl and S2 in the same phase, and the rays give the directions of the wave paths.
If we consider a point C on the perpendicular bisector of SIS 2′ the waves travelling along the rays SIC and S2C have travelled equal distances. Hence they will arrive in phase and interfere constructively to make C the centre of a bright fringe.
The next bright fringe is at A where the wave path S2A is one wavelength longer than SIA. Once more, the waves are in phase, making A the centre of a bright fringe. Similarly, B is the centre of a bright fringe where the path difference between S2B and SIB is two wavelengths. Subsequent bright fringes will be formed where the path differences are three, four, etc. wavelengths. The same explanation applies to the bright fringes formed on the side opposite to C, namely, at AI’ BI’ and so on. In between the bright fringes we get the dark ones (not shown on the diagram). The centres of these will be situated where the wave paths differ in length by 0.5 A, 1.5 A, 2.5 A, and so on, i.e., where the path difference is an odd number of halfwavelengths.
If, for convenience, we talk in terms of half-wavelengths, we may sum up the whole situation by saying: For bright fringes: wave path difference = zero or an even number of halfwavelengths. For dark fringes: wave path difference = an odd number of half-wavelengths.