# What happens to the central bright fringe if the overlapping of the waves in phase do not happen crest on crest

In a Young's double slit experiment,we get the central bright fringe in the middle of the screen taking that the waves coming from the slits being in phase overlap each other with crest on crest or trough on trough,

but what if they overlap in some other stage like if the overlapping takes place with points of any other intermediate displacement or no displacement that is with phase 180 degrees,

if that happens we should get a dark fringe instead of a bright one and the central bright fringe may get displaced up or down the screen,

so does the position of the bright fringe depend on the distance between the slit and screen and a small displacement may result in dark fringe in the center.

The condition for constructive interference at a point P is that the waves arrive there in phase. Only twice every period will the waves arrive crest-on-crest or trough-on-trough. When this happens the resultant wave at P will have peak displacement. But that's the same for any wave passing through a point: the wave will have peak displacement only twice a cycle. The point is that when waves of equal amplitude arrive in phase the displacement at any time will be twice the displacements of the individual waves.

Elementary explanations of constructive interference often stress "peak-on-peak or trough-on-trough". This can be misleading, as your question suggests.

If the waves, of amplitude $$A,$$ arrive at P differing in phase by angle $$\phi,$$ the amplitude of the resultant wave at P is $$|2A \cos \frac{\phi}{2}|.$$

• thanks a lot,cleared all confusions,just one thing in "If the waves, of amplitude A, arrive at P differing in phase by angle ϕ, the amplitude of the resultant wave at P is |Acosϕ2|. " , in |Acosϕ2|. when the waves are in phase ie ϕ = 0,resultant comes as A where as it should be 2A,how it comes to 2A,thanks. – sachin Apr 1 '19 at 16:02
• That was very silly of me. Now corrected! – Philip Wood Apr 1 '19 at 17:32
• thanks,l request if u can reach my other post what should clear all my queries in wave optics,physics.stackexchange.com/questions/467409/… – sachin Apr 2 '19 at 6:15
• I'll have a look, but can't do so for a few hours – by which time you'll probably have received a good answer anyway. – Philip Wood Apr 2 '19 at 6:56

Its only called the central fringe because it's directly between the two slits. The coherent photons have equal distances to travel and reach the center in-phase.On the left and right side of the central fringe is a dark fringe because the photons travel different lengths leaving them 180 degrees out of phase.

• thanks,just wanted to know,by coherent we mean two waves should have the same frequency and phase but m finding if two waves are having same frequency they are automatically in phase and if they are in phase they are automatically having same frequency,can u clear this issue. – sachin Apr 2 '19 at 6:18
• @sachin Photons or waves with the same frequency can be in or out of phase. – Bill Alsept Apr 2 '19 at 6:52