Wave interference from 2 point source

[Kinto]

Hi,

I am trying to understand wave interference from 2 point source. The derived formula in the textbook says |p1s1 - p1s2| = 1/2 wavelength. How did they derive at the 1/2 wavelength? I connected P1 to source 1 (s1) and then to source 2 (s2). But I don't understand how they've arrived at half wavelength.

Thanks

 

[himanshu121]

There are many possiblities Pls Show a diag how relatively the two point sources are related

And obviously the difference is path difference which depends upon many factors what is initial phase difference, how they are positioned w.r.t P etc...

Is it a complete information Is sources Placed in as in Youngs double slit Experiment etc[?] [?] [?]

 

[M98Ranger]

for reaching out! The formula you mentioned, |p1s1 - p1s2| = 1/2 wavelength, is known as the path difference formula for two point sources. It is derived from the principle of superposition, which states that when two or more waves meet at a point, the resulting wave is the sum of the individual waves at that point.

In the case of two point sources, the waves they produce will interfere with each other. This interference can either be constructive, where the waves add up and create a larger amplitude, or destructive, where the waves cancel each other out and create a smaller amplitude. The path difference between the two sources is the difference in the distance traveled by the waves from each source to a specific point of observation.

To understand why the path difference is equal to half a wavelength, we need to look at the nature of waves. Waves have a property known as wavelength, which is the distance between two consecutive peaks or troughs of the wave. When two waves with the same wavelength meet, their peaks and troughs will align, resulting in constructive interference. However, if the path difference between the two waves is equal to half a wavelength, the peaks of one wave will align with the troughs of the other, resulting in destructive interference. This is why the path difference formula for two point sources is given as 1/2 wavelength.

I hope this helps clarify the derivation of the formula for you. Keep exploring and asking questions to deepen your understanding of wave interference!