Why is the central maximum brightest in double slit interference?

[journeytospace]

hi all...it is said that constructive interference happens when the path difference is nlambda and i think wavelength,frequency and amplitude of light going through both slits is the same then
why is the central maxima is the brightest spot?
why the brightness decreases when n increases?

Since the amplitude is same why there is difference in the brightness of the bright fringes?

 

[trinitron]

Because the amplitudes of the waves that constructively interfere are different at 'different n'.

 

[journeytospace]

why does the amplitude changes and why the central fringe is the brightest one(why not other fringes)..can u explain in detail about it?..

 

[trinitron]

Each of the slits acts as a radial light source (in the right half of the plane). You can think of it like this: Lines of equal field intensity are semi-circles. The intensity at a point on the circle is inversely proportional to its size, or in other words its distance from the point source. Now if you draw the screen, the screen's center is on a smaller circle (drawn around the source) than a point further away is.

 

[ZapperZ]

hi all...it is said that constructive interference happens when the path difference is nlambda and i think wavelength,frequency and amplitude of light going through both slits is the same then
why is the central maxima is the brightest spot?
why the brightness decreases when n increases?

Since the amplitude is same why there is difference in the brightness of the bright fringes?

This has nothing to do with quantum mechanics. I'm moving it out of there.

Zz.

 

[Claude Bile]

The diffraction pattern of a double-slit is a actually a convolution between the characteristic sinc^2 single-slit pattern that has a bright central peak and secondary peaks at either side of the central peak, and the characteristic cos^2 fringes.

The finite number of visible peaks comes about because of the finite width of the slits. As one reduces the width of the slits, the diffraction pattern will approach the ideal cos^2 case.

Each of the slits acts as a radial light source (in the right half of the plane).

This is wrong, slits don't act like point sources, they have a characteristic sinc^2 emittance profile. The reason the brightest fringe is in the centre is for the same reason single-slit diffraction has a bright central peak - it all boils down to the Huygens-Fresnel principle of secondary wavelets.

Claude.