What Causes Equal Interference Amplitudes in Light Diffraction Patterns?

[waley]

Here's a picture that was in my textbook - they are the patterns of interference and diffraction of a light wave. I don't get why the interference amplitudes are all equal. Aren't they supposed to be higher in the middle and lower as they move away from the center??

 

[mfb]

Why do you expect them to be different?
The single-slit pattern makes them different, so what you actually see (the red curve) is different, but the two slits always show the same constructive interference in all these maxima.

 

[waley]

Why do you expect them to be different?
The single-slit pattern makes them different, so what you actually see (the red curve) is different, but the two slits always show the same constructive interference in all these maxima.

Doesn't intensity decrease as you go further from the central max?

 

[mfb]

Only from the single-slit-like pattern. That's what the graph shows.

 

[waley]

Only from the single-slit-like pattern. That's what the graph shows.

I thought the purple line on the graph showed the interference pattern of a double slit. I get that the product of the interference and diffraction patterns should produce a pattern with descending intensity, it's just the equal amplitudes of the purple line that's tripping me up. So are you saying that intensity of a double slit interference pattern is constant?

 

[mfb]

In the limit of infinitely narrow slits, and with the approximation that the whole screen has the same distance to the slits (apart from the path differences between the slits), yes.

 

[waley]

In the limit of infinitely narrow slits, and with the approximation that the whole screen has the same distance to the slits (apart from the path differences between the slits), yes.

Ohh I think I get it. It's only with diffraction that you consider a finite slit width. Thanks for the help

 

[sophiecentaur]

The calculated interference pattern never gives the totally right answer but it gives a good idea of how narrow the peaks will be. What you do for a better answer is to multiply the interference pattern by the slit diffraction. It only works when ALL slits are identical.

 

[jtbell]

What you do for a better answer is to multiply the interference pattern by the slit diffraction.

For example, as below, for two slits with non-negligible width:

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/dslit.html