Adding a polarizer is a nice variant of the experiment. I think I never heard it before. I like it, but I disagree with the expected result.
If the slit A has no polarizer and slit B has a polarizer, then in the "wall" you will the sum of 50% of the interference pattern and 50% of the diffraction pattern of A(I'm not sure about the 50%-50% split, something like that.) I.E. you will see the interference pattern, but it will not be so sharp, the black lines will not be so black, the white lines will not be so white.
I think it's better to put an horizontal polarizer on A and a vertical polarizer in B. If you don't add any other polarizer you will see the sum of the diffraction patters of A an B, without interference lines.
If you put a polarizer, the result depends on the direction:
* If it is horizontal you will see only the diffraction pattern of A (without interference lines).
* If it is vertical you will see only the diffraction pattern of B (without interference lines).
* At 45° you will see the diffraction pattern like in the original double slit experiment.
* At the other 45° you will see the inverted diffraction pattern, the black lines will be white and the white lines will be black. (All of this bounded by the diffraction pattern.)
* At other angles, you get some mix of the diffraction patterns and the interference patterns.
It would be nice to see an experimental realization of this.
If the slit A has no polarizer and slit B has a polarizer, then in the "wall" you will the sum of 50% of the interference pattern and 50% of the diffraction pattern of A(I'm not sure about the 50%-50% split, something like that.) I.E. you will see the interference pattern, but it will not be so sharp, the black lines will not be so black, the white lines will not be so white.
I think it's better to put an horizontal polarizer on A and a vertical polarizer in B. If you don't add any other polarizer you will see the sum of the diffraction patters of A an B, without interference lines.
If you put a polarizer, the result depends on the direction:
* If it is horizontal you will see only the diffraction pattern of A (without interference lines).
* If it is vertical you will see only the diffraction pattern of B (without interference lines).
* At 45° you will see the diffraction pattern like in the original double slit experiment.
* At the other 45° you will see the inverted diffraction pattern, the black lines will be white and the white lines will be black. (All of this bounded by the diffraction pattern.)
* At other angles, you get some mix of the diffraction patterns and the interference patterns.
It would be nice to see an experimental realization of this.