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It is only the act of trying to measure what it is that disengages the cloaking device and the particle or wave nature is revealed. Look for a particle, and you’ll find a particle. Look for a wave instead, and instead you’ll find a wave.
Let’s say you put the vertical polarizer on the right slit while horizontal polarizer is put on the left slit. The screen still receive the result of superposition of light coming from both slit, with different phases according to their distances. Since two combining light sources have perpendicular polarization to each other, the combined light is generally elliptically polarized.Different points on the screen will get circularly polarized light with various eccentricity. The eccentricity is 1 when the combining lights have the same phase (or multiple of 180⁰), and 0 when there is 90⁰ phase difference (or its odd multiple). So, when light coming from right and left slit have the same phase, the result is linearly polarized light with 45⁰ polarization angle. When there is 90⁰ phase difference, the result is circularly polarized light.So if you observe the screen using an additional polarization filter in front of your eyes, you can see dark fringes when the light from some area on the screen is blocked by the polarizer. You can use either left or right circular polarizer, or use linear polarizer rotated at positive or negative 45⁰.You can also get interference pattern by producing interleaving dark spots on the screen using additional polarization filter in front of the screen which will block the light on some area while allowing light from other area.