The phase difference between light bouncing off two aligned mirrors is NOT random. This is what you are missing. Non-coherent light only means it is made of ma

The phase difference between light bouncing off two aligned mirrors is NOT random. This is what you are missing. Non-coherent light only means it is made of many wavelengths at the same time (Think of it as the sum of many « coherent lights »). Interference does happen even for incoherent light, within each wavelength. Example: oil iridescence on water is interference which works on « incoherent » light.