In a double slit experiment, the ideal slit width and separation are related to the size of the particles being fired at them through a phenomenon known as diffraction. Diffraction is the bending and spreading of waves around obstacles or through narrow openings.
When particles (such as electrons, photons, or even larger particles) are fired at the double slits, they exhibit wave-like properties and undergo diffraction as they pass through the slits. The size of the particles and the dimensions of the slits play a crucial role in determining the diffraction pattern observed on the screen behind the slits.
If the size of the particles is much smaller than the slit width and separation, the diffraction effects become more prominent. In this case, the particles behave more like waves and produce an interference pattern on the screen—a series of light and dark fringes resulting from constructive and destructive interference of the waves.
The ideal slit width is generally considered to be on the order of the wavelength of the particles or smaller. If the slit width is too wide compared to the particle's wavelength, the diffraction effects diminish, and the interference pattern becomes less pronounced. Conversely, if the slit width is too narrow, the diffraction pattern becomes blurred and less distinguishable.
The separation between the slits also affects the interference pattern. When the slit separation is smaller compared to the particle's wavelength, the interference fringes become more closely spaced. As the slit separation increases, the fringes become wider apart.
It's important to note that in the double slit experiment, the behavior of particles is often described using wave-particle duality, where particles can exhibit both particle-like and wave-like characteristics. The ideal slit width and separation are determined based on the desired interference pattern and the properties of the particles being used in the experiment.