Yes, in Young's double slit experiment, the intensity of light does depend on the slit width. The double slit experiment demonstrates the wave-like nature of light and the phenomenon of interference.
When a beam of light passes through two closely spaced slits, it diffracts and creates a pattern of alternating bright and dark fringes on a screen placed behind the slits. These fringes are the result of constructive and destructive interference between the light waves passing through the two slits.
The intensity of light at each point on the screen is determined by the superposition of the electric fields from the individual waves arriving at that point. The intensity is directly proportional to the square of the electric field amplitude. Therefore, if the electric fields from the two slits are in-phase and add constructively, the intensity at that point will be relatively high. Conversely, if the electric fields are out-of-phase and cancel each other out, the intensity will be low.
The slit width affects the diffraction pattern and, consequently, the interference pattern. If the slits are made narrower, the diffraction of light increases. This leads to broader and less distinct interference fringes. As a result, the intensity of light at each point on the screen decreases.
In summary, the intensity of light in Young's double slit experiment depends on the slit width. Narrower slits result in broader interference fringes and lower light intensity, while wider slits produce narrower interference fringes and higher light intensity.