Final answer:
The intensity of light on the screen is determined by the interference of direct light from the source and the light reflected from the mirror, which forms an image source and doubles the path length. Using the small angle approximation, path differences can be calculated to describe the varying intensity pattern on the screen as a function of height y.
Step-by-step explanation:
To determine the intensity of light on a screen as a function of the height y above a mirror for a point source of light S emitting a single wavelength λ0 and situated a small distance d above a plane mirror, we must consider the path difference between the direct light from the source and the light reflected from the mirror. The light from the mirror forms an image of the point source, essentially doubling the distance the light travels (2d) to reach the same height y on the screen.
Using the small angle approximation, the angle θ made with the normal of the screen is θ ≈ y/l. The path difference is equal to the extra distance ∆x the light from the image source has to travel compared to the direct light and is given by ∆x = lθ. Substituting the expression for θ, we get ∆x = yl/l = y.
The intensity pattern on the screen is due to the interference between these two waves with path difference ∆x and can be described by a set of interference fringes with varying intensity depending on this path difference. Generally, the central maximum has the highest intensity because there is no path difference, and the intensity diminishes for paths with increasing y, which correlate with higher-order maxima or minima of the interference pattern.