Final answer:
The intensity of a two-slit interference pattern is determined by the equation d sin θ = mλ, and involves the superposition of light waves from the slits, creating fringes of varying intensity on the screen, with the central maximum being the brightest.
Step-by-step explanation:
To derive the formula that gives intensity as a function of wavelength, slit geometry, and position on the detector screen in a two-slit interference experiment, we need to understand and apply principles of wave optics. According to double slit interference, we can describe the pattern on the screen as a series of bright and dark fringes. The angle θ representing these fringes for any order m is given by the equation d sin θ = mλ, where d is the distance between the slits, λ is the wavelength of the light, and m is the order number of the fringe.
The intensity on the screen can be understood as resulting from the constructive (m integer) and destructive (m half-integer) interference of the light waves emanating from the slits. The central maximum has the greatest intensity, and the intensity falls off for fringes farther from the center. To fully derive the intensity pattern, one must consider the diffraction effects due to each slit and then the interference pattern due to the combination of slits.