Conditions for Obtaining Well Defined and Steady Interference Pattern

A real double-slit experiment only produces a clean, clearly visible interference pattern if several practical conditions are met, some already implicit in the derivation above but worth stating explicitly and together:

1. The two sources must be COHERENT (Section 7.8.1) -- this is the single essential requirement for any sustained pattern at all; without it, the positions of maxima and minima drift continuously and average out to a uniform, featureless intensity, exactly why the two secondary sources are always derived from one single original source in practice.

2. The light must be MONOCHROMATIC (a single wavelength). Since both the fringe positions (Eq. for $y_n$) and the fringe width $\beta = \lambda D/d$ depend directly on $\lambda$, different wavelengths produce fringe patterns of different spacing that do not coincide -- so with ordinary white light, the resulting pattern is a smeared, coloured overlap of many single-wavelength patterns rather than a set of sharp, well-defined fringes (Young's very first experiment, in fact, used pinholes rather than slits, illuminated by sunlight, and produced exactly such a coloured pattern with a white central fringe).

3. The two interfering waves must have EQUAL amplitude. Only when the amplitudes are equal does the destructive-interference intensity fall all the way to exactly zero (Section 7.8.2's $I=4I_0\cos^2(\phi/2)$ result assumed equal amplitudes) -- giving the sharpest possible CONTRAST between bright and dark fringes; unequal amplitudes leave a nonzero residual intensity even at the dark-fringe centres, washing out the contrast.

4. The slit separation d must be much SMALLER than the slit-to-screen distance D ($D \gg d$) -- this was used explicitly in deriving the path-difference formula, and physically ensures the fringe width $\lambda D/d$ comes out large enough to actually be resolved and measured on the screen, rather than being compressed into an unobservably thin band.

5. The slits themselves must be NARROW. If a slit is too wide, light reaching a given screen point from different locations along that SAME slit no longer travels identical distances, so the light from within one slit begins interfering with itself, blurring the sharp fringe pattern that would otherwise result from the two slits alone. …