Solution (source code)

= Solution

A <mercury-vapor lamp> is an extended, spontaneously emitting source, so practical <interference> requires spatial filtering and spectral selection. A narrow illuminated source slit gives sufficient <spatial coherence>; selecting one strong spectral line improves <temporal coherence> and avoids overlapping differently spaced <interference fringes>.

In the classical <double-slit experiment>, both apertures are illuminated by the same narrow source. The arrangement is symmetric, permits direct measurement and adjustment of slit separation, and has equal optical materials in the two paths. Its main drawbacks are low transmitted <intensity> through narrow apertures, the need for a well-made closely spaced slit pair and alignment, and the finite single-slit <diffraction> envelope. A broad source washes out <interference fringes>.

<Lloyd's mirror> uses the direct wave from a narrow source and the reflected wave, which appears to come from its virtual image behind a plane mirror. It requires only one physical source slit; the mirror can be adjusted to make a small effective source separation without manufacturing a double aperture. Only the direct-reflected overlap region shows <interference fringes>. Finite mirror size, alignment, surface quality, unequal <intensities> and the <polarization>-dependent reflection coefficient can reduce visibility. For the usual grazing reflection from glass, the reflected electric wave acquires approximately a $\pi$ <phase shift>, so the zero path-difference position is dark rather than the bright central fringe of the symmetric classical <double-slit experiment>. Both arrangements still require adequate <spatial coherence> and <temporal coherence>.