Irradiance Distribution in a Lloyd Mirror Interference Pattern*,**

The Lloyd mirror interference pattern reappears and disappears in a periodic manner at distances from the mirror edge greater than the distance to the initial point of disappearance. In certain cases bright lines appear where, according to the textbook theory, which assumes spectrally homogeneous radiation and a slit source of infinitesimal width, dark lines should appear. A photograph of such a pattern is shown, measured values of the relative irradiance as a function of distance from the mirror edge are presented, and a theoretical determination which accounts for certain features of this variation of irradiance with distance is outlined.If we let IR=relative irradiance at a distance P from edge of mirror, θ=angular tilt of mirror, α=angular subtense of slit, ν0=wave number of radiation, ν1=width of wave band, and ω=2πν0, then IR=2ωα(ν1/ν0)-(1/P)Si[Pω(1+12(ν1/ν0)(2θ+α)]+ (1/P)Si[Pω(1-12(ν1/ν0)(2θ+α)]+ (1/P)Si[Pω(1+12(ν1/ν0)(2θ-α)]- (1/P)Si[Pω(1-12(ν1/ν0)(2θ-α)].If spectrally homogeneous radiation is assumed, then IR1=0.50−0.50 cos4πPθν0(sin2πPν0α/2πPν0α).