Lloyd's Mirror
Category : JEE Main & Advanced
A plane glass plate (acting as a mirror) is illuminated at almost grazing incidence by a light from a slit \[{{S}_{1}}\]. A virtual image \[{{S}_{2}}\] of \[{{S}_{1}}\] is formed closed to \[{{S}_{1}}\] by reflection and these two act as coherent sources. The expression giving the fringe width is the same as for the double slit, but the fringe system differs in one important respect.
The path difference \[{{S}_{2}}P-{{S}_{1}}P\] is a whole number of wavelengths, the fringe at P is dark not bright. This is due to \[{{180}^{o}}\] phase change which occurs when light is reflected from a denser medium. At grazing incidence a fringe is formed at O, where the geometrical path difference between the direct and reflected waves is zero and it follows that it will be dark rather than bright.
Thus, whenever there exists a phase difference of a \[\pi \] between the two interfering beams of light, conditions of maximas and minimas are interchanged, i.e., \[\Delta x=n\lambda \](for minimum intensity)
and \[\Delta x=(2n-1)\lambda /2\] (for maximum intensity)
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