A narrow slit S transmitting light of wavelength λ is placed a distance d above a large plane mirror as shown in figure (17-E1). The light coming directly from the slit and that coming after the reflection interfere at a screen ∑ placed at a distance D from the slit. (a) What will be the intensity at a point just above the mirror, i.e., just above O’ (b) At what distance from O does the first maximum occur?
(a) In this case, interference would occur when light from the slit interferes with the right reflected off by the mirror. the mirror produces a phase shift of 
which occurs in destructive interference. Hence, the intensity directly above O would be zero.
(b)Here, we project back the ray to its virtual image S’. The distance between S and S’ is 2d.
The first maximum occurs at 
.
Let the maximum occur at a point “y” above center.
The path difference becomes, 
and this should be equal to 
.
