A narrow slit S transmitting light of wavelength is positioned a distance d above a large plane mirror. Light arriving directly from the slit and light arriving after reflection interfere at a screen placed a distance D from the slit. At what distance from O (the point on the screen at the plane of the mirror) does the first maximum occur?

Step-by-step solution

In Lloyd's mirror experiment, the setup is equivalent to Young's Double Slit Experiment (YDSE). The real source S and its virtual image S' formed by the plane mirror act as two coherent sources. The distance between the real source S and the virtual source S' is a = 2d . The path difference between the direct ray and the reflected ray at a distance y from O on the screen is given by: x = y a D = y(2d) D When light reflects from the denser medium (the mirror), it undergoes a phase change of , which is equivalent to