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 interference pattern is formed by the direct light from the slit S and the reflected light from the plane mirror. The reflected light can be considered to originate from a virtual source S' located at a distance d below the mirror. Thus, the direct source S and the virtual source S' act as two coherent sources separated by a distance 2d . For a point O on the screen exactly at the level of the mirror, the geometric path length of the direct ray is SO = D^2 + d^2 . The geometric pat