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Lloyd Single Mirror

This experiment for the production of interference fringes was performed by Lloyd in 1834. He used a plane mirror about 30 cm in length and 6 to 8 cm in breadth. The mirror M is either a flat polished metal or a piece of black glass so that no reflection takes place from the black of mirror. S is a source of monochromatic light and B is the image of S formed by reflection. S corresponds to one of the coherent sources (viz. A). Hence S and B are very close and the rays from S are reflected almost at grazing incidence. Interference fringes are produced on the screen placed at a distance D from S in the shaded portion EF.

But there is one difference in this case. The central fringe, instead of being bright is dark. If the screen is brought at the end R of the mirror M, such that the point C of the screen touches the end of the mirror, C comes that the point C of the screen touches the end of the mirror, C comes at the centre of the dark fringe. C is equidistant from A and B. According to the theory it should lie at the centre of a bright fringe. Here, one of the two beams producing interference fringes has undergone a phase change of π. The direct beam from S cannot undergo a phase change. Therefore, only the reflected beam undergoes a phase change of π. Due to this reason, the central fringe instead of being white is dark in this case. This experiment proves that a light beam after reflection from an optically denser medium undergoes a phase change of π.

One objection can be raised here, as to why the central fringe in the case of Fresnel’s double mirror is bright and not dark. In the case of Fresnel’s double mirrors both the interfering beams are reflected and both undergo a phase change of π. Therefore, the path difference is not altered as in the case of Lloyd’s single mirror.