GEOMETRICAL PATH & OPTICAL PATH
Displacement of fringe on introduction of a glass slab in the path of the light coming out of the slits- On introduction of the thin glass-slab of thickness t and refractive index , the optical path of the ray SP increases by t(u-1). Now the path difference between waves com- ing form S, and S at any point P is Ap S2P - (S,P t (Hu-1)) - (S,P-S,P) t(u 1) ap = d sin -t( -1) yd and Ap D t(u -1) y << D as well. for central bright fringe, Ap 0 - t(u - 1)
ya and Ap- -t( -1) D If y << D as well. for central bright fringe, ap:0 yd t(u-1). The whole fringe pattern gets shifted by the same distance * Notice that this shift is in the direction of the slit before which the glass slab is placed. If the glass slab is placed before the upper slit, the fringe pattern gets shifted upwards and if the glass slab is placed before the lower slit the fringe pattern gets shifted downwards.
Solved Examples In a YDSE with d = 1 mm and D = 1 m, slabs of (t = 1 m, = 3) and (t = 0.5 m, = 2) are introduced in front of upper and lower slit respectively. Find the shift in the fringe pattern. Optical path for light coming from upper slit S, is
S,P +1um (2-1) S2P +0.5 um Similarly optical path for light coming from S, is S2P0.5 um (2-1) S2P 0.5 Lum Path difference : ap-(S2P + 0.5 m)-(SP + 2tm) -(SP-SP)-1.5 m. yd for central bright fringe p-0 1.5um y-1mm x 1m 1.5 mm. The whole pattern is shifted by 1.5 mm upwards.
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