Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
In a Young's double-slit experiment, let A and B be the two slits. A thin film of thickness t and refractive index u is placed in front of A. Let\[\beta =\]fringe width. Then the central maximum will shift (1) towards A (2) towards B (3) by \[t(\mu -1)\frac{\beta }{\lambda }\] (4) by \[\mu t\frac{\beta }{\lambda }\]A) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: D
Solution :
Central maximum will shift towards point A. For a certain point P on the screen at a distance\[x\]from the centre of the screen, path difference \[\Delta =\frac{xd}{D}.\]Path difference introduced due to sheet \[=(\mu -1)t\]. For central maximum at P, \[\frac{xd}{D}=t(\mu -1)\] or \[x=t(\mu -1)\frac{D}{d}\] Now \[\beta =\frac{D\lambda }{d}\] \[\therefore \] \[\frac{D}{d}=\frac{\beta }{\lambda }\] Hence, \[x=t(\mu -1)\frac{\beta }{\lambda }\]
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