# The interference pattern is observed at ‘P’ due to the superimposition of two rays coming out from a source ‘S’ as shown in the figure. The value of ‘’ for which maxima is obtained at ‘P’ is : (R is a perfect reflecting surface) :

Lloyd's mirror Experiment -

$S_{2}P-S_{1}P= n\lambda$

$S_{2}P-S_{1}P= \left ( n+1/2 \right )\lambda$

- wherein

minima

maxima

For maxima at P

$\Delta x= (n-1/2 )\lambda$

$x \cos 30 \degree = l \\ \Rightarrow x = \frac{2l }{\sqrt 3 }$

$\Delta x = \frac{2l}{\sqrt 3}+ \frac{2l}{\sqrt 3 } - 2l = (n- 1/2 )\lambda$

Or

$\frac{4l}{\sqrt3}-2l = (n-1/2 )\lambda$

or

$l = \frac{(2n-1)\lambda \sqrt 3 }{4(2-\sqrt 3 )}$

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