question_answer

Two identical coherent sources placed on a diameter of a circle of radius R at separation \[\frac{1}{\sqrt{2}}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\] symmetrically about the centre of the circle. The sources emit identical wavelength X each. The number of points on the circle with maximum intensity is \[\frac{1}{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C\]

A)  20 

B) 22

C) 24                                          

D) 26

Correct Answer: A

Solution :

 Path difference at P is \[1.96\times {{10}^{-20}}\] For intensity to be maximum \[\Omega \]                 \[\Omega \]\[\frac{i}{{{i}_{0}}}=\frac{4}{11}\]                    (n = 0, 1,???)                 \[\frac{i}{{{i}_{0}}}=\frac{3}{11}\] \[\frac{i}{{{i}_{0}}}=\frac{2}{10}\]\[\frac{i}{{{i}_{0}}}=\frac{1}{11}\] \[\sqrt{2}\]\[4R\Omega .\] Substituting \[{{w}_{1}}\]\[{{w}_{2}}\]or n = 1, 2, 3, 4, 5,..... Therefore, in all four quadrants, there can be 20 maxim as. There are more maxim as at \[\frac{-({{w}_{2}}-{{w}_{1}})}{5Rt}\] and \[\frac{-n({{w}_{2}}-{{w}_{1}})}{5Rt}\] But a = 5 corresponds to \[\frac{-n({{w}_{2}}-{{w}_{1}})}{Rnt}\]and \[\frac{-n({{w}_{2}}-{{w}_{1}})}{Rt}\]which are coming only twice. While we have multiplied it four times. Therefore, total number of maxim as still 20.