QJEEAdv17Ph1887: JEE Advanced 2017 Physics - Class 12 JEEAdv17Ph1887 Solution: Two coherent monochromatic point sources and of wavelength are…

At any point P on circumference, the path difference, $\Delta$ x = d sin $\theta$

At P₁, $\theta$ = 0 $^\circ$ $\Rightarrow$ $\Delta$ x = 0

At P₂, $\theta$ = 90 $^\circ$ $\Rightarrow$ $\Delta$ x = d

For constructive interference, $\Delta$ x = n $\lambda$

$\therefore$ $n = {d \over \lambda } = {{1.8\,mm} \over {600\,nm}} = {{1.8 \times {{10}^{ - 3}}m} \over {600 \times {{10}^{ - 9}}m}} = 3000$

Since, n is integer, hence P₂ corresponds to bright spot and also it corresponds to maximum order of fringe.

Now, $\Delta$ x = d sin $\theta$

d $\Delta$ x = d cos $\theta$ d $\theta$ or R $\lambda$ = d cos $\theta$ d $\theta$

$\therefore$ $d\theta \propto {1 \over {\cos \theta }}$

Hence, as $\theta$ increases, cos $\theta$ decreases and consequently d $\theta$ increases.