A) \[\cos \theta =3\lambda /2d\]
B) \[\cos \theta =\lambda /4d\]
C) \[\sec \theta -\cos \theta =\lambda /d\]
D) \[\sec \theta -\cos \theta =4\lambda /d\]
Correct Answer: B
Solution :
[b] \[\therefore PR=d\Rightarrow PO=d\sec \theta \]and \[CO=PO\cos 2\theta =d\sec \theta \cos 2\theta \] is Path difference between the two rays \[\Delta =CO+PO\] \[=(d\sec \theta +d\sec \theta \cos 2\theta )\] Phase difference between the two rays is \[\phi =\pi \](One is reflected, while another is direct) Therefore condition for constructive interference should be \[\Delta =\frac{\lambda }{2},\frac{3\lambda }{2},...\] Or \[d\sec \theta (1+cos2\theta )=\frac{\lambda }{2}\] Or \[\frac{d}{\cos \theta }(2co{{s}^{2}}\theta )=\frac{\lambda }{2}\Rightarrow \cos \theta =\frac{\lambda }{4d}\]You need to login to perform this action.
You will be redirected in
3 sec