question_answer

In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is \[\frac{1}{8}th\] of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is    [JEE MAIN Held on 08-01-2020 Evening]

A) 0.568   

B) 0.760

C) 0.853   

D) 0.672

Correct Answer: C

Solution :

\[\Delta x=\lambda \,/\,8\] \[\therefore \] Phase difference \[\Rightarrow \,\,\Delta \phi =\frac{\pi }{4}\] \[l={{l}_{0}}{{\cos }^{2}}\left( \frac{\Delta \phi }{2} \right)={{l}_{0}}{{\cos }^{2}}\left( \frac{\pi }{8} \right)\] \[\therefore \,\,\,\,\,\,\,\,\frac{l}{{{l}_{0}}}=0.853\]