Question

The path difference between two interfering waves at a point on the screen is $\frac{\lambda }{6}$from central maximum. The ratio of intensity at this point and that at the central fringe will be:

• A. $0.75$
• B. $7.5$
• C. $85.3$
• D. $853$

Answer 1

The correct option is A $0.75$

At a point with phase difference $\theta$ the intensity is given by $I=2a^2(1+cos\theta )$

The maximum intensity is given by $4a^2$
For path difference $\lambda /6$, the phase difference is given by:

$\theta =2\pi \Delta x/\lambda =2\pi /6=\pi /3$
Thus the ratio is $\frac{2a^2(1+cos\theta )}{4a^2}=\frac{1+cos\theta }{2}$
$=\frac{1+1/2}{2}=0.75$