Question

The path difference between two interfering waves at a point on the screen is $\lambda /6$. The ratio of intensity at the point and that the central bright fringe will be (Assume that internally due to each slit in same).

• A. 0.853
• B. 8.53
• C. 0.75
• D. 7.5

Answer 1

The correct option is C 0.75

Given that,

Path difference $x=\frac{\lambda }{6}$

We know that,

$I=I_0{\cos }^2\left(\frac{\varphi }{2}\right)$

$\frac{I}{I_0}={\cos }^2\left(\frac{\varphi }{2}\right)....\left(I\right)$

Now, the phase difference is

$\varphi =\frac{2\pi }{\lambda }\times x$

$\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{6}$

$\varphi =\frac{\pi }{3}$

Now, put the value of $\varphi$ in equation (I)

$\frac{I}{I_0}={\cos }^2{30}^0$

$\frac{I}{I_0}=\frac{3}{4}$

$\frac{I}{I_0}=0.75$

Hence, the value of ratio of the intensity at the point is $0.75$