Question

In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is ${\frac{1}{8}}^{\text{th}}$ of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is

• A. $0.853$
• B. $0.672$
• C. $0.568$
• D. $0.760$

Answer 1

The correct option is A $0.853$

$\text{Given, Path difference,}\Delta x=\frac{\lambda }{8}$
$\text{Phase differences,}\Delta \varphi =\frac{2\pi }{\lambda }\Delta x=\frac{2\pi }{\lambda }\times \frac{\lambda }{8}=\frac{\pi }{4}$

Relation of intensity with phase difference is
$I=I_0{\cos }^2\left(\frac{\Delta \varphi }{2}\right)$

Here $I_0$ is intensity of central bright fringe

On substitution,

$\Rightarrow \frac{I}{I_0}={\cos }^2\left(\frac{\frac{\pi }{4}}{2}\right)={\cos }^2\left(\frac{\pi }{8}\right)$

$\Rightarrow \frac{I}{I_0}=0.853$