Question

Consider an YDSE that has different slits width, as a result, amplitudes of waves from two slits are A and $2A$, respectively. If $I_0$ be the maximum intensity of the interference pattern, then intensity of the pattern at a point where phase difference between waves is $\varphi$, is :-

• A. $I_0{\cos }^2\varphi$
• B. $\frac{I_0}{3}{\sin }^2\frac{\varphi }{2}$
• C. $\frac{I_0}{9}[5+4\cos \varphi ]$
• D. $\frac{I_0}{9}[5+8\cos \varphi ]$

Answer 1

Answer: (C)

As amplitudes are $A$ and $2A$,
so intensities would be in the ratio $1:4$,
let us say $I$ and $4I$.
$I_{\max }=I_0=I+4I+2\sqrt{4I^2}=9I$
$\Rightarrow I=\frac{I_0}{9}$
Intensity at any point, $I^{\prime }=I+4I+2\sqrt{4I^2}\cos \varphi ;I^{\prime }=5I+4I$
$\cos \varphi =\frac{I_0}{9}(5+4\cos \varphi )$