Question

The intensity at the central maxima $\left(0\right)$ in a Young's double slit experiment is $70$. If the distance OP equals one-third of the fringe width of the pattern. Show that the intensity at point P would be $\frac{I_0}{4}$.

Answer 1

The intensity at a distance y from central maxima is given by,

$I=I_0{cos}^2\left(\frac{\pi dy}{\lambda D}\right)$

$Nowy=x=\frac{Fringewidth}{3}=\frac{\lambda D}{3d}$

$I=I_0{cos}^2\left(\frac{\pi dy}{\lambda D}\right)=I_0{cos}^2\frac{\pi }{3}=\frac{10}{4}$