Question

Two circular aperture $S_1$, and $S_2$ of radii $1m$ and $2mm$. A parallel beam of light $\frac{7}{22}W{m}^{-2}$ and wavelength $600nm$ is incident normally as shown in the figure. A transparent film of thickness $200nm$ having refractive index ${\mu }_1=2$ is placed in front of $S_1$, and other transparent film of thickness $200nm$ and refractive index $1.5$ is placed in front of other slit. The resultant power (in $\mu W$ ) at the centre of screen is _____

Answer 1

Answer: 7

$\Delta x=\left({\mu }_1-1\right)t_1-\left({\mu }_2-1\right)t_2$
$=(2-1)200-(1.5-1)200=200-100=100nm$
$\therefore \varphi =\frac{2\pi }{\lambda }\Delta x=\frac{2\pi }{600}\times 100=\frac{\pi }{3}$
$\therefore P=P_1+P_2+2\sqrt{P_1{P}_2}\cos \theta$
$=I_0\pi r_1^2+I_0\pi r_2^2+2\sqrt{I_0\pi r_1^2\times I_0\pi r_2^2}\cos \frac{\pi }{3}=7\mu W$