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  4. Two circular aperture S1, and S2 of radii 1 m and 2 mm. A parallel beam of light (7/22) Wm -2 and wavelength 600 nm is incident normally as shown in the figure. A transparent film of thickness 200 nm having refractive index μ1=2 is placed in front of S1, and other transparent film of thickness 200 nm and refractive index 1.5 is placed in front of other slit. The resultant power (in μ W ) at the centre of screen is

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

Wave Optics

Solution:

$\Delta x=\left(\mu_{1}-1\right) t_{1}-\left(\mu_{2}-1\right) t_{2}$
$=(2-1) 200-(1.5-1) 200=200-100=100 \,nm$
$\therefore \phi=\frac{2 \pi}{\lambda} \Delta x=\frac{2 \pi}{600} \times 100=\frac{\pi}{3}$
$\therefore P=P_{1}+P_{2}+2 \sqrt{P_{1} P_{2}} \cos \theta$
$=I_{0} \pi r_{1}^{2}+I_{0} \pi r_{2}^{2}+2 \sqrt{I_{0} \pi r_{1}^{2} \times I_{0} \pi r_{2}^{2}} \cos \frac{\pi}{3}=7\, \mu W$