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In Young's double slit experiment, the two slits act as coherent sources of equal amplitude $a$ and of wavelength $\lambda$. In another experiment with the same set up, the two slits are sources of equal amplitude $a$ and wavelength $\lambda$, but are incoherent. The ratio of intensities of light at the mid point of the screen in the first case to that in the second case is
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$2: 1$
When sources are coherent, intensity at mid point is
$I_{\max }=(a+a)^2=4 a^2$
When sources are incoherent, no interference occurs. Intensity at mid point is
$\begin{aligned} & I=I_1+I_2=a^2+a^2=2 a^2 \\ & \therefore \frac{I_{\text {max }}}{I}=\frac{4 a^2}{2 a^2}=2: 1\end{aligned}$
$I_{\max }=(a+a)^2=4 a^2$
When sources are incoherent, no interference occurs. Intensity at mid point is
$\begin{aligned} & I=I_1+I_2=a^2+a^2=2 a^2 \\ & \therefore \frac{I_{\text {max }}}{I}=\frac{4 a^2}{2 a^2}=2: 1\end{aligned}$
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