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  4. In Young's double slit experiment, the two slits act as coherent sources of equal amplitude a and of wavelength λ. In another experiment with the same set up, the two slits are sources of equal amplitude a and wavelength λ, 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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Q. 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

AIIMSAIIMS 2009Wave Optics

Solution:

When sources are coherent, intensity at mid point is
$I_{max}=\left(a+a\right)^{2}=4a^{2}$
When sources are incoherent, no interference occurs. Intensity at mid point is
$I=I_{1}+I_{2}=a^{2}+a^{2}=2a^{2}$
$\therefore \frac{I_{maX}}{I}=\frac{4a^{2}}{2a^{2}}=2 : 1$