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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 $λ$ . In another experiment with the same setup, the two slits are sources of equal amplitude A and wavelength $λ$ but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is:

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a

$1 : 1$

b

$1 : 2$

c

$2 : 1$

d

$\sqrt{2} : 1$

answer is C.

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Detailed Solution

If the two sources are coherent, the resultant amplitude at the midpoint of the screen due to interference = A + A = 2 A. Therefore, intensity is $I_{1} \propto (2 A)^{2}$ or $I_{1} =$ $k \times 4 A^{2}$ where k is a constant of proportionality. But if the sources are not coherent, their intensities simply add up at the midpoint, i.e

$I_{2} \propto (A^{2} + A^{2}) or I_{2} = k \times 2 A^{2} ∴ \frac{I_{1}}{I_{2}} = \frac{4 k A^{2}}{2 k A^{2}} = 2$

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