Question

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 the intensity of light at the midpoint of the screen in the first case of that in the second case is

• A. 1:1
• B. 1:2
• C. 2:1
• D. $\sqrt{2}:1$

Answer 1

The correct option is C

2:1

If the two sources are coherent, the resultant amplitude at the midpoint of the screen due to interference=A+A=2A. Therefore, intensity is $I_1)\propto (2A{)}^{2}or{I}_1=k\times 4A^2$ where k is constant of proportionality. But if the sources are not coherent, their intensities simply add up at the midpoint,
i.e,
$I_2\propto (A^2+A^2)or{I}_2=k\times 2A^2\therefore \frac{I_1}{I_2}=\frac{4k{A}^2}{2k{A}^2}=2:1$