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 source of equal amplitude n 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

• A. $2:1$
• B. $1:2$
• C. $3:4$
• D. $4:3$

Answer 1

Answer: (A)

$2:1$

Case 1: coherent sources

$x_1=nsin\left(\omega t\right)$

$x_2=nsin\left(\omega t\right)$

$x_{r1}=x_1+x_2=2nsin\left(\omega t\right)$

$I_{r1}=4n^2$

Case 2: incoherent sources i.e. ${90}^o$ phase shift

$x_1=nsin\left(\omega t\right)$

$x_2=ncos\left(\omega t\right)$

$x_{r2}=x_1+x_2=\sqrt{2}nsin(\omega t+\pi /4)$

$I_{r2}=2n^2$

$I_{r1}:I_{r2}=2:1$