Two beams of light having intensities $I$ and $4I$ interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\pi/2$ and $\pi/3$ at points $A$ and $B$ respectively. The difference between the resultant intensities at the two points is $xI$. The value of $x$ will be.

Coherent sources are those sources for which

Which optical phenomena can be explained by the wave nature of light?

$A$ and $B$ are two interfering sources where $A$ is ahead in phase by $54^{\circ}$ relative to $B$. The observation is taken from point $P$ such that $PB-PA=2.5 \lambda$. Then the phase difference between the waves from $A$ and $B$ reaching point $P$ is (in rad) (in $\pi$)

Two identical radiators have a separation of $d = \lambda /4$ where $\lambda$ is the wavelength of the waves emitted by either source. The initial phase difference between the sources is $\pi /4$. Then the intensity on the screen at a distant point situated at an angle $\theta = 30^\circ$ from the radiators is (here $I_o$ is the intensity at that point due to one radiator alone):

Two identical light waves having phase difference $\phi$ propagate in the same direction. When they superpose,the intensity of the resultant wave is proportional to