In an interference pattern,two waves of intensities $I$ and $4I$ are used. At point $A$,the phase difference is $\frac{\pi}{2}$,and at point $B$,the phase difference is $\pi$. The difference in intensities at points $A$ and $B$ is: (in $I$)

For constructive interference to take place between two monochromatic light waves of wavelength $\lambda$, the path difference should be

Two point sources $S_1$ and $S_2$ separated by a distance $10 \mu m$ emit light waves of wavelength $4 \mu m$ in phase. $A$ circular wire of radius $40 \mu m$ is placed around the sources as shown in the figure,where $O$ is the centre of the circle and $OS_1 = OS_2$. Determine the nature of the interference at points $A, B, C,$ and $D$.

Two light waves of intensities $I$ and $4I$ superpose at a point with a phase difference of $\pi / 2$. Calculate the resultant amplitude at that point.

Two light beams of intensities $4\,I$ and $9\,I$ interfere on a screen. The phase difference between these beams on the screen at point $A$ is $0$ and at point $B$ is $\pi$. The difference of resultant intensities,at the points $A$ and $B$,will be $....I$.

The interference pattern is obtained with two coherent light sources of intensity ratio $4:1$. If the ratio $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is $\frac{5}{x}$,then the value of $x$ will be equal to: