Two waves of intensity ratio $1:9$ cross each other at a point. The resultant intensities at the point are $I_1$ when the waves are incoherent and $I_2$ when the waves are coherent with a phase difference of $60^{\circ}$. If $\frac{I_1}{I_2} = \frac{10}{x}$,then $x = . . . . . . . . . . .$

Two coherent light sources $A$ and $B$ are at a distance $3\lambda$ from each other (where $\lambda$ is the wavelength). Find the distances from $A$ on the $x$-axis at which constructive interference occurs.

Which of the following is not a correct statement?

In the adjacent diagram,$CP$ represents a wavefront and $AO$ & $BP$ are the corresponding two rays. Find the condition on $\theta$ for constructive interference at $P$ between the ray $BP$ and the reflected ray $OP$.

In the figure below,$P$ and $Q$ are two equally intense coherent sources emitting radiation of wavelength $20\, m$. The separation between $P$ and $Q$ is $5\, m$ and the phase of $P$ is ahead of that of $Q$ by $90^{\circ}$. $A, B$ and $C$ are three distinct points of observation,each equidistant from the midpoint of $PQ$. The intensities of radiation at $A, B, C$ will be in the ratio

Two waves having amplitudes in the ratio $5:1$ produce interference. The ratio of the maximum to minimum intensity is