Two coherent monochromatic light beams of intensities $4 I$ and $9I$ are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $xI$. The value of $x$ is . . . . . . .

In an interference experiment,two coherent waves $S_1$ and $S_2$ are represented by $y_1 = 10 \sin(\omega t)$ and $y_2 = 10 \sin(\omega t - \pi/6)$ respectively. When these waves superimpose to form an interference pattern,the maximum intensity is ....... (Assume $K = 1$)

If two sources emit light waves of different amplitudes, then:

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 sources of intensity ratio $9:4$ produce interference. The intensity ratio of maxima and minima of the interference pattern is

Two coherent sources of light interfere. The intensity ratio of two sources is $1:4$. For this interference pattern,if the value of $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is equal to $\frac{2\alpha + 1}{\beta + 3}$,then the value of $\frac{\alpha}{\beta}$ will be: