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 . . . . . . .

The resultant amplitude of the interference of two waves $y_1 = 4 \sin \omega t$ and $y_2 = 3 \sin (\omega t + \frac{\pi}{3})$ is:

The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of the same thickness, is $1$. The thickness of the air column is (Refractive index of air $\mu_a = 1.0003$, Wavelength of yellow light in vacuum $\lambda_0 = 6000 \text{ Å}$)

$n$ identical waves each of intensity $I_0$ interfere with each other. The ratio of maximum intensities if the interference is $(i)$ coherent and $(ii)$ incoherent is:

The path difference between two interfering waves at a point on the screen is $171.5$ times the wavelength. If the path difference is $0.01029 \, cm$,find the wavelength in $\mathring{A}$.

Light waves from two coherent sources arrive at two points on a screen with path difference of zero and $\lambda / 2$. The ratio of the intensities at the points is