Two coherent sources whose intensity ratio is $64: 1$ produce interference fringes. The ratio of intensities of maxima and minima is

If the ratio of the intensities of two waves producing interference is $49: 16$,then the ratio of the resultant maximum intensity to minimum intensity will be

Two coherent monochromatic point sources $S_1$ and $S_2$ of wavelength $\lambda = 600 \ nm$ are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance $d = 1.8 \ mm$. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $\Delta \theta$. Which of the following options is/are correct?
$[A]$ $A$ dark spot will be formed at the point $P_2$
$[B]$ At $P_2$ the order of the fringe will be maximum
$[C]$ The total number of fringes produced between $P_1$ and $P_2$ in the first quadrant is close to $3000$
$[D]$ The angular separation between two consecutive bright spots decreases as we move from $P_1$ to $P_2$ along the first quadrant

Two coherent sources of intensities $I_{1}$ and $I_{2}$ produce an interference pattern on a screen. The maximum intensity in the interference pattern is

$A$ beam with wavelength $\lambda$ falls on a stack of partially reflecting planes with separation $d$. The angle $\theta$ that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where $n = 1, 2, \dots$)

Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first wave travels a path $L_{1}$ through a medium of refractive index $n_{1}$ while the second wave travels a path of length $L_{2}$ through a medium of refractive index $n_{2}$. After this the phase difference between the two waves is: