Write the condition for constructive interference in terms of path and phase difference.

Interference fringes are produced on the screen by using two light sources of intensities $I$ and $9I$. The phase difference between the beams is $\pi / 2$ at point $P$ and $\pi$ at point $Q$ on the screen. The difference between the resultant intensities at points $P$ and $Q$ is $(\cos 90^{\circ}=0, \cos 180^{\circ}=-1)$. (in $I$)

Two beams of light having intensities $I$ and $4I$ interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\pi/2$ and $\pi/3$ at points $A$ and $B$ respectively. The difference between the resultant intensities at the two points is $xI$. The value of $x$ will be.

Write down the principle of superposition and what is interference? Write down its types.

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

Which phenomena can be explained by the wave nature of light?