A beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45°$ relative to that of $A.$ If intensity of the emergent light is $\frac{I_0}{N}$, then value of $N$ is

Two coherent monochromatic point sources $S_1$ and $S_2$ of wavelength $\lambda =600 \mathrm{nm}$ are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance $d=1.8 \mathrm{mm}.$ This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. Total number of fringes produced between $P_1$ and $P_2$ is close to _____.

In the diagram shown below, $CP$ represents a wavefront and $AO$ and $BP$, the corresponding two rays. The condition of $\theta$ for constructive interference at $P$ between the ray $BP$ and reflected ray $OP$ is $\cos \theta =\frac{\lambda }{Nd}$, then $N$ is

Two point coherent sources $S_1$ and $S_2$ (of wavelength $\lambda$ ) are placed as shown in figure. $D$ is mid point of $S_1{S}_2.$ The source $S_1$ is ahead of phase by $\frac{\pi }{2}$ relative to the source $S_2,$ then