91Ó°ÊÓ

The amplitude of electric field for both waves is $2\mathrm{μ³Õ}/\mathrm{m}$,

The phase difference for both waves is $\mathrm{ϕ}=39.6\text{rador}2269°$,

The angular frequency of both waves is $\mathrm{Ó\neg }=1.26×{10}^{15}\mathrm{rad}/\mathrm{s}$,

The phase difference of fringe pattern varies with the path difference. For minimum phase difference path difference should be minimum and vice versa.

The resultant electric field at point P is given as:

$E=2E_0\cos \left(\frac{\mathrm{Ï•}}{2}\right)$

Substitute all the values in equation.

$\begin{array}{rcl}E& =& 2(2\mathrm{μ³Õ}/\mathrm{m})\cos \left(\frac{2269°}{2}\right)\\ & =& 2.32\mathrm{μ³Õ}/\mathrm{m}\end{array}$

Therefore, the resultant electric field at point P is $\begin{array}{rcl}& & 2.32\mathrm{μ³Õ}/\mathrm{m}\end{array}$.

The ratio of intensity at point P to intensity at center of interference pattern is given as:

$\frac{I_P}{I_{cen}}=4{\cos }^2\left(\frac{\mathrm{Ï•}}{2}\right)$

Substitute all the values in equation.

$$\begin{gathered} \frac{I_P}{I_{cen}}=4{\cos }^2\left(\frac{2269°}{2}\right) \\ \frac{I_P}{I_{cen}}=1.35 \end{gathered}$$

Therefore, the ratio of intensity at point P to intensity at center of interference pattern is $1.35$.

The phase difference for both waves in terms of wavelength of wave is given as:

${\mathrm{ϕ}}_{\mathrm{λ}}=\left(\frac{\mathrm{ϕ}}{2\mathrm{π}}\right)\mathrm{λ}$

Substitute all the values in equation.

$\begin{array}{rcl}{\mathrm{ϕ}}_{\mathrm{λ}}& =& \left(\frac{39.6\text{rad}}{2\mathrm{π}}\right)\mathrm{λ}\\ & =& 6.3\mathrm{λ}\end{array}$

The point P lies between sixth of maximum and seventh of minimum fringe.

Therefore, the point P is lying between sixth maxima and seventh minima of phasor diagram.

The rate of rotation of phasor will be equal to the angular frequency of both waves.

The rate of rotation of phasor is given as:

$\frac{d\mathrm{Ï•}}{dt}=\mathrm{Ó\neg }$

Substitute all the values in the above equation.

$\frac{d\mathrm{ϕ}}{dt}=1.26×{10}^{15}\mathrm{rad}/\mathrm{s}$

Therefore, the rate of rotation of phasors is $1.26×{10}^{15}\mathrm{rad}/\mathrm{s}$.

The angle between the phasors will be equal to the phase difference between both waves.

The angle between phasors is given as:

$\begin{array}{rcl}\mathrm{θ}& =& \mathrm{ϕ}\\ & =& 39.6\text{rad}\\ & =& \left(39.6\text{rad}\right)\left(\frac{180°}{\mathrm{π}}\right)\\ & =& 2269°\end{array}$

Therefore, the angle between phasors is$2269°$