Question

The relationship between phase difference $\Delta \varphi$ and the path difference $\Delta x$ between two interfering waves is given by
($\lambda$ = wavelength)

• A. $\Delta x=\left(\frac{2\pi }{\lambda }\right)\Delta \varphi$
• B. $\Delta \varphi =\left(\frac{2\pi }{\lambda }\right)\Delta x$
• C. $\Delta \varphi =\left(\frac{\lambda }{4\pi }\right)\Delta x$
• D. $\Delta \varphi =2\left(2\pi \right)\Delta x$

Answer 1

The correct option is B $\Delta \varphi =\left(\frac{2\pi }{\lambda }\right)\Delta x$

Angle between $P_1$ and $P_2$ = ${30}^{\circ }$ (given)
Angle between $P_2$ and $P_3$ $=\theta ={90}^{\circ }-{30}^{\circ }={60}^{\circ }$
The intensity of light transmitted by $P_1$ is $I_1=\frac{I_0}{2}=\frac{32}{2}=16\frac{W}{m^2}$
According to Malus law the intensity of light transmitted by $P_2$ is $I_2=I_{1}co{s}^2{30}^{\circ }=16{\left(\frac{\sqrt{3}}{2}\right)}^2=12\frac{W}{m^2}$
Similarly intensity of light transmitted by $P_3$ is $I_3=I_{2}co{s}^2\theta =12co{s}^2{60}^{\circ }=12{\left(\frac{1}{2}\right)}^2=3\frac{W}{m^2}$