Question

In young's double-slit experiment using mono chromatic light of wavelength A the intensity of light at a point on the screen where path difference is $\lambda$ is K units. What is the intensity if light at a point where path difference is $\lambda /3$?

Answer 1

$I=I_1+I_2+2\sqrt{I_1{I}_2}cos\varphi$

$I=I_1=I_2=I_0$

$K=I_0{+I}_0{+2I}_{0}cos2\pi =4I_0$

$K^{\prime }=I_0{+I}_0{+2I}_{0}cos2\pi /3$

$K^{\prime }=I_0{+I}_0{+2I}_0\left(\frac{1}{2}\right)=I_0$

$\frac{K^{\prime }}{K}=\frac{I_0}{{4I}_0}=\frac{1}{4}=K^{\prime }=\frac{K}{4}$