Double-slit experiment and watching the electrons

[naima]

Do you know if S M TAN is Shina Tan? He looks very young.

 

[Cthugha]

Do you know if S M TAN is Shina Tan?

No. S M Tan is Sze Meng Tan.

 

[naima]

thank you.
There is a 3/2 factor in the visibility formula. From which identity does it come?

 

[naima]

We begin with an integral from zero to pi of a function of the angle $\theta$.
Using x = cos ($\theta$.) visibility of the fringes becomes
$A\int_{-1}^1 (1+x^2) e^{i u x} dx$.
Integrating it twice by parts we get
$4A [\frac{sin u}{u}+\frac{cos u}{u^2}-\frac{sin u}{u^3}]$.
"u" being the distance of slits divided by the wavelength of the photon when it decreases to zero the limit of visibility must be 1. We need so a normalization factor and the good formula is
$3/2 [\frac{sin u}{u}+\frac{cos u}{u^2}-\frac{sin u}{u^3}]$.

We can compute the visibility when u = 1. It is when we watch the electrons with light having for wavelength the distance
between the slits. We have V(1) = 3/2 cos(1) = 0.8
So the visibility is still very good!