Understanding Jones Matrixes for Linear Polarization

[strange_quark]

I have a very basic question regarding jones matrixes.

So for Linear polarized light in the x direction the jones matrix would be (1,0)

And for linear polarized light in the y direction the jones matrix would be (0,1)

But when light is linearly polarized in a 45 degree angle from the x-axis the jones matrix becomes (1/sqrt(2) *(1,1)

my question is: what is the 1/sqrt(2) doing there?

I mean if you draw this point in a x,y system the angle is going to be 45 degrees no matter how large the x and y coordinate are going to be assuming they are equal to each other

 

[blue_leaf77]

what is the 1/sqrt(2) doing there?

Just convention to make the energy unit equal to unity.

 

[M Quack]

The length of the Jones vector is sometimes considered as intensity. So the 1/sqrt(2) is there for normalization, to make the length of the vector 1.