Physics307L:People/Giannini/Scratch Sheet

[math]\displaystyle{ L_1=q_1\lambda_1/2n\,\! }[/math]

[math]\displaystyle{ L_2=q_2\lambda_2/2n\,\! }[/math]

which gives us:

Eq.1 [math]\displaystyle{ c=\nu_1\lambda_1\,\! }[/math]

Eq.2 [math]\displaystyle{ c=\nu_2\lambda_2\,\! }[/math]

Now we say

Eq.3 [math]\displaystyle{ \Delta\nu=\nu_1-\nu_2\,\! }[/math]

then we can use [math]\displaystyle{ 2\cdot Eq.1 - 2\cdot Eq.2 }[/math]

which then gives us

[math]\displaystyle{ c=2\nu_1\lambda_1-\nu_2\lambda_2\,\! }[/math]

which, upon substitution of Eq.3, we get

[math]\displaystyle{ c=\nu_1(2\lambda_1-\lambda_2)+\Delta\nu\lambda_2\,\! }[/math]

[math]\displaystyle{ TEM_00\,\! }[/math]