- #1
timetraveller123
- 621
- 45
Homework Statement
i don't understand where the 1.22 number comes from like in
##
sin \theta = 1.22 \lambda /D
##
so i tried to derive but to not much help
Homework Equations
electric field at distance R due to slit of length D is
##
E = \frac{\epsilon_l D}{R} sinc(\frac{kD}{2}sin \theta)sin(wt - kR)
##
so i thought of breaking the circle into series of strips with theta being zero so sinc being 1
The Attempt at a Solution
##
\epsilon_ l = \epsilon_a dx\\
D= \sqrt{R^2 - x^2}\\
R = R+x sin\theta\\
dE = \frac{\epsilon_A dx 2 \sqrt{R^2 - x^2}}{R}sin(wt - kR + kxsin\theta)\\
E= \frac{2 \epsilon_a}{R} \int _{-R}^{R} \sqrt {R^2 - x^2}sin(wt -kR + kxsin\theta)dx\\
E = \frac{2 \epsilon_a}{R} sin(wt - kR) \int_{-R}^{R} \sqrt {R^2 - x^2} cos(kx sin \theta)dx\\
##
the other term drops out as it is odd
i tried to put this into integral calculator but it didnt give an answer so help where does the 1.22 come from[/B]