Problem Set 8: Diffraction

Problem Set 8: Diffraction#

A plane wave of intensity \(10 mW/cm^2\) and wavelength \(\lambda = 600nm\) is incident onto a rectangular slit of dimensions 1mm X 0.2mm. Create a normalized plot of the diffracted beam 1mm away from the slit.
A plane wave of intensity \(10 mW/cm^2\) and wavelength \(\lambda = 600nm\) is incident onto a rectangular slit of dimensions 1mm X 0.2mm. Create a normalized plot of the diffracted beam 100mm away from the slit.
Show that the angular Fraunhofer diffraction equation for a single slit of width b is given by

(3)#\[\begin{equation} I\left(\theta\right)=I\left(0\right)\left(\frac{\sin{\left(\frac{kb}{2}\sin{\theta}\right)}}{\frac{kb}{2}\sin{\theta}}\right)^2. \end{equation}\]
A plane wave with irradiance of \(10 mW/cm^2\) and wavelength \(\lambda = 600 nm\) is incident onto a rectangular slit of dimensions 1mm X 0.2mm. What is the peak irradiance 10 m away from the slit?
A plane wave of intensity \(10 mW/cm^2\) and wavelength \(\lambda = 600 nm\) is incident onto a rectangular slit of dimensions 1mm X 0.2mm. A lens with a focal length of f=20mm and a diameter of D=10mm is placed immediately after the aperture. Plot the normalized diffraction pattern at the plane z=20mm. Create a gray scale image of the plot using Matlab or Python.
The big ugly satellite dishes have a diameter of 3.5m, an f#=0.38, and operate in the C-band (f=5GHz). Notice the f# of a satellite dish is much smaller than most optical lens systems. This is because the dish is parabolic and only operates at a very small field of view. If 100W of power is uniformly illuminated over the dish, what is the maximum intensity at the satellite? Use a distance between the satellite dish and the satellite of 36,000km.
A plane wave with wavelength \(\lambda = 600 nm\) is incident onto a circular aperture of diameter \(D = 10 \mu m\) that has a square obscuration in which the corners of the square touch the circle (\(W=7.07 \mu m\)). See Fig. 8. A lens of focal length f=10mm is placed immediately after the aperture. What is the intensity pattern on a screen located at the focus of the lens? Just plot the normalized pattern.

Fig. 8 Aperture where the light is blocked except for the black portion.#
On the web site http://laser.physics.sunysb.edu/~thomas/report1/lens_report.html it explains that a magnifying glass is used to start a fire. About halfway down is a set of numbers calculating the irradiance of magnifier 1 with specifications of f=15cm, D=4.7cm, and incident irradiance of \(1 kW/m^2\). Calculate the maximum irradiance at the focal plane of the lens.