Question

(8.0.10) In class we showed that intensity distribution for single slit diffraction is given by I(θ) = I(0) [sin( β/ 2)/( β/2)]. ( β = ka sin(theta) , "a" is the slit width and k = 2π/λ ). (a) Show that the maxima in the diffraction pattern occur at θ for which tan( β/ 2) = β/2. (b) An obvious solution to this equation is β = 0, which corresponds to the central maximum. By sketching the functions tan(β/2) and β/2 as functions of β/2 on the plot, roughly estimate two values of β/2 other than zero which satisfy this equation. (c) Either by trial and error, numerical analysis or by asking your fancy calculators, find the smallest two positive values of β/2 which satisfy the condition derived in (a) to three significant figures.

(8.0.20) Light with wavelength λ = 600 nm diffracts through a slit with width 0.2 mm. (a) Using your results from the problem 8.0.10, find the values of θ for which the five maxima closest to the center occur. (You may include positive, negative, and zero values for theta.) (b) If the electric field at the center of the diffraction pattern oscillates with amplitude 60V/m, find the intensity at each of the maxima you identified in part (a).

You have to answer 8.0.10 and 8.0.10 because they are related!

Answer #1

**Solution:**

given that

In class we showed that intensity distribution for single slit diffraction is given by I(θ) = I(0) [sin( β/ 2)/( β/2)]. ( β = ka sin(theta) , "a" is the slit width and k = 2π/λ )..

A single slit, 2000 nm wide, forms a diffraction pattern when
illuminated by monochromatic light of 520-nm wavelength. A. What is
the largest angle from the central maximum at which the intensity
of the light is zero? B. Find the angle at which the fourth minimum
of the pattern occurs away from the central maximum

1.a)
A diffraction pattern is produced on a viewing screen by using a
single slit with blue light. Which of the following is true?
1)Using red light will broaden the pattern; widening the slit will
also broaden the pattern. 2)Using red light will narrow the
pattern; widening the slit will broaden the pattern. 3)Using red
light will broaden the pattern; widening the slit will narrow the
pattern. 4)Using red light will narrow the pattern; widening the
slit will also narrow...

documentclass{article}
\usepackage{array}
\usepackage{tabulary}
\usepackage{amsmath}
\begin{document}
C=capacitance of equivalent ckt.[7]
\begin{equation}
C=\dfrac{\epsilon_{ef}\epsilon_{o}L_{e}W}{2 h} F
\end{equation}
where\
\begin{center}
$F=\cos ^{ - 2} ({\pi}X_{f}/L)$
\end{center}
L=inductance of equivalent ckt.[7]
\begin{equation}
L=\frac{1}{({2\pi}f_{r})^{2}C}
\end{equation}\
$\Delta L$=additional series inductance
\begin{equation}
\Delta L=\frac{Z_{01}+Z_{02}}{16\pi{f_{r}}F} tan(\pi{f_{r}{L_{n}}}/C)
\end{equation}\
$Z_{01} and Z_{02}$ are the characteristics impedances of microstrip lines with width of
$w_{1} and w_{2}$ respectively.The values
\begin{equation}
Z_{01}=120\pi/(\frac{w_{1}}{h}+1.393+0.667\ln(\frac{w_{1}}{h}+1.444))
\end{equation}\
$$
Z_{02}=120\pi/(\frac{w_{2}}{h}+1.393+0.667\ln(\frac{w_{2}}{h}+1.444))
$$
\
where\
$$w_{1}=w-2{P_{s}}-W_{s}$$
\
and\
$$w_{2}=2{P_{s}}-W_{s}$$
The capacitance$\Delta C$ between center wing and side wing is calculated as...

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