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 )..

In the single slit diffraction pattern, the distance between
the second and fifth dark fringes is 1 cm and the distance between
the slit and the screen is 200 cm. The wavelength of the light used
is 600 nm
a) Find the width of the slit. (considering that theta is too
small, it can be accepted that tan theta = sin theta)
b) Find theta click for the third dark fringe.

Consider the limit of the intensity distribution for diffraction
from a single slit
when the width of the slit is much larger than a wavelength.
Describe the
resulting pattern.

2-) A diffraction/interference pattern using a red helium-neon
laser as a light source is observed on a screen a distance of 1.20
m from the element(s) producing the pattern. Using positive values
to indicate distances to the right of the center of the pattern on
the observing screen and negative values for distances to the left
of the center, the following data is taken :
Maxima(Cm) Minima(cm)
-6.60 -6.10
-5.40 -4.75
-4.30 -3.60
-3.00 -2.35
-1.80 -1.20
+1.70 +1.15
+3.00...

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...

Item 1
In the case below, the original source material is given along
with a sample of student work. Determine the type of plagiarism by
clicking the appropriate radio button.
Original Source Material
Student Version
In contrast to the transmittal model illustrated by the
classroom lecture-note taking scenario, the constructivist model
places students at the center of the process--actively
participating in thinking and discussing ideas while making meaning
for themselves. And the professor, instead of being the
"sage on the...

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