Exam 2, Fall 2021 Problem 1: A light wave is travelling along z direction. A left circularly polarized light passes through a linear polarizer at with the horizontal and then passes through a...

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Exam 2, Fall 2021 Problem 1: A light wave is travelling along z direction. A left circularly polarized light passes through a linear polarizer at with the horizontal and then passes through a y-polarizer. Find the final polarization (output) of the wave using the Jones matrices and vectors. Show all the steps. Problem 2: What is the angular half-width (from central maximum to first minimum) of a diffracted beam for a slit width of (a) (b) (c)? Problem 3: Write down the Jones vector for the wave that is polarized at and the jones matrix that has the transmission axis at with horizontal. Now if the polarized light passes through the polarizer what would be the polarization of the wave. Find the final polarization (output) of the wave using the Jones matrices and vectors. Show all the steps. Problem 4: Given the dispersion relation , compute both the phase velocity and group velocity. Problem 5: (50 points) Design a problem or thought experiment and solve it or explain approach that would provide the guideline to solve the problem or run the experiment. (Do not copy from the book or google, you will be graded based on your ability of thinking differently, not on accuracy) The problem should be from one of the following: 1. polarization, 2. diffraction, Interference 3. Fourier analysis (Coherence) (Just prepare one question and its solution from any topic from above. It worth 50 points.)
Answered 3 days AfterNov 18, 2021

Answer To: Exam 2, Fall 2021 Problem 1: A light wave is travelling along z direction. A left circularly...

Ravindra Kumar answered on Nov 21 2021
106 Votes
Exam 2, Fall 2021
Problem 1:
A light wave is travelling along z direction. A left circularly polarized light passes through a linear polarizer at with the horizontal and then pas
ses through a y-polarizer. Find the final polarization (output) of the wave using the Jones matrices and vectors. Show all the steps.
Solution:
Given,
Direction of propagation of light wave = z direction
Left circularly polarized light passes through the polarizer at an angle
We know that a linearly polarized light which is propagating in +z direction can be represented as
For x direction, we can write
Now, substituting the values,
From Jones matrix
Problem 2:
What is the angular half-width (from central maximum to first minimum) of a diffracted beam for a slit width of (a) (b) (c)?
Solution    
We know that,
Half-angular width
a)
Slit width
Now, substituting the values in the above equation,
b)
Silt width
Now, substituting the values in the above equation,
c)
Silt width
Now, substituting the values in the above equation,
Problem 3:
Write down the Jones vector for the wave that is polarized at and the jones matrix that has the transmission axis at with horizontal. Now if the polarized light passes through the polarizer what would be the polarization of the wave. Find the final polarization (output) of the wave using the Jones matrices and vectors. Show all the steps.
Solution
Given,
Polarization angle
Transmission axis for the Jones matrix
So, net angle between the transmission axis and parallel to plane of incidence
Now, substituting the angle,
Problem 4:
Given the dispersion relation , compute both the phase velocity and group velocity.
Solution
Given,
The dispersion relation
Phase velocity

Group velocity
Now, taking the differentiation of the...
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