Question
Derive the Mueller matrix for a quarter-wave plate with its fast axis at $-45^{\circ}$. Check that this matrix effectively cancels the one in Problem $8.81,$ so that a beam passing through the two wave plates successively remains unaltered.
Step 1
Step 1: First, we need to find the values of $cos2\alpha$, $sin2\alpha$, $cos\phi$, and $sin\phi$ for $\alpha = -45^{\circ}$ and $\phi = \pi/2$. Show more…
Show all steps
Your feedback will help us improve your experience
Mahendra K and 91 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use Table 8.6 to derive a Mueller matrix for a half-wave plate having a vertical fast axis. Utilize your result to convert an $\mathscr{R}$ -state into an $\mathscr{S}$ -state. Verify that the same wave plate will convert an $\underline{\zeta}-$ to an 9 - state. Advancing or retarding the relative phase by $\pi / 2$ should have the same effect. Check this by deriving the matrix for a half-wave plate with a horizontal fast axis.
Beginning with the Mueller matrix for an arbitrary retarder provided in the previous problem, show that it agrees with the matrix in Table 8.6 for a quarter-wave plate with a vertical fast axis.
Confirm that the matrix $$\left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}\right]$$ will serve as a Mueller matrix for a quarter-wave plate with its fast axis at $+45^{\circ}$. Shine linear light polurized at $45^{\circ}$ through it. What happens? What emerges when a horizontal $\mathscr{P}$ -state enters the device?
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
