Problem Statement
Elliptically polarized light has the ellipse’s major-to-minor axis ratio of $E_1/E_2 = 2$, with the major axis horizontal. Find the intensities $I_{\max}$ and $I_{\min}$ through a polarizer rotated by angle $\phi$, and the degree of polarization.
Given Information
- See problem statement for all given quantities.
Physical Concepts & Formulas
This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention to units and sign conventions.
- See the step-by-step solution for the specific equations applied.
- All quantities are in SI units unless otherwise stated.
Step-by-Step Solution
Step 1 — Identify given quantities and set up the problem: $$I(\phi) = E_1^2\cos^2\phi + E_2^2\sin^2\phi$$
$$I_{\max} = E_1^2 = 4E_2^2 \;(\phi=0), \quad I_{\min} = E_2^2 \;(\phi=90°)$$
$$P = \frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}} = \frac{4E_2^2-E_2^2}{4E_2^2+E_2^2} = \frac{3}{5} = \boxed{0.6}$$
Step 2 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Step 3 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Worked Calculation
$$I(\phi) = E_1^2\cos^2\phi + E_2^2\sin^2\phi$$
$$I_{\max} = E_1^2 = 4E_2^2 \;(\phi=0), \quad I_{\min} = E_2^2 \;(\phi=90°)$$
$$P = \frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}} = \frac{4E_2^2-E_2^2}{4E_2^2+E_2^2} = \frac{3}{5} = \boxed{0.6}$$
$$I(\phi) = E_1^2\cos^2\phi + E_2^2\sin^2\phi$$
$$I_{\max} = E_1^2 = 4E_2^2 \;(\phi=0), \quad I_{\min} = E_2^2 \;(\phi=90°)$$
$$P = \frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}} = \frac{4E_2^2-E_2^2}{4E_2^2+E_2^2} = \frac{3}{5} = \boxed{0.6}$$
Answer
$$P = \frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}} = \frac{4E_2^2-E_2^2}{4E_2^2+E_2^2} = \frac{3}{5} = \boxed{0.6}$$
Physical Interpretation
The numerical answer is physically reasonable — matching expected orders of magnitude and dimensional analysis. The result confirms the theoretical prediction and provides quantitative insight into the system’s behaviour.
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