Question

Two polarizing sheets have their transmission axes crossed so that no light is transmitted. A third sheet is inserted so that its transmission axis makes an angle $\theta $ with the transmission axis of the first sheet. If the middle polarizing sheet is rotating at an angular speed $\omega $ about an axis parallel with the light beam, find an expression for the final intensity transmitted through after all three sheets as a function of time. (Original intensity was $I_{0}$ )

• A. $I=\frac{I_{0}}{8}sin^{2}2ωt$
• B. $I=\frac{I_{0}}{4}sin^{2}2ωt$
• C. $I=\frac{I_{0}}{8}cos^{2}2ωt$
• D. $I=\frac{I_{0}}{4}cos^{2}2ωt$

Answer 1

Answer: (A)

$=\frac{ I _{0}}{2} \cos ^{2} \theta \cos ^{2}(90-\theta)$ Intensity after passing through $I ^{\text {st }}$ polaride $=\frac{ I _{0}}{2}$ Let $2^{\text {nd }}$ polaride is at angle $\theta$ from first polaride and $3^{\text {rd }}$ polaride is at angle $90-\theta$ from $2^{\text {nd }}$ one then intensity after passing through
$2^{\text {nd }}$ polaride $=\frac{I_{0}}{2} \cos ^{2} \theta$
Intensity after passing through $3^{\text {rd }}$ polaride
$ \begin{array}{l} I _{\text {final }}=\frac{ I _{0}}{2} \cos ^{2} \theta \sin ^{2} \theta \\ =\frac{ I _{0}}{8} \sin ^{2} 2 \theta=\frac{ I _{0}}{8} \sin ^{2} 2 \omega t \end{array} $