Question

Three polarizers are arranged as shown in the figure.

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asked 2021-02-24

Three polarizers are arranged as shown in the figure. If theincident beam of light is unpolarized, and has an intensity of 1.60\(\displaystyle\frac{{W}}{{m}^{{2}}}\), find the transmitted intensity for each of thefollowing cases.
image
(a) when \(\displaystyle\theta_{{2}}={22.3}^{\circ}\) and \(\displaystyle\theta_{{3}}={42.6}^{\circ}\)
(b) when \(\displaystyle\theta_{{2}}={42.26}^{\circ}\) and \(\displaystyle\theta_{{3}}={22.3}^{\circ}\)

Answers (1)

2021-02-25
I = 1.6 \(\displaystyle\frac{{W}}{{m}^{{2}}}\)
since the light is unpolarized at first
\(\displaystyle{I}={\left({0.5}\right)}\cdot{\left({1.6}\ \frac{{W}}{{m}^{{2}}}\right)}={0.8}\frac{{W}}{{m}^{{2}}}\)
Then use \(\displaystyle{I}={I}_{{0}}{\cos{{2}}}\theta\)
a.\(\displaystyle{I}={0.8}\cdot{\cos{{2}}}{\left({22.3}^{\circ}\right)}={0.684}\frac{{W}}{{m}^{{2}}}\)
\(\displaystyle{I}={0.684}\cdot{\cos{{2}}}{\left({42.6}^{\circ}-{22.3}^{\circ}\right)}={601.67}{m}\frac{{W}}{{m}^{{2}}}\)
b. \(\displaystyle{I}={0.8}\cdot{\cos{{2}}}{\left({42.6}^{\circ}\right)}={0.433}\frac{{W}}{{m}^{{2}}}\)
\(\displaystyle{I}={0.433}\cdot{\cos{{2}}}{\left({22.3}^{\circ}-{42.6}\right)}={879.6}{m}\frac{{W}}{{m}^{{2}}}\)
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