Question

# Three polarizers are arranged as shown in the figure.

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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.

(a) when $$\displaystyle\theta_{{2}}={22.3}^{\circ}$$ and $$\displaystyle\theta_{{3}}={42.6}^{\circ}$$
(b) when $$\displaystyle\theta_{{2}}={42.26}^{\circ}$$ and $$\displaystyle\theta_{{3}}={22.3}^{\circ}$$

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. $$\displaystyle{I}={0.8}\cdot{\cos{{2}}}{\left({42.6}^{\circ}\right)}={0.433}\frac{{W}}{{m}^{{2}}}$$
$$\displaystyle{I}={0.433}\cdot{\cos{{2}}}{\left({22.3}^{\circ}-{42.6}\right)}={879.6}{m}\frac{{W}}{{m}^{{2}}}$$