# Only 25% of the intensity of a polarized light wave passes through a polarizing

Only 25% of the intensity of a polarized light wave passes through a polarizing filter. What is the angle between the electric field and the axis of the filter?

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Step 1
Equation for intensity of light through a polarizer
$$\displaystyle{I}_{{{T}{r}{a}{n}{s}{m}{i}{\mathtt{{e}}}{d}}}={I}_{{{I}{n}{c}{i}{d}{e}{n}{t}}}{\left({\cos{\theta}}\right)}^{{2}}$$
Step 2
Rearrange
$$\displaystyle{\frac{{{I}_{{{T}{r}{a}{n}{s}{m}{i}{\mathtt{{e}}}{d}}}}}{{{I}_{{{I}{n}{c}{i}{d}{e}{n}{t}}}}}}={\frac{{{1}}}{{{4}}}}={{\cos}^{{2}}\theta}$$
Step 3
Solve
$$\displaystyle{\cos{\theta}}={\frac{{{1}}}{{{2}}}}\Rightarrow\theta={6}^{\circ}$$
Result
$$\displaystyle{60}^{\circ}$$