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

\(\displaystyle{60}^{\circ}\)

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

\(\displaystyle{60}^{\circ}\)