A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3{\mathrm{W}\mathrm{m}}^{-2}$ ${}^{}$ falls normally on a polarizer (cross sectional area $3\times {10}^{-4}{\mathrm{m}}^2$ ${}^{}{}^{}$ ) which rotates about its axis with an angular speed of $31.4\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}$ $$ . The energy of light passing through the polariser per revolution, is close to:

<p><span class="mathml" contenteditable="false"> <math> <mrow></mrow> <mi>E</mi> <mo>=</mo> <mo> (</mo> <mi>I</mi> <mo>)</mo> <mo> (</mo> <mi>t</mi> <mo>)</mo> <mo> (</mo> <mi>A</mi> <mo>)</mo> <mfenced open="?" close="?" separators="|"> <mrow> <mrow> <msup> <mrow> <mrow> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>? </mo> <mi>θ</mi> </mrow> </mrow> </mfenced> </math> </span></p><p><span class="mathml" contenteditable="false"> <math> <mo>⇒</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mo> (</mo> <mn>3.3</mn> <mo>)</mo> <mfenced open=" [" close="]" separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>31.4</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mfenced open=" [" close="]" separators="|"> <mrow> <mrow> <mn>3</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfenced> <mo>×</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span></p><p><span class="mathml" contenteditable="false"> <math> <mo>⇒</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mn>0.99</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> </math> </span></p>

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