**Polarization and Intensity of Light****Question:**An ideal polarizer with its transmission axis rotated 30° to the vertical is placed in a beam of unpolarized light of intensity 10 W/m². After passing through the polarizer, what is the intensity of the beam?a) 10 W/m² b) 5.0 W/m² c) 8.7 W/m² d) 7.5 W/m² **Explanation:**When unpolarized light passes through a polarizer, the intensity of the light is reduced. The intensity \(I\) of the polarized light after passing through an ideal polarizer can be calculated using Malus's Law, which is given by:\[ I = I_0 \cdot \cos^2(\theta) \]where:- \(I_0\) is the initial intensity of the unpolarized light,- \(\theta\) is the angle between the light's initial polarization direction and the axis of the polarizer.For unpolarized light, the initial intensity is reduced by half after passing through the first polarizer:\[ I' = \frac{I_0}{2} \]Here, \(I_0 = 10 \, \text{W/m}^2\) and \(\theta = 30^\circ\):\[ I' = \frac{10 \, \text{W/m}^2}{2} = 5 \, \text{W/m}^2 \]After the polarizer at 30°, the intensity is:\[ I = 5 \, \text{W/m}^2 \cdot \cos^2(30^\circ) \]\[ \cos(30^\circ) = \sqrt{3}/2 \]\[ I = 5 \, \text{W/m}^2 \cdot \left(\frac{\sqrt{3}}{2}\right)^2 \]\[ I = 5 \, \text{W/m}^2 \cdot \frac{3}{4} \]\[ I = \frac{15}{4} \, \text{W/m}^2 \]\[ I = 3.75 \, \text{W/m}^2 \]Since none of the options directly match this result, further calculations should be double-checked,

Given data: Intensity of unpolarized light (I0) = 10 W/m2 Angle (θ) = 30°,to the vertical Required: The intensity of the beam after passing through the polarizer According to Malus's law I = I0cos2θ= (10 W/m2)(cos30°)2=7.5 W/m2 The intensity of the beam after passing through the polarizer is equals to 7.5 W/m2 Hence, the correct answer is option (d)

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An ideal polarizer with its transmission axis rotated 30° to the vertical is placed in a beam of unpolarized light of intensity 10 W/m². After passing through the polarizer, what is intensity of the beam? a) 10 W/m² b) 5.0 W/m² c) 8.7 W/m² d) 7.5 W/m²

An ideal polarizer with its transmission axis rotated 30° to the vertical is placed in a beam of unpolarized light of intensity 10 W/m². After passing through the polarizer, what is intensity of the beam? a) 10 W/m² b) 5.0 W/m² c) 8.7 W/m² d) 7.5 W/m²

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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