s three perfectly polarizing sheets are spaced 2 cm apart and in parallel planes.The transmission axis of the second sheet is 30^circ relative to the first one. The transmission axis of the third sheet is 90^circ relative to the first one . Unpolarized light impinges on the first polarizing sheet.What percent of this light is transmit- ted out through the third polarizer [1]?

To solve this problem, we need to consider the Malus's law, which describes the intensity of light passing through two polarizers. The intensity of light after passing through the first polarizer is given by:<br /><br />\[ I_1 = I_0 \cos^2(\theta) \]<br /><br />where \( I_0 \) is the initial intensity of the unpolarized light and \( \theta \) is the angle between the transmission axis of the first polarizer and the direction of the electric field of the light.<br /><br />After passing through the first polarizer, the light becomes partially polarized. The intensity of this polarized light after passing through the second polar given\[ I_2 = I_1 \cos^2(\phi) \]<br /><br />where \( \phi \) is the angle between the transmission axis of the second polarizer and the direction of the electric field of the polarized light from the first polarizer.<br /><br />Finally, the intensity of the light after passing through the third polarizer is given by:<br /><br />\[ I_3 = I_2 \cos^2(\psi) \]<br /><br />where \( \psi \) is the angle between the transmission axis of the third polarizer and the direction of the electric field of the polarized light from the second polarizer.<br /><br />In this case, the angles are given as follows:<br />- \( \theta = 0^{\circ} \) (since the transmission axis of the first sheet is aligned with the direction of the electric field of the unpolarized light)<br />- \( \phi =^{\circ} \) (the transmission axis of the second sheet is \( 30^{\circ} \) relative to the first one)<br />- \( \psi = 90^{\circ} \) (the transmission axis of the third sheet is \( 90^{\circ} \) relative to the first one)<br /><br />Substituting these values into the equations, we get:<br /><br />\[ I_1 = I_0 \cos^2(0^{\circ}) = I_0 \]<br /><br />\[ I_2 = I_1 \cos^2(30^{\circ}) = I_0 \cos^2(30^{\circ}) \]<br /><br />\[ I_3 = I_2 \cos^2(90^{\circ}) = I_0 \cos^2(30^{\circ}) \cos^2(90^{\circSince \( \cos(90^{\circ}) = 0 \), the intensity of the light transmitted through the third polarizer is zero.<br /><br />Therefore, the percentage of the initial light that is transmitted through the third polarizer is 0%.