Answer to Question #164105 in Optics for Akinibom Sandra

Question

  Unpolarized Ught falls on two polarizer sheets whose axes are at right-angles.

      (a.) What fraction of the incident light intensity is transmitted?

       (b.) Nhat fraction is transmitted if a third polarizer is placed between the first two so that its axis

       makes a 45° angle with each of their axes?

Answer 1

(a). Final intensity $I_f=0$ The unpolarized light that is incident on a polarizer will be polarized in the same direction of the optical axis of the polarizer. This means that the direction of polarization in the first polarizer sheets is perpendicular to the second polarizer sheets. Therefore, it will not go through the second polarizer sheet hence the final intensity for this part will be equal to zero.

(b). Intensity on first polarizer sheets:

$I_1=\frac{I_o}{2}\:$

Intensity on the second polarizer sheets:

$I_2=I_1cos^245^{\circ }= \frac{I_o}{2}cos^245^{\circ }$

So for the third polarizer the angle will be: $90^{\circ }-45^{\circ }=45^{\circ }$

Fraction of the third polarizer sheets will be:

$I_3=I_2cos^245^{\circ }=\frac{I_o}{2}cos^245^{\circ }cos^245^{\circ }=0.125I_o$