Answer
(a) The transmitted intensity is $\frac{I_0}{8}$
(b) When the middle sheet is removed, the transmitted intensity is zero.
Work Step by Step
(a) Since the light is unpolarized initially, the intensity of the light after passing through the first polarizing sheet is $\frac{I_0}{2}$
We can use the law of Malus to determine the intensity of the light after passing through the second polarizing sheet.
$I_2 = \frac{I_0}{2}~cos^2(45^{\circ}) = \frac{I_0}{4}$
We can determine the intensity of the light after passing through the third polarizing sheet.
$I_3 = \frac{I_0}{4}~cos^2(45^{\circ}) = \frac{I_0}{8}$
The transmitted intensity is $\frac{I_0}{8}$
(b) Since the light is unpolarized initially, the intensity of the light after passing through the first polarizing sheet is $\frac{I_0}{2}$
We can use the law of Malus to determine the intensity of the light after passing through the second polarizing sheet.
$I_2 = \frac{I_0}{2}~cos^2(90^{\circ}) = 0$
When the middle sheet is removed, the transmitted intensity is zero.
