#### 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.