Two polaroids $$A$$ and $$B$$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $$C$$ is placed between $$A$$ and $$B$$ bisecting angle between them. If intensity of unpolarised light is $$I_0$$ then intensity of transmitted light after passing through polaroid $$B$$ will be:

Three polaroids A, B, and C are arranged such that:

- Pass axes of A and B are perpendicular to each other

- C is placed between A and B at 45° to both

The unpolarized light of intensity $$I_0$$ passes through in sequence:

To begin, after Polaroid A,

$$ I_1 = \frac{I_0}{2} $$

(Unpolarized light through a polaroid gives half the intensity)

Next, after Polaroid C (at 45° to A),

By Malus's law:

$$ I_2 = I_1 \cos^2 45° = \frac{I_0}{2} \times \frac{1}{2} = \frac{I_0}{4} $$

From this, after Polaroid B (at 45° to C, or 90° to A),

$$ I_3 = I_2 \cos^2 45° = \frac{I_0}{4} \times \frac{1}{2} = \frac{I_0}{8} $$