Given below are two statements: one is labelled as Assertion (A)...

When unpolarized light of intensity $I_0$ passes through the first polaroid, the transmitted intensity is $I_1 = \dfrac{I_0}{2}$.

Let the middle polaroid be at an angle $\theta$ with respect to the first. The third polaroid is crossed with the first, so its angle with the middle polaroid is $(90^{\circ} - \theta)$.

The final transmitted intensity is:
$I = I_1 \cos^2\theta \cos^2(90^{\circ} - \theta)$
$I = \dfrac{I_0}{2} \cos^2\theta \sin^2\theta = \dfrac{I_0}{8} \sin^2(2\theta)$

For maximum intensity, $\sin^2(2\theta) = 1$, which gives $2\theta = 90^{\circ} \Rightarrow \theta = 45^{\circ}$. Thus, the Reason is true.

Substituting $\theta = 45^{\circ}$, the maximum transmitted intensity is I_\max = \dfrac{I_0}{8}. The Assertion states it is $\dfrac{I_0}{4}$, which is incorrect because it ignores the initial $50\%$ intensity drop for unpolarized light. Thus, the Assertion is false.

Answer: Assertion is false but Reason is true.