Unpolarized light of intensity I0 passes through three successive polarizers such that the pass axis of the second is at 30^{circ} to the first, and…

After the first polarizer, intensity becomes $I_1 = I_0 / 2$. The angle between the first and second is $30^{\circ}$, so $I_2 = I_1 \cos^2(30^{\circ}) = (I_0 / 2) \times (3/4) = 3I_0 / 8$. The angle between the second and third is $60^{\circ} - 30^{\circ} = 30^{\circ}$. Thus, final intensity $I_3 = I_2 \cos^2(30^{\circ}) = (3I_0 / 8) \times (3/4) = 9I_0 / 32$. Wait, angle with first is $60^{\circ}$, angle of third with second is $60^{\circ} - 30^{\circ} = 30^{\circ}$. So $I_3 = I_2 \cos^2(30^{\circ}) = (3I_0/8) \times (3/4) = 9I_0/32$. Let's re-verify: $I_0/2 \times (\sqrt{3}/2)^2 \times (\sqrt{3}/2)^2 = I_0/2 \times 3/4 \times 3/4 = 9I_0/32$.