Unpolarised light of intensity I0 passes through three ideal polaroids in succession. The pass axis of the second makes an angle of 30^° with that of…

The first polaroid transmits half of the unpolarised intensity: $I_1=I_0/2$. Malus's law applies at each later polaroid with the angle between consecutive pass axes: $I_2=I_1\cos^2 30^\circ=\dfrac{I_0}{2}\cdot\dfrac34=\dfrac{3I_0}{8}$, and then $I_3=I_2\cos^260^\circ=\dfrac{3I_0}{8}\cdot\dfrac14=\dfrac{3I_0}{32}$. The last angle to use is between the second and third axes ($60^\circ$), not between the first and third ($90^\circ$, which would wrongly give zero). Omitting the initial factor of $\tfrac12$ gives $3I_0/16$.