Unpolarised light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is?

Let initial intensity be I0.
Intensity of the beam after passing through A is I1 = I0/2
Given that intensity after C is I0/2. Then the angle between A and C is zero.
A polarizer B is introduced between A and C then by Malus' law:
After B, Ib = I0/2 * cos²θ
And after C, Ic = Ib * cos²θ
So given Ic = I0/8
From here solving all the three equations:
I0/8 = I0/2 * cos⁴θ
1/4 = cos⁴θ
cos²θ = 1/2
θ = 45°