Intensity of polaroids at an angle

[Sasha26]

Homework Statement

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of 7? b) 25? c) 250?

Homework Equations

The first polaroid decreases the intensity by 1/2, so that's I1 = 0.5I0.
I also have I2 = I1(cos theta)^2.

The Attempt at a Solution

I think it might just be the wording that's getting me, but here's my interpretation:

In the first polaroid, 1/2 the intensity is removed. That makes I1 equal to 0.5 I0.
In the second polaroid, 1/7 of I0 is removed. That makes I2 = 0.5I0 - (1/7 I0), or 5/14 I0.

So then I've got I2 = I1(cos theta)^2 --> 5/14 I0 = 0.5 I0 cos(theta)^2. This gives me 32 as theta, which is incorrect. I haven't tried to work out the rest as there seems to be something wrong with my procedure and they're all essentially the same problem.

Any help is much appreciated!

 

[Redbelly98]

To reduce I1 by a factor of 7 means that

I2 = (1/7) I1