Intensity of light after passing thru polaroid

[somecelxis]

Homework Statement

Two pieces of polaroid are arranged so they are initially parallel . One of the polaroid is rotated until the intensity of the light beam from the two polaroid is 1/3 of its initial intensity . Calculate the angle turned thru the polaroid

Homework Equations

The Attempt at a Solution

i assume it's a non-polarised passing thru the first polaroid , then the second polaroid is rotated.
so i have Intensity after passing thru 1st polaroid (I 1 ) = 0.5 intensity of non-polarised (I 0)...
for light ray emerging from second polaroid = (I 2 ) = 0.5(I 0) ( (cos θ )^2) .finally i found out my θ = 35.3° the ans form the book is 54.7°

why i am wrong?
the initial light ray is polarised or non- polarised? how to determine it? it's not stated in the question...

 

[nrqed]

Homework Statement

Two pieces of polaroid are arranged so they are initially parallel . One of the polaroid is rotated until the intensity of the light beam from the two polaroid is 1/3 of its initial intensity . Calculate the angle turned thru the polaroid

Homework Equations

The Attempt at a Solution

i assume it's a non-polarised passing thru the first polaroid , then the second polaroid is rotated.
so i have Intensity after passing thru 1st polaroid (I 1 ) = 0.5 intensity of non-polarised (I 0)...
for light ray emerging from second polaroid = (I 2 ) = 0.5(I 0) ( (cos θ )^2) .finally i found out my θ = 35.3° the ans form the book is 54.7°

why i am wrong?
the initial light ray is polarised or non- polarised? how to determine it? it's not stated in the question...

It sounds like they did not phrase the problem correctly. With the precise phrasing you wrote, you are correct (assuming initial unpolarized light). But if interpret the question as meaning: at what angle is the intensity equal to 1/3 it was before entering the second polarizer (in other words, by "initial" we mean before the second polarizer, not before the two polarizers) then we get the answer they give.