As after B intensity of light does not drops, it means both A and B are alligned in single line means their plane of polarization is same.



Let C makes an angle $$\theta $$ with A then C will make $$\theta $$ with B also, as both A and B are alligned in a single line.

So, after C intensity is = $${{\rm I} \over 2}$$ cos²$$\theta $$ , and , intensity after B = $${{\rm I} \over 2}$$ cos²$$\theta $$ $$ \times $$ cos²$$\theta $$

   According to question,

$${{\rm I} \over 2}$$ cos⁴$$\theta $$ = $${{\rm I} \over 8}$$

$$ \Rightarrow $$\,\,\, CO⁴$$\theta $$ = $${{\rm I} \over 4}$$

$$ \Rightarrow $$$$\,\,\,$$ cos$$\theta $$ = $$ = {1 \over {\sqrt 2 }}$$ = cos45^o

$$\therefore\,\,\,$$ $$\theta $$ = 45^o