'$$n$$' polarizing sheets are arranged such that each makes an angle $$45°$$ with the proceeding sheet. An unpolarized light of intensity $$I$$ is incident into this arrangement. The output intensity is found to be $$\frac{I}{64}$$. The value of $$n$$ will be:

Unpolarized light of intensity $$I$$ passes through $$n$$ polarizing sheets, each making $$45°$$ with the preceding sheet. Output intensity = $$I/64$$.

After the first polarizer: $$I_1 = I/2$$ (Malus's law for unpolarized light).

After each subsequent polarizer (angle $$45°$$): $$I_{k+1} = I_k \cos^2 45° = I_k/2$$.

After $$n$$ sheets: $$I_n = \frac{I}{2} \times \left(\frac{1}{2}\right)^{n-1} = \frac{I}{2^n}$$.

Given $$I_n = I/64 = I/2^6$$: $$2^n = 64 = 2^6$$, so $$n = 6$$.

The correct answer is Option B: 6.