11. A certain ray, when passing through a flat glass plate, attenuates to $a \%$ of its original intensity for every $1 \mathrm{~mm}$ of thickness. Experiments have shown that when 10 pieces of $1 \mathrm{~mm}$ thick flat glass are stacked, the intensity of the ray after passing through these 10 pieces of glass is the same as the intensity after passing through a single piece of $11 \mathrm{~mm}$ thick flat glass, indicating that the gaps between each pair of glass plates also cause attenuation. To ensure that the intensity does not exceed that after passing through a single piece of $20 \mathrm{~mm}$ thick flat glass, what is the minimum number of $1 \mathrm{~mm}$ thick flat glass plates that need to be stacked (Note: Assume the gaps between each pair of flat glass plates are the same)?
11. After passing through a gap, the intensity of the ray attenuates to $x \%$ of its original value. According to the problem, $(a \%)^{10}(x \%)^{9}=$ $(a \%)^{11}$, thus $x \%=(a \%)^{\frac{1}{9}}$; If the ray passes through $n$ pieces of glass to meet the requirement, then $(a \%)^{20} \geqslant(a \%)^{n}(x \%)^{n-1}$, which gives $n \geqslant$ 18.1, i.e., 19 pieces.