Does this privacy screen have a matte and glossy side, and what is each side used for?

Yes. It is reversible, with a matte side for anti-glare and a glossy side for increased clarity.

What size display is this privacy screen designed for?

It is designed for 23.8-inch widescreen displays with a 16:9 aspect ratio.

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StarTech Magnetic Monitor Privacy Screen for 23.8" 16:9 Widescreen Display, Removable Filter, Anti-Glare/Glossy Sides, TAA Compliant