Is a 0.5 cm thick obsidian plate good to see the Sun directly?
NO. Do not trust your eyesight to anything other than a product that has been specifically designed to protect it.
For a good starter resource on eye safety for seeing the Sun, see e.g. this AAS eclipse-viewing resource. Use only certified Sun-viewing eyeglasses, or welding glasses of shades 12 or 14 $-$ and only purchase either of those from a reputable vendor.
If the object you have in your hand is
0.5 cm thick obsidian plate,
and that is all that you can tell us about it, then it is not safe to use for solar viewing. Obsidian is a type of glass and, like all naturally-occurring glass, there's a substantial amount of variability in its properties. The only way to tell whether a specific sample is safe to use is to measure directly how much UV light it lets through: it is the UV light that causes the most damage, and you cannot see it with the naked eye.
What are the risks of using unsafe products (or using products not certified to be safe, which is the same thing as unsafe products) to view the Sun? You risk losing your eyesight, and it's simply not worth the risk.