Reflection of projected light (cookie)?

I'm trying to model the behavior of projected light as it reflects off of a curved mirror and hits the inside of a hollow sphere (kind of like how a planetarium works).

When I look for reflection, I find cubemaps. As in, if I wanted to I could create a curved mirror that looks realistic, but it doesn't actually reflect any light if I put a spotlight next to it.

Is there anything in Unity that can do this? If I use a cookie to project an image out of a spotlight, is there anything I can use to actually reflect/distort the image onto another surface like a real curved mirror would do?

Thanks.