I frequently shoot inside of museums that have glass or plexiglass or acrylic display cases. A huge problem is reflections from the glass spoiling the image. The reflections include both overhead lights, extraneous objects and self reflection when doing 90-degree shots. I have tried circular polarizers but it makes no significant difference. Will a linear polarizer be more effective, or more or less the same as the circular?
They are the same as to effect. The circular type is actually a linear up front followed by a "retarder" filter. The first one does the deed and the second one scrambles the polarized light so it won't disrupt auto focus and metering functions.
The polarization of reflected light depends on the angle that it hits.
Light that bounces directly back at you (The source is either between you and the object, or behind you) is hardly polarized at all. Light that glances off at about 50 degrees or less (Brewster's angle" strongly polarized.
Reflecting off a metal surface doesn't change light's polarization.
Ways you can use this:
Make sure that your light is coming from more than 45 degrees from the reflecting surface.
Use your own light sources, and overpower the ones that are providing bad reflections.
Use cheap polarizing film, polarize the light sources to reduce the amount reflected in the first place.
Reverse this process and take another photo that increases the reflections. Now you have something you can use to subtract from the image. By choosing a suitable coefficient you can eliminate the reflection. This requires both shots to be done from a tripod.
Change your angle of shooting relative to the case so that the reflected light is no longer at a near 90 degree angle.
Ask the curators to open the case for you.