I think you're referring to two different "mirror" attributes. The mirror modifier duplicates and reverses geometry over a chosen axis or offset object. The mirror you're talking about (reflectivity) would require a ray traced renderer, so it's not available in webGL.
A close second would be to add an envmap/cubemap to your material, which gives the effect that your model reflects its environment. To do this, you need two things.
Here's an example:
- Make sure your material has a reflectivity value.
- Make sure your material has a envmap.
Here's how I did that in the above example: http://novak.us/labs/UmDemo/
var path = "textures/images/blurredRoom_";
var format = '.jpg';
var urls = [
path + 'px' + format, path + 'nx' + format,
path + 'py' + format, path + 'ny' + format,
path + 'pz' + format, path + 'nz' + format
];
var reflectionCube = THREE.ImageUtils.loadTextureCube( urls );
reflectionCube.format = THREE.RGBFormat;
UMLogo.children[0].material.envMap = reflectionCube;
UMLogo.children[0].material.reflectivity = 0.6;
UMLogo.children[2].material.envMap = reflectionCube;
UMLogo.children[2].material.reflectivity = 0.6;
I hope that helps.