Do mirrors increase the amount of light in a room? So if you have a light bulb in a room, and you had a tool to measure the amount of light that's in the room, then let's assume the amount of light only caused by the bulb is "1"
If you place a mirror next to the bulb, does the amount of light in the room in crease to "2"?
Can you keep going so that the light in the room in creases to 3..etc with more mirrors?
How far can you take this?  Also, is it actually adding light to the room, or is it simply causing the same photons to move faster (reflecting from one mirror to the next) making it seem like there is more light in the room, but there really isn't?
Made me think, so I thought I ask here :)
 A: Dear Sev, first of all, a simple thing. Light in the vacuum always moves by the speed 299,792,458 meters per second: this fact is exactly true because of the modern definition of one meter. The speed of light in the air is just 0.03% smaller than the speed of light in the vacuum. Nothing ever travels faster than light in the vacuum.
Second, mirrors typically reflect less than 100% of coming light - something like 70%. But that's not the main problem here.
Third, the energy is conserved, so you can't produce much more "light" by putting mirrors. You can't illuminate 100 households by having 1 light bulb and "copying" it by mirrors. Why not? While you may increase - and almost double - the "amount of light" that is hitting a particular area, this fact is (more than) balanced by the fact that the light that would be absorbed by the area occupied by the mirror itself is not absorbed.
So when it comes to the energy budget, ideal mirrors (that reflect 100% of light, just for the sake of simplicity) only rearrange the distribution of light - which areas finally absorb it and which areas just reflect it. The total amount of light that is absorbed is given by the total amount of light that is emitted on the light bulb - and it only depends on the light bulb (and its power).
If you consider light as a "practical thing allowing us something to to be seen", then you want the light to be reflected, e.g. by a book. But the counting for a book that reflects some light - so that we can read it - is similar as the counting for an object that absorbs the light. Mirrors may increase the amount of light reflected by a particular book, but they may not increase the amount of light reflected by the whole room, assuming it has a uniform albedo.
If you look at a light bulb and a nearby mirror, you may see "two light bulbs" and a doubled amount of light, so to say. But this is only true from certain directions. From other directions, the outcome is different and often opposite. For example, if you place your eyes behind the mirror, so that the light bulb is on the opposite side of the mirror than you, then you see no light bulb directly - and no unreflected light from a light bulb (and no light bulb light reflected only by mirrors).
This lesson is much more general. Mirrors - and any other gadgets - may move energy from one place to another, or transform it from one form to another. But they never change the total amount of energy.
Cheers
LM
A: I think that the other two answers miss an interesting point of your question. Lets put a light bulb inside 100% reflecting sphere. All emitted photons will stay inside the sphere and intensity of light will continuously increase to infinity.
Real mirrors are never 100% reflective but there are mirrors with 99.98 reflectivity (these are dichroic mirrors that work only in a narrow wavelength range). With such mirrors light can reflect 1000 times before escaping the sphere so light intensity inside the sphere will be 1000 times higher compared to a lamp without mirrors. The energy conservation is not violated because new photons are not created.
What we just created is actually an optical resonator although normally we have a one-dimensional case with two parallel mirrors and a laser pulse trapped between them (as in Cavity ring-down spectroscopy). Concave mirrors are used for better light trapping.
A: By "light in the room" I assume you mean Energy given off by the light bulb per second, this is commonly know as "Power" (measured in units of watts). You can also define how much power is hitting a certain area, for example the newspaper you may be reading. This new quantity is called Intensity (watts per area). 
By putting mirrors in the room you never change the total "Power", the energy coming out of the light bulb in a certain amount of time. Instead you change the intensity, i.e. how much light is hitting your newspaper, but it's always at the expense of a darker area of the room elsewhere.
To address the last part of your post, light always moves at the same speed. 
