geometric-opticslaseropticsreflection
Theoretically, if I shined a laser at a mirror at an angle of 0 degrees so that the light was perfectly reflected back to the light source, then I should not be able to see the light because it is not reflected to my eyes.
|
| me
|
|============ laser
|
|
|
However this is evidently not the case, as I am able to see the laser point on the mirror. Why is this the case? My initial assumption is that it is due to diffuse reflection on the imperfect mirror's surface, but I am not sure.
No, there's no need for screens in the movie theaters to be mirrors i.e. specular reflectors. Quite on the contrary, it's completely necessary for them not to be mirrors i.e. to be diffuse reflectors.
If the screen were a specular reflector, the light would return back into the direction of the projector and would never reach the eyes of the viewers who aren't sitting on the line in which the projector is directed. If the screen were a mirror, the viewers would only see themselves and the projector but couldn't see any magnified versions of the objects that are supposed to be in the movie.
In reality, each point of the screen – which is a diffuse reflector – effectively becomes a source of light whose intensity depends on the amount of incident light at this point and this source is located directly in the plane of the screen. So these sources of light are not images (in the sense of real or virtual images of mirrors or lens) at all. More precisely, the only image of the real "object" – the object on the screen – is formed in the viewers' eyes.
It's important for the projector to sharply illuminate each point of the screen differently, by the correct intensity of light of the right color. This requires precise optics that chooses the right directions of light rays for each point of the movie between the projector and the screen. On the other hand, each point of the screen is a diffuse reflector and much like real objects in the real world, it emits light to all directions so that all viewers may see it, regardless of the location of their chair.
You are getting reflections from the front (glass surface) and back (mirrored) surface, including (multiple) internal reflections:
It should be obvious from this diagram that the spots will be further apart as you move to a more glancing angle of incidence. Depending on the polarization of the laser pointer, there is an angle (the Brewster angle) where you can make the front (glass) surface reflection disappear completely. This takes some experimenting.
The exact details of the intensity as a function of angle of incidence are described by the Fresnel Equations. From that Wikipedia article, here is a diagram showing how the intensity of the (front) reflection changes with angle of incidence and polarization:
This effect is independent of wavelength (except inasmuch as the refractive index is a weak function of wavelength... So different colors of light will have a slightly different Brewster angle); the only way in which laser light is different from "ordinary" light in this case is the fact that laser light is typically linearly polarized, so that the reflection coefficient for a particular angle can be changed simply by rotating the laser pointer.
As Rainer P pointed out in a comment, if there is a coefficient of reflection $c$ at the front face, then $(1-c)$ of the intensity makes it to the back; and if the coefficient of reflection at the inside of the glass/air interface is $r$, then the successive reflected beams will have intensities that decrease geometrically:
$$c, (1-c)(1-r), (1-c)(1-r)r, (1-c)(1-r)r^2, (1-c)(1-r)r^3, ...$$
Of course the reciprocity theorem tells us that when we reverse the direction of a beam, we get the same reflectivity, so $r=c$ . This means the above can be simplified; but I left it in this form to show better what interactions the rays undergo. The above also assumes perfect reflection at the silvered (back) face: it should be easy to see how you could add that term...
Best Answer
Your question touches on several issues that confound the "perfect" situation:
Scattering
This will allow you to see the laser light at angles other than the reflected (specular) direction. This can (and does) come from:
Coherent Addition / Subtraction
If you are arranged "perfectly" such that the reflection is coming back towards the laser, this sets up another resonator. (Lasers are resonating cavities: https://en.wikipedia.org/wiki/Optical_cavity) This causes all sorts of problems!