How do mirrors create images despite scattered light?

[ViolentCorpse]

Hi!

I have two questions:

1) I'm a little confused about image formation. Suppose there's an illuminated object place in front of a mirror. The object has a rough surface causing a diffuse reflection so when lights hits the object, the rays will be scattered all around the room. Now the difficulty that I'm having in understanding is that; Even though the mirror will cause a specular reflection, how is the mirror able to form a complete image of the object if the light incident on it is so scattered? Wouldn't the information of the image carried by that light have to be uniformly incident on the mirror for there to be an exact reflection of the real object?

2) If a laser light is shined on a wall, the dot it makes on the wall can be viewed from every possible direction in the room. For such a narrow beam of light, it seems weird that it would reflect in so many different angles, rather than just one?

Thank you! :)

 

[Jolb]

1) I'm a little confused about image formation. Suppose there's an illuminated object place in front of a mirror. The object has a rough surface causing a diffuse reflection so when lights hits the object, the rays will be scattered all around the room. Now the difficulty that I'm having in understanding is that; Even though the mirror will cause a specular reflection, how is the mirror able to form a complete image of the object if the light incident on it is so scattered? Wouldn't the information of the image carried by that light have to be uniformly incident on the mirror for there to be an exact reflection of the real object?

To help make sense of this, keep in mind some of the basic principles of ray optics. Diffuse reflections are different from specular reflections in that the incident light on a diffuse reflector is reflected in all directions, unlike a specular reflector where angle of incidence is angle of reflection.

Because the reflection of the light off the mirror is specular, the image you see of the object through the image in the mirror is similar in almost every way to the real object. Using ray optics, what your eye sees coming from the mirror is equivalent to what would be coming from "virtual objects" sitting behind the mirror. Take a look at this picture:

So even though the dog in the picture is a diffuse reflector, whether you look at him through the mirror or directly at him doesn't change whether you see a nice clear image. They're basically equivalent. [To be totally clear, I should say that the mirror image of the dog looks exactly equivalent to what you would see if the mirror were removed and the dog were placed in the position of the image, with his left and right sides reversed.]

2) If a laser light is shined on a wall, the dot it makes on the wall can be viewed from every possible direction in the room. For such a narrow beam of light, it seems weird that it would reflect in so many different angles, rather than just one?

If your wall were a perfectly smooth surface, then it would reflect in just one direction. This is what happens with a mirror (or, for something that's even more perfectly smooth, a silicon wafer), and this is the origin of specular reflection. The reason that normal walls don't reflect specularly is because they are not perfectly smooth, leading to diffuse reflection. Here's the best analogy I can give for this:

Start with a super fresh piece of aluminum foil, right out of the box. It is almost mirror like, because it is still very smooth. You could get your laser pointer to reflect off it like a mirror. [This is specular reflection.]

Now try crumpling the aluminum foil up and flattening it back out. It won't reflect your laser pointer along one angle any more--the beam gets reflected off a bunch of different little faces of the aluminum foil, scattering the light to different places around the room. [This is diffuse reflection.] You haven't changed the reflectivity of the aluminum, just the texture of the surface. The same thing happens at the microscopic scale, so the microscopic texture of the wall is what causes it to reflect diffusely rather than specularly.

 

[ViolentCorpse]

Fantastic explanation!

Thank you so much, Jolb! Really appreciate it. :)

So if I want to see the spot of incident laser light on the mirror/aluminum foil, I can only view at the angle it is being reflected?

I'm also a little confused why only specularly reflecting surfaces reflect images of other objects while diffusely reflecting surfaces only reflect their own image..

 

[Jolb]

So if I want to see the spot of incident laser light on the mirror/aluminum foil, I can only view at the angle it is being reflected?

Well, according to the picture in my previous post, if someone were to reflect a laser pointer off a miror into your eye, it would be equivalent to having someone stand in the position of the virtual image and shine the laser directly into your eye. (And it won't look like a spot on the wall--it will look painfully bright like when you visit the opthomologist.) Unless you're in a smoky room, you don't see the laser traveling through the air, so why should you see anything happen at the mirror? In reality, though, mirrors tend to accumulate a layer of dirt, so unless you make your mirror very clean, you can probably see the laser spot partially reflecting diffusely off the dirt.

I'm also a little confused why only specularly reflecting surfaces reflect images of other objects while diffusely reflecting surfaces only reflect their own image..

It's confusing when you say "reflect their own image". What normal objects do is reflect the incident light coming onto them. The only thing that changes between specular and diffuse reflection is what angle the incident light gets reflected toward.

Because a diffuse reflector reflects incident light in all directions, it doesn't matter very much where the incident light comes from (for example, you can read a newspaper with a light over your left shoulder, your right shoulder, whatever, and the words are visible regardless). Because the origin of the light doesn't matter much, a diffuse reflector is in many ways similar to something which emits its own light isotropically like a lightbulb. Surely a lightbulb does not reflect anything--it just emits light in all directions.

I think you're also confused on the concept of light beams vs. images. An image is something that's usually formed with lenses/curved mirrors (or maybe a pinhole camera). For example, if you wanted to view the "image" coming from a video projector, you would want to shine it onto a diffuse reflector like a white screen. If you were to have a mirror in the place of a screen in a movie theatre, then what the moviegoers would see would be equivalent to if they were looking directly into the movie projector. So in order to view an image, you want to project it onto a diffusely reflecting surface (unless you can somehow shine it directly into your eye like a telescope.) Note, though, that the vocabulary I'm using in this paragraph is the standard terminology, but the picture in my last post uses an inconsistent vocabulary--I would call the dogs the "real object" and the "virtual object" since the word "image" refers to things like what a video projector projects.

 

[ViolentCorpse]

I understand. I think a better question would've been: What's there in a mirror that makes it form a virtual object? Why do we see the newspaper itself when it is illuminated rather than our reflection on it?