# Two mirrors

1. Apr 14, 2007

### gazepdapi1

I need some help guys with this one. Say you have two mirrors like in the image below, with some angle phi between them. The question is how many images would be formed if the angle between them changed to 20, 30, 40, 60, 90, or 0 degress. Is there some sort of equation that will give you this?
thanks a lot.
nertil1http://img139.imageshack.us/my.php?image=untitledwy0.jpg"

Last edited by a moderator: Apr 22, 2017
2. Apr 14, 2007

### Staff: Mentor

There is no observer to observe any images in that pic.

3. Apr 14, 2007

### gazepdapi1

Yeah sorry, imagine there is an observer looking at the vertical mirror, although I don't think it would matter because the same amount of images would be formed on each mirror, I think.
thanks

4. Apr 15, 2007

### lpfr

The number of images is (360/angle -1). When the result is an integer, all is OK. When it is no the case (say, 3.65) it means that some images are "cut" by the junction between the mirrors and that what you see depends on the position of the observer.

5. Apr 15, 2007

### gazepdapi1

thanks a lot man but can you show me how you derived that formula please?

Last edited: Apr 15, 2007
6. Apr 16, 2007

### lpfr

Draw the image of each mirror reflected on the other one. Draw the image of the mirror and their images reflected by the mirrors and their images. Repeat this until you fill the plan.
You will see the pan divided in angles equal to the angle between mirrors. If the angle does not divide 360° exactly, there will be "a problem" in the opposite side to the middle of the mirrors.
Now draw an object between the mirrors rather near one of them. A small arrow perpendicular to the near mirror will do.
Draw the images of the arrow as reflected in each mirror. Draw the reflected images of all the arrows (real and images) in all the mirrors. Count the images.
Do this for angle = 180° (equal to a single mirror), 90°, 60°, 45°, etc. count each time. Extrapolate.
But, better that all this, take two mirrors and watch what you see as the angle changes.

7. Apr 16, 2007

### pallidin

As a novice, I yet ponder if the photon intensity of the initial and subsequent reflections largely determine the number of theorectically detectable reflections within a given mirrored angle set.

8. Apr 17, 2007

### lpfr

When there are a lot of photons there is no need to talk about them. They behave as a whole.

Current mirrors do not reflect 100% of the received light. They only reflect about 92-94%.
Then after several reflections, images dim. Moreover, in back-silvered mirrors, light must traverse twice the front glass. After several reflections, you began to see the images get greener and greener. You can see this, locking at the reflections of two mirrors forming a small angle.

Physicist know how to make mirrors that reflect almost 100% of the light. They are built as a super sandwich of dielectrics of controlled thickness. They are called "dielectric mirrors".