How do you calculate the location of the third virtual image?

[aleksbooker]

Homework Statement

Two 3.0m wide mirrors meet at a corner. Taking the corner as the origin of the x/y axis, A red ball is placed at point A (-1m, -2m).

1) How many images are seen by an observer at point O? [Point O is not given coordinates, but looks to be at approximately (-3m, -3m)].

2) What are the (x,y) coordinates of each image?

Homework Equations

The Attempt at a Solution

I figured there were at least two virtual images, one behind each mirror at a point perpendicular to the red ball. So there's an image directly north of the ball (-1m, 2m) and directly east of the ball (1m, -2m).

Apparently, the third image is located at (1m, 2m) and I have no idea why or how I would have found that. I know that light from the ball strikes both mirrors before reaching the observer, and that the angles of incidence are all the same, but I don't know how to calculate *what* the angle of incidence is! :(

 

[haruspex]

Each mirror reflects everything in front of it, i.e. everything that you would see if you were placed in the mirror looking out. In that position, how many images would you see?

 

[aleksbooker]

Should I then mentally extend the top mirror beyond the corner so that it "sees" the reflection from the bottom right mirror?

 

[haruspex]

Should I then mentally extend the top mirror beyond the corner so that it "sees" the reflection from the bottom right mirror?

Yes, but that's usual. An object placed in front of a mirror, but not directly in front (i.e. off to the side a bit) still produces an image in the mirror. It's just that you have to stand off to the other side to see it.

 

[aleksbooker]

Cool. Thanks for confirming/clarifying. :)