Number of images formed by 3 mutually perpendicular plane mirrors

[Amith2006]

Sir/Madam,
1)The 2 adjacent walls and the ceiling of a rectangular room are mirror surfaced.What is the number of images of himself does an observer sees?
If it was the case of 2 mirrors I know it is 3. But here there are 3 mirrors which are mutually perpendicular. But if we take 2 mirrors at a time then the total number of images is 9. What do you say Sir/Madam?
2)A convergent beam of light is incident on a convex mirror of radius of curvature 60 cm as shown in figure. What is the nature and position of the image formed by it?
I solved it in the following way:
Let u, v and f be the object distance, image distance and focal length of the convex mirror respectively.
Here u = + 10 cm, f = +30 cm
1/u + 1/v = 1/f
v = (uf)/(u-f)
= (10 x 30)/(10 – 30)
= -15 cm
Hence the image formed is virtual and 15 cm in front of the mirror. Is it right?
3)A convex mirror of focal length f produces an image (1/n)th of the size of the object. What is the distance of the object from the mirror?
I solved it in the following way:
Magnification = 1/n = -(v/u)
i.e. v = -(u/n)
1/u + 1/v = 1/f
1/u – (n/u) = 1/f
By solving I get,
u = (1-n)f
Are my sign conventions right? Sometimes the diagram may not be clear. So I will try to describe the diagram. A convergent beam of light serves as a virtual object which appears to converge at a distance of 10 cm behind the mirror.

 

[berkeman]

On question -1-, I would guess that you get one additional image at the corner of the 3 planes. Since it is a cube corner, you should get a reflection from it back to you in the middle of the room. I don't know if it's a real image, though. Have to try it or else do some ray tracing sketching to figure that out. So you'd get the 3 reflections from the planes, the 2 reflections from the 2 edges, and the 1 from the corner. Is a total of 6 the correct answer for question -1-?

 

[kyle8921]

1) Based on the information provided, it seems that the observer would see a total of 9 images of themselves. This can be calculated by taking into account the reflections from each of the three mirrors. Each mirror will produce 3 images, resulting in a total of 9 images.

2) Your calculations for the nature and position of the image formed by the convex mirror seem correct. It is a virtual image located 15 cm in front of the mirror. However, it is always important to double check your calculations and consider any potential sources of error.

3) Your sign conventions seem correct based on the information provided. However, it is always best to double check your calculations and make sure they are consistent with the diagram provided. Additionally, it is important to consider the direction of the light rays and their reflections when solving problems involving mirrors.