Kaleidoscope Mirror Systems

The kaleidoscope creates reflections of reflections of a direct view of objects.  This results in what is often referred to as a kaleidoscopic image.  It is the mirror system within the kaleidoscope that produces this effect.

Most Kaleidoscopes use either a 2-mirror or a 3-mirror system. 

The 2-mirror system is made up of two mirrors joined together to form an angle. A non-reflecting third side is added to form a triangle.  When viewing the scope, people look though this triangle at the object chamber.  The configuration they see is a single circular image called a mandala. 

The 3-mirror system is made up of three mirrors joined together to form a triangle. When this configuration is viewed, a continuously reflecting pattern is seen.

In this article all the basic mirror systems will be described.  They are:

  • Spiral (1-Mirror) Systems
  • 2-Mirror Systems
  • 3-Mirror Systems
  • 4-Mirror Systems
  • Polyangular Mirror Systems
  • Tapered Mirror Systems
  • Multiple Mirror Systems

Some artists have discovered ways to make amazing 3-D images by using odd mirror configurations.  Many of them are explained on these sites by Wayne Schmidt:

Below is a picture of a modern scope and the 3-D image it creates.

   

Here are some photos and videos of 3-D kaleidoscopes and there images from Janet & Frank Higgins (personal favorites are "St Basil 2010", "Super Carousel" and "Cube"). 


Spiral (1-Mirror) Systems

The scope's cylinder shaped body or a cylinder tube inside the scope is covered with a reflective material which produces a spiraling effect of colors up toward the viewer.   This type of mirror system can also be called a 1-mirror system since only a single reflective material (mirror) is used.  

Below are two images from the same spiral scope.

 

Objects in the object cell of these scopes are used more to create colors then shapes since all the viewer sees is a swirl of color coming towards them.  

While not often used in kaleidoscopes, you see it used more often in jewelry scopes (rings, necklaces and earrings).  The extremely small size of jewelry scopes makes it hard to create small enough mirror systems.  For that reason many jewelry scopes utilize the spiral mirror system.

Below is a photo showing two jewelry scopes that utilize the spiral mirror system.  A necklace and an earring.


2- Mirror Systems

The 2-miiror system is configured in a triangular shape. Two sides are mirrors and the third side blackened.

It produces one central image in the middle of the viewing field.  That central image is circular in shape and is a reflection of the objects being viewed. 

The angle of the 2-mirrors determined the number of reflections that comprise the image circle.   The tighter the angle the higher the number of reflections (called folds).  Every two folds forms a point.  An image circul with 5 points will have 10 folds or reflections.

The following mathmatical formulars will calculate he number of folds and points:

  • Folds = 360 didided by the angle of the 2 mirrors
  • Points = 180 divided by the angle of the 2 mirrors 

Here are the calculations for the common angles used with 2-mirror systems:

Angle of Mirrors Folds Points
90 Degrees 4 2
60 Degrees 6 3
45 Degrees 8 4
36 Degrees 10 5
30 Degrees 12 6
25.7 Degrees 14 7
22.5 Degrees 16 8
20 Degrees 18 9
18 Degrees 20 10
16.3 Degrees 22 11
15 Degrees 24 12
12 Degrees 30 15
10 Degrees 36 18
9 Degrees 40 20
6 Degrees 60 30
5 Degrees 72 36

The image created by a 2-mirror system will be symmetrical if the mirror angle is an even divider of 360 degrees.  If the angle doesn't divide evenly into 360, for example 50 degrees (360 / 50 = 7.2), it will produce a non-symmetric pattern.

Below are three pictures of the same image inside the same scope.   The mirror angles are at 36 degrees (5 points), 33 degrees (5.5 points) and 30 degrees (6 points).  Notice the half point on the bottom of the center picture.

   


3-Mirror Systems

The 3-mirror system is configured in a triangular shape.  Alll three sides are mirrors.  With this system, images are reflected throughout the entire field of view producing honeycomb-like patterns.

There are four comon configurations of 3-mirror systems in order of popularity:

  • The 60-60-60 Equilateral Triangle
  • The 30-60-90 Right triangle
  • The Isosceles Triangle (has two equal sides)
  • The 45-45-90 Isosceles Right Triangle

Below are the characteristics of each: 

Equilateral Triangle

Equilateral Triangle

Three equal sides
Three equal angles, always 60°

Scalene Triangle

Right Triangle

No equal sides
No equal angles, one 90°

Isosceles Triangle

Isosceles Triangle

Two equal sides
Two equal angles

Scalene Triangle

Isosceles Right Triangle

Two equal sides
Two equal angles,  one 90°

 
Each of these images would be repeated throughout the entire field of view. 

Below are examples of the three most popular types of 3-mirror systems (the 60-60-60 equilateral triangle, the isosceles triangle and the 30-60-90 triangle) .  Notice that the last scope is a view of the mirrors after the wheels were removed (the second photo shows the 30-60-90 scope's mirror system up close).

Below are the images from the 3 scopes (order - equilateral triangle, isosceles triangle and the 30-60-90 triangle).

  


4-Mirror Systems

The 4-mirror system is created when 4 mirrors are connected together.  They come in three common configurations:

  • Square
  • Rectangular
  • Diamond

 

The square and rectangular configurations create basically the same pattern except the square 4-mirror configuration (shown above) produces repeated square patterns while 4-mirror rectangular configuration produces repeated rectangular patterns. These are created by angling the 4 mirrors at 90 degrees to each other.  The images created are striped patterns since the reflections move directionally up, down, left and right .  This is often known as a "Parade" or "Chorus Line" effect.

Below are 3 photos showing the "Chorus Line" effect.

     

The diamond configuration creates an image with multiple focal points.  It is created by angling the 4 mirrors at angles other than 90 degrees therefore forming a diamond.  This mirror system is sometimes known as twin 2-mirror systems. The image it creates is a double mandala.

 Below is a view of the diamond  configured 4-mirrored scope (notice the double mandala).

 


Polyangular Mirror Systems

Polyangular scopes come is 2-mirror and 4-mirror configurations.  

2-Mirror Polyangular Scopes

The 2-mirror polyangular scope is a 2-mirror design with the additional variation to allow the mirror(s) to be adjusted, changing the angle of the "V" and thus the number of reflections or points.  An additional controller on these scopes allows the viewer to change the angle of the mirror assembly those controlling the number of points of symmetry of the interior image. 

2-Mirror polyangular scopes will have different mirror angle ranges.  Some will produce 2 to 7 point stars while other may produce 5 to over 30 point stars.  The outside of polyangular scopes look no different than normal scopes however they are harder to find. 

Below is 6 photos showing the same objects from a 2-mirror polyangular scope in a 2, 3, 4, 5, 6 & 7 point variations.

          

   

    

4-Mirror Polyangular Scopes

4-Mirror polyangular scopes are extremely rare.  They product a variety of images when there mirrors are physically changed from a very flat diamond shape to a square shape. The images produced start out as repeated square patterns when the mirrors are square shaped to a double mandala pattern as the mirrors are flattened into a diamond.  The flatter the diamond shape of the mirrors, the more points the double mandalas get.

Below is a polyangular 4-mirror scope shown in a square (90 degree angles) and then diamond shape.

Below are the square and then diamond views of the same objects.


Tapered Mirror Systems

Tapering the mirrors means that the mirrors which are usually rectangular in shape are now slightly tapered making then an isosceles trapezoid.  This is done equally to all mirrors so that when they are connected to make the mirror system they are similar to a pyramid.  

Below are two views of the same 3-mirror tapered scope.

   

Usually the lager end is used for viewing and the object chamber is attached to the smaller end.  When this done, an amazing spherical 3-D image is created.  When the scope is viewed through the smaller end, the actual and virtual images are enlarged to more visibly examine the objects in the object chamber. This also allows more light to enter the system, increasing the overall brightness.

Below is the image from a 3-mirror tapered scope.  Notice that is appears to be 3-dimensional.

Tapered mirror systems come in 3 or more sides. 

Pictures of 3-mirror (the scope the above image in from) and 4-mirror tapered scopes.

 


Multiple Mirror Systems

Three common types of multiple mirror systems exist:

  • Binocular Scopes
  • Multiple Mirror Systems in a Single Scope
  • Companion Scopes

Binocular Scopes

This is simply creating two scope bodies and joining them together to view a single object chamber.   They look like binoculars and, like binoculars, the person using the scope uses both their eyes to view the scope.  Each body has its own mirror system and eye piece.  The two mirror systems are usually identical.

The below photo shows the front and back of the same wooden 3-mirror binocular scope.

   

Below is a stained glass 4-mirror binocular scope

   

Multiple Mirror Systems in a Single Scope

Some scopes contain multiple mirror systems next to each other within a single body.  The most popular configuration is a 2 and 3-miror combination.  Other scopes contain three unique mirror systems.  Popular versions are 2, 3 and 4 mirror system combinations and 2, 3 and spiral mirror combinations.

Below photo shows  a scope containing 2 & 3-mirror systems and the images through the eye piece.

 

Each mirror system has its own viewing hole within the eye piece.

Below photo shows the eye piece of a scope containing 3 unique mirror systems

Companion Scopes

Another form of a multiple mirror system is when the object chamber is in the middle and the mirror systems all face toward it in a single scope.  This is often referred to as a "Companion" scope because two or more people can view the scope at the same time.

Photo of a 2 and 3-mirror "Companion" scope