Do Kaleidoscopes Need a Lens? Eyepiece, Focus and Tube Length
By Rocco (Roi) Ramon - licensed architect, founder of Studio Yabaye
The mirrors of a kaleidoscope do not focus anything. They are flat, and a flat mirror only redirects light. Sharpness depends on two other things: the distance between the eye and the objects at the far end of the tube, and the eye of the person looking. A kaleidoscope lens, where one is fitted, matches the two.
I work here from David Brewster's "A Treatise on the Kaleidoscope" (Edinburgh, 1819), referred to below as the Treatise. Brewster states when an eyepiece lens is required, what focal length it should have, and when it should be removed.
Why a short kaleidoscope looks blurred
The human eye focuses by changing the curvature of its own lens. This has a limit. The closest distance at which an eye can hold an object in sharp focus is called the near point. Optics textbooks use 25 cm as the conventional near point of a normal adult eye. Anything closer is seen blurred.
In a kaleidoscope the objects sit at the far end of the mirrors, so the viewing distance is roughly the length of the mirrors. In Chapter VI of the Treatise, Brewster builds the simple kaleidoscope with two reflectors "about five, six, seven, or eight inches long". That is 12.7 to 20.3 cm. Each of those lengths is shorter than a 25 cm near point. In a short instrument without a lens, the object plane is closer than the eye can focus.
What an eyepiece lens does
Brewster's rule is in Chapter VI. If the reflectors are shorter than the shortest distance at which the eye sees distinctly, the eye end needs "a convex lens, whose focal length is equal to, or an inch or two greater than, the length of the reflectors".
Brewster gives the rule without the ray optics. The standard thin-lens explanation is this:
Focal length equal to the tube length. The objects lie in the focal plane. Light from each object point leaves the lens as a parallel bundle, as if from a far object, and a normal eye sees it with its focusing muscle relaxed.
Focal length slightly longer than the tube. The objects lie just inside the focal length. The lens forms an enlarged virtual image further away than the real objects. The eye focuses a little, within its range.
Focal length shorter than the tube. The objects lie beyond the focal plane. The light reaching the eye converges, and a normal eye cannot focus converging light.
This is consistent with Brewster's rule, which gives no value shorter than the reflector length. In Chapter XIV, on microscopic kaleidoscopes, he gives a reason for the longer value: the focal length should be greater than the distance of the objects from the eye, "so that the eye, by a little exertion, may be able to obtain distinct vision". The reflected images lie further from the eye than the sector seen directly, so a lens adjusted exactly to the nearest part of the picture would not suit the rest.
Long tubes that need no lens
If the mirrors are longer than the observer's near point, the objects are already at a distance the eye can focus on, and no lens is needed. With the conventional figure, that means a mirror length above roughly 25 cm. The boundary is not fixed, because the near point differs from eye to eye and moves away with age.
Age, eyesight and glasses
Presbyopia. The eye's lens loses flexibility with age and the near point moves away from the eye. An instrument without an eyepiece lens can become blurred for a person who once saw it sharply. Reading glasses correct this, because they do the same job as the eyepiece lens.
Short sight. Brewster ends his lens rule with an exception. The lens "must be removed when the instrument is to be used by persons who are shortsighted". An uncorrected short-sighted eye focuses on near objects and not on distant ones. The bare object plane may suit it, while a lens that sends out parallel light gives it a blur.
Glasses on or off. Where the eyepiece lens is fixed, try both ways. With distance glasses or contact lenses on, a short-sighted eye behaves like a normal eye and suits an instrument with an eyepiece lens. With glasses off, it may suit an instrument without a lens, or see a lensed one poorly.
Eye position. Glasses hold the eye away from the eyepiece. Brewster writes in Chapter VI that "it is of the greatest importance that the eye get as near as possible to the reflectors". If the field looks narrow with glasses on, compare it with glasses off.
The lens at the other end: telescopic kaleidoscopes and teleidoscopes
A lens at the object end has a different job.
In Chapter VIII of the Treatise, Brewster describes what happens when the object plate is withdrawn from the reflectors of a simple kaleidoscope. At a distance of one-tenth of an inch the picture begins to distort at the centre. A distant view cannot be placed at the mirror ends. Its image can.
In Brewster's compound, or telescopic, kaleidoscope the inner tube holds the reflectors and an outer tube carries a convex lens ahead of them. The lens forms an image of the outside scene, and the inner tube is drawn out until that image falls at the end of the reflectors. The mirrors then multiply the image as they would an object plate. Brewster notes that when the lens is too small, the brass rim holding it bounds the field and the pattern becomes irregular.
That image lies at the far end of the mirrors, so a short telescopic kaleidoscope needs the eye-end lens for the same reason as a short simple one.
What a glass sphere does at the front of a teleidoscope
A glass sphere is a convex lens with a short focal length. By the ball lens formula, for glass with a refractive index of 1.5 the focal point lies three quarters of the sphere's diameter from its centre, which is one quarter of a diameter behind its rear surface.
Near-fixed focus. With so short a focal length, the image of a subject a few metres away and the image of the horizon form at almost the same place. The sphere can sit at a fixed distance from the mirrors.
Wide field. A sphere accepts light from a wide angle, so a large part of the scene enters the pattern at once.
Inverted, reduced image. The image is upside down and reversed left to right.
In the Studio Yabaye teleidoscope the glass sphere sits at the front and a lens sits at the eye end. The difference between the two instrument families is set out in kaleidoscope vs teleidoscope.
Checklist: how to judge focus
Light. Use direct, preferably strong light. In dim light the pupil opens and depth of focus drops.
One hard edge. Pick an object with a hard outline and judge whether the edge is a line or a band. Colour hides blur.
Glasses on and off. Note which is sharper and which gives the wider field.
Blur or misalignment. Blur softens every edge. A mirror fault shows as a step at the joints between sectors while the edges stay sharp. See what to look for when buying a kaleidoscope.
Teleidoscope. Point it at a subject about 1 m away and at one beyond 10 m, and compare sharpness.
FAQ
Do kaleidoscopes need a lens?
Only when the mirrors are shorter than the distance at which the viewer's eye can focus. Brewster's 1819 Treatise, Chapter VI, calls for a convex lens at the eye end in that case, with a focal length equal to the length of the reflectors or an inch or two greater.
Why is my kaleidoscope blurry?
The usual cause is distance. The objects sit at the far end of the mirrors, and in a short instrument that is closer than the eye's near point, conventionally 25 cm for a normal adult eye. Other causes are low light, a missing or mismatched eyepiece lens, or the wrong glasses for that instrument.
What focal length should a kaleidoscope eyepiece lens have?
Brewster specifies a convex lens with a focal length equal to the length of the reflectors, or an inch or two greater. With the objects in or just inside the focal plane, the light leaves the lens nearly parallel, and a normal eye sees the pattern sharply with little or no focusing effort.
Should I wear glasses when looking through a kaleidoscope?
Try both. A short-sighted person wearing distance glasses sees like a normal eye and suits an instrument with an eyepiece lens. Without glasses, the same person may see a lensless instrument sharply. Brewster wrote in 1819 that the lens must be removed for short-sighted users. Reading glasses help presbyopic viewers.
What does the lens at the front of a teleidoscope do?
It forms an image of the outside scene at the ends of the mirrors. Brewster's Chapter VIII states that when an object plate is withdrawn from the reflectors, the picture begins to distort at the centre at one-tenth of an inch. The lens places the image of a distant view at the mirror ends.
What does the glass sphere on a teleidoscope do?
A glass sphere acts as a convex lens of short focal length, about three quarters of its diameter for glass of index 1.5. It forms an inverted, reduced image of a wide part of the scene close behind itself. Near and far subjects are imaged at almost the same place.
About Studio Yabaye
Studio Yabaye builds kaleidoscopes and teleidoscopes with front-surface mirror systems in a brass tube, cut, fitted and hand-finished in the studio. Every instrument has a lens at the eyepiece, and the lens differs from model to model. Each object wheel is poured and composed by hand, so no two pieces are alike. The studio is based in Israel and ships worldwide. The current range is at all products, and questions can be sent through the contact page.
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