Single lens telescopes (1 Viewer)

[Binastro]

Although this is not usually discussed in optics text books there are apparently chapters on this in some books although I haven't found any references.

For me using my better eye, which is 2.5 dioptres far sighted, if I use a plus 1 dioptre or 1000mm focal length 40mm aperture single uncoated lens I get a magnification of about 3 times if the lens is held 650mm in front of my eye.

With a cemented doublet of about 700mm focal length I get a 2.2x magnification with the lens 500mm in front of my eye

With a 450mm focal length lens I get a 2x magnification with the lens about 300mm in front of my eye.

Does anyone have a formula predicting the magnification relating focal length, distance in front of the eye, and possibly the eye prescription and maybe the accommodation of the eye?
I have very little accommodation.

I am told that the one lens telescope works because of the small size of the observer's pupil and the angles produced by rays bent by the curves of the lens.

Regards
B.

 

[Binastro]

This morning in good light I viewed two crows sitting on chimney pots at 124m distance.

Using the 1.4 dioptre, 700m focal length Nikon close up multicoated cemented doublet at about 500mm in front of my eye, I saw quite a lot of detail. The beaks and the heads moving separately from the bodies.

In effect my vision improved to 20/8 or 20/7 by magnification of about 2.4x.

The lens is a mild zoom lens ranging from 1.8x to 2.4x at a distance (3x at 3m).

Looking at street objects from 10m to 20m the view is beautiful with the sun behind me.
Much detail that is not seen with unaided eyes.

I still have not worked out a formula giving magnification.

The variables are:

The focal length of the lens or dioptre.

The distance in front of my eye.

The prescription of my eye.

The accommodation of my eye.

The size of my pupil.

A young person with a lot of accommodation might do well.

Although the Nikon close up lens is multicoated and has a transmission of about 98.5%, I get good results from a 1 dioptre single uncoated lens with a magtnification of about 3x.

I think that the image is related to a simple magnifier of say 3x.
In this case the magnification ranges from 1x or unmagnified when touching the object to 3x at 25cm or 4x when the magnifier is placed next to the eye.

A simple magnifier is actually a zoom lens.

B.

 

[opisska]

Being far-sighted really helps, because you can focus convergent rays - a normal or near-sighted person can only focus divergent rays. This allows you to use a single lens as a Galilean telescope, while the rest of us can only use it as a Keplerian one, meaning we must position the eye furhter from the lens than it's focal length is - and see the image upside down.

You having 2.5D is the same as me holding a 2.5D concave lens in front of my eye - 2.5D is 40 cm, so with you eye relaxed, you should hold the 1D convex lens at 60 cm (so that it's focus coincides with the virtual focus of the hypothetic 2.5D lens your eye is giving you) and should see image 2.5x magnified - the magnification being the ratio of the focal lengths of the objective and the (integrated to your eye) eyepiece.

I would have to sit down and draw how it works when the foci do not coincide (eye is accommodated to some distance) - naively I am surprised with the low distances to the other lenses, but maybe I am thinking something wrong, negative optics is confusing.

The Keplerian version is much more straightforward - I put my eye as close to the focus from outside as I can accommodate and the closer I go, the bigger the magnification, but the worse the strain

 

[Binastro]

Thank you very much Jan for your help as I have been struggling with this.

An optical lecturer talks of the angles accounting for the magnification, and that this system works because of the small size of our pupils.

At age about thirty when I didn't need glasses and had quite good accommodation, a group of us used a 2,000mm f./16 observatory refractor and got magnifications of about 5 or so for distance objects.
We did this by using our accommodation.

This system of single lens distant magnification must have military significance if no telescope is available.

For me the simplicity is significant.

I leave the thin lens, the size of a 62mm photo filter on the kitchen worktop.

If I want to see detail outside I lift the lens and have instant magnification.
There is none of the hassle of lifting a binocular, placing it correctly at the eyes and using the focus.

The magnification of the single lens is low, but gives me instant Supervision with no losses.

The Yerkes and other large refractors with 20,000mm focal lengths should be interesting without eyepieces.

Regards,
B.

 

[Binastro]

I keep the Nikon 700mm fl close up lens on my work top in a small plastic clear bag.

It is particularly useful looking at objects 7m to 18m away.
At 7m the magnification is 2.8x and at 18m 2.4x.
The detail seen is very impressive.

Sometimes I use it up to 30m.

Beyond this I use the 8x32BA binocular, which is far far superior at long distances from 70m to 120m.

I am using some accommodation and also some depth of focus with small eye pupil size.
In good light the view is better.

Yesterday, for some reason my eyes were very rested and I could increase the magnification, presumably by having more accommodation.

I wonder how good the view would be with someone having +4D far sight and good accommodation?
What magnification could be achieved?

Regards,
B.