Re: Focal length, dioptre, magnification


Subject: Further details on Magnification

Magnification


The magnification of a magnifying glass depends on where it is placed
between the user's eye and the object being viewed, and the total
distance between the eye and the object. Magnifying glasses are
typically described in terms of their magnifying power, which is
equivalent to angular magnification (this should not be confused with
optical power, which is a different quantity). The magnifying power is
the ratio of the sizes of the images formed on the user's retina with
and without the lens.[3] For the "without" case, it is typically
assumed that the user would bring the object as close to the eye as
possible without it becoming blurry. This point, known as the near
point, varies with age. In a young child it can be as close as 5 cm,
while in an elderly person it may be as far as one or two metres.
Magnifiers are typically characterized using a "standard" value of
0.25 m.

The highest magnifying power is obtained by putting the lens very
close to the eye and moving the eye and the lens together to obtain
the best focus. The object will then typically also be close to the
lens. The magnifying power obtained in this condition is MP0=1/4 Φ+1,
where Φ is the optical power in dioptres, and the factor of 1/4 comes
from the assumed distance to the near point. This value of the
magnifying power is the one normally used to characterize magnifiers.
It is typically denoted "m×", where m=MP0. This is sometimes called
the total power of the magnifier (again, not to be confused with
optical power).

Magnifiers are not always used as described above, however. It is much
more comfortable to put the magnifier close to the object (one focal
length away). The eye can then be a larger distance away, and a good
image can be obtained very easily; the focus is not very sensitive to
the eye's exact position. The magnifying power in this case is roughly
MP=1/4 Φ.

A typical magnifying glass might have a focal length of 25 cm,
corresponding to an optical power of 4 dioptres. Such a magnifier
would be sold as a "2×" magnifier. In actual use, an observer with
"typical" eyes would obtain a magnifying power between 1 and 2,
depending on where lens is held. An older person might obtain an
actual magnifying power of 8 or more with this lens, however, due to
the eye's longer near point distance.

Enjoy,




On Oct 13, 10:18 pm, otisbr...@xxxxxxxxxxxxxx wrote:
Subject: General Equations for Optical Calculations.

Since this subject develops on sci.med.vision -- here
are the equations.

Re: Some Optical Equations for Analysis

The power of a lens in diopters.

1 / f = P

Where

f = Focal Length in Meters

P = Power in diopters

Motivation for using "Diopter" Values:

The power of lenses can be added (within reason).

P = P1 + P2

See the thin-lens formula for reference.

===========

Magnifying Power (telescope)

Mag = - F / f

Where F is the focal length of the objective

f = Focal length of eye-piece.

================

Focal Length, Image and Object Calculations:

1 / p + 1 / q = 1 / f

Where:

f = Focal Length of Lens

p = Object Distance to Lens

q = Image Distance to lens

==========

Magnification Equation

I / O = - ( q / p )

Where:

I = Image Size

O = Object Size

p = Object Distance to Lens

q = Image Distance to lens

=============

Combining Thin Lenses

1 / f = 1 / f1 + 1 / f2

Where:

f = Total focal length

f1 = First lens focal length

f2 = Second lens focal length

Enjoy,

===============

On Oct 13, 5:07 pm, Jan <nospam@nospam> wrote:



Andy schreef:

Dave, thank you for the information.

I think I didn't give you enough background. My query is for a
handheld magnifying glass. In such a case a think magnification is
stated as a fixed value such as "x8" (although the lens position will
determine the actual magnification that is achieved).

Now keep it simple for me please!

Yes sir!!!

The magnification standaard for a handheld glass is the diopters devided
by 4, period.

I have several of these and wanted to label them bytheir power. I
determined the focal length by using the sun and seeing how far away
from the lens the sharped image of the was. My example said 12 cm.

So you showed me that 12 cm focal length is 1/0.12 = 8.33 dioptres.

So in this case you have to call this handheld a 8.33/4= 2 times
magnifying glass, period.

This is a world wide standard industrie qualification.

Jan (normally Dutch spoken- Hide quoted text -

- Show quoted text -

.

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