Optics of Convex Lenses, Magnifiers and Telescopes.

Lenses:

A lens is defined as a portion of a refracting media border by two curved surfaces, which have a common axis. When each surface forms part of a sphere, the lens is called spherical lens.

 

Spherical lenses are either convex lenses (plus lenses or converging lenses) or concave lenses (minus lenses or diverging lenses).

Convex lenses:

A convex lens causes convergence of incident of light

Forms of Convex lenses.

Bi-Convex

Plano-Convex

Meniscus

Dioptric power of lenses. Vergence: 

The reciprocal of the second focal length expressed in meter gives the vergence power of the lens in diopters (D) thus

F = 1/f‑

Where F is vergence power of the lens in diopter and f is the second focal length in meters.

A converging lens of second focal length 5cm has a power of

  F=1/f =1/0.10 =10D

SPECTACLES:

Spectacles are the low vision aids that are most often prescribed.

They are simply reading glasses with higher powers than normal, providing a shorter focal distance, resulting in relative distance magnification. 

When selecting spectacles for a patient, it is important to keep in mind the patient refractive error. If a patient is 4 D myopic, he already has a “ built-in” 4D reading add. If the dioptric demand for appropriate magnification is 6D, only the remaining 2D needs to be provided in spectacles and the reading distance will be

100/6 = 16.7cm.

Similarly for a patient with 3D hyperopia who requires +10D reading aid will need +13D spectacles for reading. 

Beyond powers of 4D to 6D, single vision glasses become necessary because reading distance is so closer and patient have to converge excessively therefore a base-in prism is included. 

Above power of 12D, spectacles are referred as microscopes. It is better to recommend monocular low vision microscope for just the preferred eye.

When using spectacles reading materials must be hold at the focusing distance of lens, which is closer to the eyes than normal.  

Touch the reading material to your nose and slowly move it away until it is in clear focus. Maintain that while reading. 

It may help to move reading material from side to side keeping the eyes still, instead of scanning material in the normal ways by moving your eyes from the beginning to the end of a line print.

HAND MAGNIFIERS:

Hand magnifiers consist of a convex lens surrounded by a plastic or metal carrier attached to a handle. 

For maximum magnification with hand magnifier, place the object at the focal point.

The distance from a hand magnifier to the printed page must be kept constant .To find this distance start the lens on the page and slowly pull it away from the print until optimal focus is reached.

Hand magnifier should be used with distance glasses. 

If the magnifier is brought closer to your eyes, bring the reading material closer as well.

STAND MAGNIFIERS : 

Stand magnifiers are similar to hand magnifiers.

 

They consist of a convex lens surrounded by a plastic or metal carrier. Instead of a handle, however, they are attached to legs or some other support. These enable the magnifier to stand freely on a page of print.

 

The legs of the stand magnifier are shorter than the focal length of the lens so divergent light comes out and the patient needs accommodation or reading glasses.

 

Always keep the distance from your eyes to the magnifier constant. Do not pull the magnifier up to your eyes, the focus will be lost.

Magnifiers Advantages Disadvantages

Spectacle Magnifiers 1.Patients are used to them and adaptation is easy.2.Leave hands free & are comfortable.3.Comparativeluy light weight 

1.Short working distance.2.With higher power depth of field becomes narrow   

Hand magnifiers 1.No need of reading glasses or accommodation2. Light weight & easy to carry around3.Illuminated & non illuminated4.Less expensive 5.Resolution is independent of the position

 1.Require steady hands & not comfortable for patients with tremors2.Bussy hands 

Stand magnifiers 1.Less expensive2.Wider range of magnification3.Fairly light weight  

1.Bulky as compare to glasses 2.Needs reading glasses or accommodation3.Low visual field4.Uncomfortable viewing posture 

Telemicroscopes 1.Large working distance2.Leave hands free3. Binocular up to 4x

1.Bulky 2.Smaller field of view3.Expensive

Telescope:An optical system that provides angular magnification without bringing about a change in vergence. It contains two optical elements. The objective lens and the eyepieceObjective lens--- positive towards the objectEye piece--- positive or Negative towards the eye and is of stronger power than objective Secondary focal plane of the objective lens coincide with the primary focal plane of the eye piece lens Parallel rays incident on the objective lens form an image at secondary focal plane and this image becomes the object for the eye piece.

Types: 

1.Galilean

2.Keplerian

o

/

Galilean Telescope: 

Objective_________ positive Eye piece_________ negative The objective lens form an optically real image of height h with the chief ray passing through the center of objective lens and forming an angle with the optical axis which becomes a virtual object for the eye piece lens. Parallel rays enter the objective lens at angle to the optic axis and a parallel bundle of emergence from the eyepiece lens at angle from the optic axis. Characterisics of G.T1.Since for a GT F e is always negative lens and F0 is always a positive lens , in the formula  M= -Fe/F0The magnification has a positive sign, which indicate the image formed is erect.

Keplerian Telescope:

It has a positive powered objective lens and a stronger positive powered eye piece lens separated such that the secondary focal point of the objective lens coincide with the primary focal point of the eye piece lens. Parallel light enters a plus objectiveThe light is focused towards the focal point of the objective Because the focal point of the objective and the focal point of the eyepiece coincide, light leaves parallel

Magnification by Telescopes: 

For either type of telescopes the angular magnification it provides is the negative of the power of the eyepiece lens (Fe) divided by the of the objective (Fo)M= -F2/F1Example: Magnification of a Galilean telescope having +10D objective lens and –20D-eyepiece lens M= -Fe/FoM= -20/-10M=2XMagnification of Keplerian Telescope having+10D objective lens and +20D eyepiece lens M=-Fe/FoM=-(+20)/10M=-20/10M= -2XThe minus sign shows that the image is inverted

Comparison of Galilean and Keplerian Telescopes:

Characteristics Galilean Keplerian

Power 4X 4X

Exit pupil Virtual I (not floating because insideTS)

Real I (floating)

Image Erect Inverted

Field of view Smaller field of view Larger field of view

Magnification Low magnification up to 4x High magnification up to 10x

Image Quality Brighter Much brighter

Design Simple Complicated

Weight Light Heavy

Path length Short Long

Bioptic Telescope:Spectacle mounted; it is drilled into the lens Called bioptic because it has two optical systems: a carrier lens and a telescope  Not mounted centrally because you would have a hard time getting around, unless special occupational needs 

Mounted superiorly – tilt head down to see through it.

Telemicroscope:

Telemicroscope is a telescope with a microscope or (plus lens) attached which allows you to see at a certain distance.

Telemicroscope allow you to see things closer; so it is like a telescope with a reading cap

Working distance is based on reading cap

 It provides high magnification at a large working distance.