LV: Focal Telescopes

These telescopes can be modified for different object distances and to correct ametropia. Both Gal and Astro.

Vergence Amplification (Freid's Formula)

Vergence entering telescope L = 1 / l

Vergence leaving L' = M2L / 1-t M L where M is the magnification and t the tube length

For practical purposes t is very small compared to l so we can simplify to L' = M2L

eg How much accomm required when a patient uses a 3x telescope for reading at 25cm?

L' = M2L = 3 squared x 4 = 36D - would have to accomm 36D which is too much even for kids

Adapting telescopes for near and intermediate viewing

1. full correction for viewing distance over objective
2. increased correction for viewing distance over eyepiece
3. increasing separation of Fe and Fo

1 Full correction for viewing distance over obj

• 'Reading cap' over objective lens. Telescope + reading cap = telemicroscope
• Used particularly w/Gal system
• Frc has focal length equal to the required WD
• Parallel light enters telescope and parallel light comes out

Total mag of telemicroscope Mtot = Mtel x Mrc (Mrc = Frc/4)

eg What magnification is achieved when using a telemicroscope w/ 3x telescope and a +4D reading cap?
= 3 x 4/4 = 3x magnification

working space frc = 1/4D = 25cm

So I can see why they use em - to get 3x with a plus lens the working dist would be tiny. Like 8.33 cm. But here it's 25cm which is way more tolerable. Increased working space makes binocular viewing more practical too - that's only possible with about 2.5x with plus lenses, but 5x w/telescopes. You do need to angle the tubes properly though. NB the overall working distance is increased by the length of the telescope too.

2. Increased correction for viewing distance over eyepiece

This isn't a practical method unless the patient already has high-powered reading add for another purpose. Magnification is difficult to calculate.

3. Increasing the separation of Fe and Fo

• A practical method but more difficult in spec mounting - becomes more front heavy as the tube length increases. Difficult to angle if binocular
• More common in astros cos they are hand held usually anyway and the image quality is better maintained

Example

2.5 Gal (Fe = -50D, Fo +20D) focussed for 25cm using a 4D reading cap

Mtel = -Fe/Fo = -(-50)/20 = 2.5x
Frc = 1/l = 1/0.25 = +4.00
Mtotal = Mtel x Mrc = 2.5 x 4/4 = 2.5x

t = f'e + f'o = -0.05 + 0.02 = 30mm

Example 2

2.5x gal focussed for 25cm by changing length so reading cap is 'incorporated' in Objective lens

so t = fo' + fe' = 1/Fo + 1/Fe = 1 /20-(1/0.25) + 1/50 = 0.0625 + (-0.02) = 42.5mm

Mtel = -Fe/Fo = -(-50)/16 = - (-50)/20-(1/0.25) = 3.13x

Frc = 1/working space = 1/0.25 = +4.00

In conclusion higher mag can be achieved by focussing the telescope rather than adding a separate reading cap BUT this causes a large increase in length. Not always practical cos the lens housing cannot expand by this amount and it may make the mounting unstable

Example w/Astro

What are the mag and length of a 3x astro telescope Fe = +60, Fo = +20 focussed for 12.5cm w/reading cap

Mtel = -Fe/Fo = -60/20 = -3x
Frc = 1/working space = 1/0.125 = +8.00D
Mtotal = Mrc x Mtel = 3x2 = 6x
t = fo' + fe' = 1/20 + 1/60 = 66.7mm

Example 2

3x astro focussed for 12.5cm by changing length

Mtel = -Fe/Fo = 60/20-8m = -5x

Frc = 1/0.125 = +8.00D

Mtot = Mtel x Mrc = -5 x (8/4) = 10x
t = fo'+fe' = 1/Fo' + 1/Fe' = (1/20-8) + (1/-60m) = 83.3mm + 16.7 = 100mm

Conclusion

For both astro and gal focusing will always provide higher magnification than a reading cap because Mtel increases when Fo decreases, but there are severe practical limitations re increase in telescope length. NB closest focus distance = longest position of telescope (t=max)