Telescopes

1. TELESCOPES
Presenter:
Nisha Bishowkarma
Bachelors of Optometry, 24th Batch, MMC, IOM

2. OBJECTIVES
By the end of this session we will be able to:
Introduce telescopes.
Describe the comparative advantages/disadvantages of Galilean
and Keplerian telescopes.
Explain the use of tube length to determine angular
magnification.
Explain the use of telescopes in ametropia.
Describe how telescopes can be adjusted for near use.

3. Introduction
• Telescope, device used to form magnified images of distant
objects.
• Generally, a telescope is focused for infinity, but telescopes can be
adapted for near-vision use.
• A low-vision patient’s distance vision can often be improved by
using a telescope.

4. Introduction
• When an emmetrope or corrected ametrope uses a telescope to
view an infinitely distant object, the light rays that enter the
telescope have zero vergence, so do the light rays that exit the
telescope.
• Since such a telescope does not have focal points, it is referred to
as an afocal optical system.

5. Galilean Telescopes
• For an infinitely distant object, a
converging objective lens forms an
image at its secondary focal plane,
which is coincident with the primary
focal plane of the eyepiece, a negative
lens.
• Parallel rays emerge from the
telescope’s eyepiece.

6. Galilean Telescopes
• Lateral magnification isn’t appropriate
since object and image both are at
infinity.
• Instead, the angular magnification is
specified.

7. • From figure we can see that,
Mang =
tanθ′
tanθ
=
h
f₂
h
f₁′
=
f₁′
f₂
• Substituting we have,
Mang = -
𝐅₂
𝐅₁
Galilean Telescopes

8. Keplerian Telescopes
• Both the objective and eyepiece of a
Keplerian telescope are positive
lenses.
• The objective lens images an infinitely
distant object at the primary focal
point of the eyepiece.

9. Keplerian Telescopes
• From figure we can see that,
Mang =
tanθ′
tanθ
=
h
f₂
h
f₁′
=
f₁′
f₂
• Substituting we have,
Mang = -
𝐅₂
𝐅₁

10. Galilean Vs. Keplerian Telescopes
Characteristic Galilean Keplerian
Objective Positive Positive
Eyepiece Negative Positive
Image orientation Erect Inverted or erect*
Location of exit pupil Within tube Outside of tube
Field of view Less Greater
Tube length Shorter Longer
Shape Straight May be bent*
Weight Generally lighter Generally heavier
*Image-erecting systems (e.g., prisms or mirrors) are included in Keplerian systems to create the
terrestrial systems that are used for clinical purposes. This may result in a bent tube.

11. Telescope Apertures, Stops, Pupils, and
Ports
Apertures stops
• The physical aperture that limits the amount of light entering the
system from this axial object is referred to as the aperture stop.
• The objective lens limits the amount of light that can enter the
telescope (both Galilean and Keplerian) , and serves as the
aperture stop.

12. Telescope Apertures, Stops, Pupils, and
Ports
Entrance pupil
• An optical system’s entrance pupil is the image of the aperture
stop formed by any lenses in front of the aperture stop.
• For both Galilean and Keplerian telescope, there are no any lenses
infront of the objective lens which is the aperture stop, so the
entrance pupil is the objective lens.

13. Telescope Apertures, Stops, Pupils, and
Ports
Exit pupil
• An optical system’s exit pupil is the image of the aperture stop
formed by lenses that follow it.
• In the case of a Galilean telescope, let’s assume the objective lens
is the aperture stop. It is followed by the minus powered ocular
(eyepiece), which forms a virtual image of the objective within
the telescope tube. This virtual image of the objective lens is the
exit pupil.

14. Telescope Apertures, Stops, Pupils, and
Ports
Exit pupil
• For a Keplerian telescope, the lens following the aperture stop is a
plus powered ocular, which forms a real image of the objective
lens to the right of the telescope. This real image of the objective
is the system’s exit pupil.
• A telescope’s exit pupil is also called a Ramsden circle. For a
Galilean telescope, it is virtual and located within the telescope,
while for a Keplerian system, it is real and located outside
(behind) the telescope.

15. Telescope Apertures, Stops, Pupils, and
Ports
Fig A: Galilean Telescope Fig B: Keplerian Telescope

16. Telescope Apertures, Stops, Pupils, and
Ports

17. • The diameters of the objective lens and Ramsden circle can be
used to determine the magnification produced by a telescope.
• The formula is as follows:
Mang =
𝐨𝐛𝐣𝐞𝐜𝐭𝐢𝐯𝐞 𝐥𝐞𝐧𝐬 𝐝𝐢𝐚𝐦𝐞𝐭𝐞𝐫
𝐑𝐚𝐦𝐬𝐝𝐞𝐧 𝐜𝐢𝐫𝐜𝐥𝐞 𝐝𝐢𝐚𝐦𝐞𝐭𝐞𝐫
Telescope Apertures, Stops, Pupils, and
Ports

18. Telescope Apertures, Stops, Pupils, and
Ports
• The physical aperture that limits an optical system’s field of view
is called the field stop.
• The image of the field stop formed by any lenses in front of it is
the system’s entrance port (sometimes called entrance window)
• The image of the field stop formed by any lenses following it is
called the exit port (or exit window).

19. Telescope Apertures, Stops, Pupils, and
Ports
As the eye moves closer to the plus lens, the field of view
(FOV) increases

20. Telescope Apertures, Stops, Pupils, and
Ports
• When viewed through a telescope, the center of the observed
image may appear brighter than its more peripheral aspects. This
reduction in peripheral brightness, which is referred to as
vignetting, occurs because some peripheral light rays do not
make it through the field stop.

21. Tube Length & Angular Magnification
• From figure, we can see that tube
length (d) is calculated as follows:
d = f₁’-f₂
Or, d =
1
F₁
+
1
F₂
By substituting the formula of angular
magnification,
Mang =
𝟏
𝟏 −𝐝𝐅₁

22. Telescopes in Ammetropia
• When using a telescope for distance viewing, a person with
spherical ametropia can either wear their distance prescription or
adjust the tube length so the vergence emerging from the
telescope is equal to their far-point vergence.
• When wearing their distance prescription, the angular
magnification is equal to that of the telescope.

23. Telescopes in Ammetropia
• If, for instance, a patient with 10.00 D of myopia wears her
spectacles when looking through a Galilean telescope that consists
of a +10.00 DS objective and -50.00 DS eyepiece, she
experiences an angular magnification of +5×.
• Suppose the patient prefers to look through the telescope without
her spectacles and to adjust the tube length instead. What would
be the tube length? What magnification would she experience?

24. Telescopes in Ammetropia
• Now, let’s consider a Keplerian telescope. A patient with 10.00 D
of myopia looks through a terrestrial telescope that has an
objective of +10.00 D and an ocular of +50.00 D. What is the
magnification when the patient wears her –10.00 D spectacles?
What would be the tube length and magnification if she were to
adjust the tube length to correct for her myopia?

25. Ametropia, Tube length and Magnification

26. Telescopes in Near Use: Telemicroscopes
When a Galilean telescope (that is focused for distance) is used to view a near object, the vergence is
amplified. Without the telescope the vergence at the eye would be less than –4.00 D, but with the
telescope it is about –20.00 D.

27. Telescopes in Near Use: Telemicroscopes
Lens caps:
• A telescope can be adapted for near use by placing a plus lens
over the objective and positioning the object at the primary focal
point of this lens.
• The plus lens images the object at infinity; therefore, the rays
that enter the telescope have zero vergence.
• A plus lens used in this manner is called a lens cap, and a
telescope fitted with a lens cap is sometimes called a
telemicroscope.

28. Telescopes in Near Use: Telemicroscopes
A lens cap is placed over the objective lens to create a telemicroscope. The working distance in
this example is 33.33 cm.

29. Telescopes in Near Use: Telemicroscopes
Numerical: A fully corrected myopic patient with age-related
macular degeneration can barely see 5 M print at a distance of 40.0
cm when looking through his bifocal add. He would like to read 1
M print and can do so with his +12.5 D magnifying glass, but must
hold the material too close to the lens to allow him to make notes
on the material. If we wish to fit this patient with a +2.5× Galilean
telescope, what power lens cap should we prescribe? How far
should the reading material be held from the telemicroscope? How
does this working distance compare with that obtained using the
magnifying glass?

30. Telescopes in Near Use: Telemicroscopes
Solution:
Equivalent viewing power = (M) (add power)
+12.50 D = (2.5) (add power)
add power = +5.00 D
The required lens cap is +5.00 D.

31. Telescopes in Near Use
Adjusting Tube Length:
• If the tube length is increased sufficiently when viewing near
objects, parallel light rays can be made to emerge from the
eyepiece.
• Increasing the tube length provides greater angular
magnification.

32. Telescopes in Near Use
A Galilean telescope has a +20.00 D objective and -50.00 D
eyepiece. The angular magnification is 2.5×, and the tube length
when focused for infinity is 3.00 cm. If the patient wishes to focus
at a distance 20.00 cm from the telescope, we consider the +20.00
D lens to consist of a +5.00 D lens cap (i.e., 100/20.00 cm = 5.00
D) and +15.00 D objective that contributes to angular
magnification. The angular magnification of the newly created
afocal telescope is +3.33× [i.e., -(-50.00 D/(+15.00 D) = 3.33×].
The tube length is 4.67 cm (i.e., 6.67 – 2.00 cm = 4.67 cm).

33. SUMMARY
• When used by an emmetropic (or optically corrected) patient to
view an infinitely distant object, the light rays entering and exiting
the telescope are parallel, resulting in afocal angular
magnification.
• Patients with ametropia may compensate for their refractive error
when using a telescope for distance viewing by wearing an optical
correction or adjusting the tube length.
• Telescopes may be adapted for near through use of a lens cap that
has a focal length equal to the object distance.

34. REFERENCES
• Schwartz Steven H. Geometrical and Visual Optics: A Clinical
Introduction, 3rd ed. New York: The McGraw-Hill Education,
2019.
• Some pictures were taken from internet.