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Introduction

Galilean telescopes, named after the great Italian scientist Galileo Galilei, are simple yet powerful optical instruments. Galileo first constructed one in 1609, and with it, he made significant astronomical discoveries¹. Today, these telescopes are not only used for stargazing but also have found their place in the field of optometry, particularly as a low vision aid² due to their ability to utilise angular magnification to increase image sizes.

Galilean Telescopes in Optics

A Galilean telescope consists of two lenses: a large converging lens (plus lens) of long focal length (the objective) and a diverging lens (minus lens) of short focal length (the eyepiece)³. This simple design results in an upright (erect) image.

Use in Optometry and Low Vision

In the realm of optometry, Galilean telescopes are used as a low vision aid. They are small, lightweight, and due to their simple optical design, they produce a bright image². However, they offer rather narrow fields of view and tend not to be sharp edge-to-edge². Despite these limitations, they are often the first choice for children and patients with peripheral field loss⁴.

Low Vision Aids Using Galilean Telescopes

Below are some examples of the low vision aids that used Galilean Telescopes to achieve their function.

Whilst this is just a short sample of the applications Galilean telescopes have to aid those with low vision, the benefits they have are clear. For further examples, I recommend the Eschenbach website, which has a comprehensive list of the telescopes available for use in low vision settings. Familiarise yourself with this website as you may find it useful when working with low vision patients in the future.

Telescope Angular Magnification Calculation

The angular magnification of a Galilean telescope is calculated by dividing the focal length of the objective lens by the focal length of the eyepiece lens^3,5. This can be represented as:

where:

• M is the magnification,
• F_e​ is the power of the eyepiece lens, and
• F_o is the power of the objective lens.

Telescope Angular Magnification: Worked Example

Let’s consider a Galilean telescope with an objective lens of +10 dioptres and an eyepiece lens of -20 dioptres. The angular magnification would be calculated as follows:

This means that the image seen through this telescope would be 2 times larger than the object seen with the naked eye.

Telescope Length

The total length of a telescope, also known as the separation distance, is a crucial aspect of its construction and functionality. It is calculated by adding the focal lengths of the eyepiece lens (f_o​) and the objective lens (f_e​). This can be represented by the formula:

where d is the separation distance or the total length of the telescope. This calculation is fundamental to the design and operation of telescopes, including Galilean telescopes used in optics and optometry.

Telescope Length: Worked Example

Lets consider the same telescope as used in the previous worked example, which had an objective lens of 10 dioptres and an eyepiece lens of -20 dioptres.

Given that the power of the objective lens is +10 dioptres and the power of the eyepiece lens is -20 dioptres, we first need to convert these powers into focal lengths:

• The focal length of the objective lens (f_o​) is the reciprocal of its power:
  f_o ​= 1 / 10 = 0.1 meters (or 10 cm)
• The focal length of the eyepiece lens (f_e​) is the reciprocal of its power:
  f_e ​= 1 / (−20) = −0.05 meters. (or -5cm)

Then, we substitute these values into the formula for the length of the telescope:

d = f_o​ + f_e ​= 0.1 + (−0.05) = 0.05 meters = 5 cm

The telescope will therefore have a distance between lenses of 5 cm.

Conclusion

Galilean telescopes, while simple in design, have a wide range of applications, from astronomy to optometry. Their use in low vision aids has proven to be particularly beneficial, offering a means to improve visual performance and quality of life for individuals with vision impairments.

Test Your Skill

The dialogue cards below will help you test your knowledge on working with angular magnification of telescopes and working out the telescope length. See how many you can get right!

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Read More

1. Britanica. Telescopes. Available at: https://www.britannica.com/science/astronomy [Accessed 21st March 2024].
   
2. Green HA, and Shuldiner RJ. Telescope glasses for low vision: When, why, how and more. Low Vision of Southern California. [Online]. Available at: https://www.lowvisioncare.com/ways-we-can-help/resources-for-eye-care-professionals/telescope-glasses-for-low-vision-when-why-how-and-more/. [Accessed 21st March 2024].
   
3. Hurley S (2018) Galileo and the telescope. Explaining Science. [Online]. https://explainingscience.org/2018/03/13/galileo-and-the-telescope/ [Accessed 21st March 2024].
   
4. Agarwal R, and Tripathi A (2021). Current modalities for low vision rehabilitation. Cureus 13(7): e16561. [Online}. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8396411/ [Accessed: 21st March 2024].
   
5. Harvey B (2016). Low vision refresher. Optician Online. [Online]. Available at: https://www.opticianonline.net/cpd-archive/4752 [Accessed: 21st March 2024].
   
6. Galilean Telescopes (2024). Eschenbach website [Online]. Available at: https://eschenbach.com/products/galilean-telescopes.asp [Accessed: 21st March 2024].