Telescope Tube Length Calculation: A Comprehensive Guide for Physics Students

Summary

Telescope tube length calculation is a crucial aspect of telescope design and construction, particularly for refractor telescopes. The tube length is typically calculated by subtracting a certain amount from the focal length of the objective lens, and this value can vary depending on the specific design and use case of the telescope. The primary consideration for determining the tube length is the location of the focal plane relative to the diagonal mirror or prism, which should be located at or outside the diagonal to ensure the full utilization of the light cone and prevent vignetting.

Understanding the Fundamentals of Telescope Tube Length Calculation

Focal Length and Objective Lens

The focal length of the objective lens is the primary factor in determining the telescope tube length. The objective lens is the primary light-gathering component of a telescope, and its focal length determines the overall magnification and light-gathering power of the instrument.

The focal length of the objective lens is typically measured in millimeters (mm) and can range from a few hundred millimeters to several meters, depending on the size and design of the telescope.

Diagonal Mirror or Prism

The diagonal mirror or prism is a crucial component in the optical path of a refractor telescope. It is used to redirect the light from the objective lens to the eyepiece, allowing the observer to view the image comfortably.

The length of the diagonal mirror or prism must be taken into account when calculating the telescope tube length, as it affects the position of the focal plane relative to the optical components.

Eyepiece Focal Length

The focal length of the eyepiece is another important factor in the telescope tube length calculation. The eyepiece is the component that magnifies the image produced by the objective lens, and its focal length determines the overall magnification of the telescope.

The eyepiece focal length is typically measured in millimeters (mm) and can range from a few millimeters to several centimeters, depending on the desired magnification and field of view.

Telescope Focal Ratio

The telescope focal ratio is the ratio of the focal length of the objective lens to the aperture (diameter) of the telescope. This value is often expressed as a number, such as f/10 or f/5, and it determines the light-gathering power and the depth of field of the telescope.

The telescope focal ratio is an important factor in the tube length calculation, as it affects the position of the focal plane relative to the optical components.

Calculating the Telescope Tube Length

To calculate the telescope tube length, you can use the following formula:

Tube Length = Focal Length – Diagonal Length – (Eyepiece Focal Length / Telescope Focal Ratio)

Where:

• Focal Length: The effective focal length of the objective lens (in millimeters)
• Diagonal Length: The length of the diagonal mirror or prism (in millimeters)
• Eyepiece Focal Length: The focal length of the eyepiece you plan to use (in millimeters)
• Telescope Focal Ratio: The focal ratio of the telescope (the ratio of the focal length to the aperture)

Let’s consider an example:

Suppose you have a 900mm f/10 refractor telescope, a 2″ (50.8mm) diagonal mirror, and a 25mm eyepiece. The tube length would be calculated as follows:

Tube Length = 900mm – 50.8mm – (25mm / 10) = 849.2mm

In this example, the tube length should be approximately 849.2mm to ensure that the focal plane is located at or outside the diagonal for most of the drawtube’s travel.

Factors Affecting Telescope Tube Length

There are several factors that can affect the telescope tube length calculation, including:

1. Optical Design: The specific optical design of the telescope, such as the use of lenses, mirrors, or a combination of both, can impact the tube length requirements.

2. Focal Plane Position: The desired position of the focal plane relative to the diagonal mirror or prism can affect the tube length calculation.

3. Eyepiece Selection: The choice of eyepiece can influence the tube length, as the eyepiece focal length is a factor in the calculation.

4. Telescope Focal Ratio: The telescope’s focal ratio can also impact the tube length, as it affects the position of the focal plane.

5. Mechanical Constraints: Physical limitations, such as the size of the telescope mount or the available space for the instrument, can also influence the tube length calculation.

Practical Considerations and Troubleshooting

When designing and constructing a refractor telescope, it is essential to consider the tube length and its impact on the optical performance of the instrument. Here are some practical considerations and troubleshooting tips:

1. Vignetting: Ensure that the focal plane is located at or outside the diagonal mirror or prism to prevent vignetting, which can reduce the effective aperture and image quality.

2. Drawtube Travel: Verify that the drawtube has sufficient travel to accommodate the calculated tube length and allow for proper focusing.

3. Mechanical Stability: Ensure that the telescope tube is sturdy and well-supported to maintain the alignment of the optical components and prevent image distortion.

4. Thermal Expansion: Consider the effects of temperature changes on the telescope’s materials, as this can affect the tube length and the overall optical performance.

5. Collimation: Regularly check and adjust the collimation (alignment) of the optical components to maintain optimal image quality.

Conclusion

Telescope tube length calculation is a critical aspect of telescope design and construction, particularly for refractor telescopes. By understanding the fundamental principles and factors involved in this calculation, physics students can design and build high-quality telescopes that deliver exceptional optical performance.

References

1. Refractor Tube Length Calculations – ATM, Optics and DIY Forum: https://www.cloudynights.com/topic/362801-refractor-tube-length-calculations/
2. Telescope Calculator: How Does Your Telescope Perform?: https://skyandtelescope.org/observing/telescope-calculator/
3. Calculating the Magnification of a Telescope – Space Math @ NASA: https://spacemath.gsfc.nasa.gov/weekly/10Page32.pdf
4. SJ6.pdf – Lehman College: https://www.lehman.edu/faculty/anchordoqui/SJ6.pdf
5. Simple Formulas for the Telescope Owner: https://skyandtelescope.org/observing/stargazers-corner/simple-formulas-for-the-telescope-owner/