Astronomical telescopes – problems and solutions

Astronomical telescopes – problems and solutions

1.

Based on the graph above, determine the telescope magnification when the viewing eye is relaxed.

Known :

The lens closest to the object is called the objective lens (focal length f_o) and forms a real image. The second lens called the eyepiece (focal length f_e) acts as a magnifier.

The focal length of the objective lens (f_o) = 100 cm

The focal length of the eyepiece lens (f_e) = 8 cm

Wanted : Telescope magnification when eye is relaxed

Solution :

M = -f_o / f_e

M = -100 cm / 8 cm

M = -12.5 X

Minus sign indicates that the image is inverted.

2.

Based on the figure above, what is the telescope magnification when the eye is relaxed?

Known :

The focal length of the objective lens (f_o) = 200 cm

The focal length of the eyepiece lens (f_e) = 5 cm

Wanted : Total magnification

Solution :

When eye is relaxed, the telescope magnification :

M = -f_o / f_e

M = -200 cm / 5 cm

M = -40 X

Minus sign indicates that the image is inverted.

3.

Based on above figure, if the distance between the eyepiece lens and the objective lens (d) = 11 times the focal length of the eyepiece lens, then what is the total magnification when the eye is relaxed.

Known :

The distance between the eyepiece lens and the objective lens = the length of telescope = 11 f_e

The focal length of the eyepiece lens (f_e) = f_e

The focal length of the objective lens (f_o) = the length of a telescope – the focal length of the eyepiece lens = 11 f_e – f_e = 10 f_e

Wanted: The telescope magnification

Solution :

M = -f_o / f_e

M = -10 f_e / f_e

M = -10 X

Minus sign indicates that the image is inverted.

4. What is the total magnification of the astronomical telescope?

Known :

The distance between objective and eyepiece lens (l) = 126 cm

The focal length of the eyepiece lens (f_e) = 6 cm

The focal length of the objective lens (f_o) = 120 cm

Wanted: The total magnification

Solution :

Based on the above figure, the final image at infinity, so the eye is relaxed.

The total magnification of the astronomical telescope :

1. What is the primary function of an astronomical telescope? Answer: The primary function of an astronomical telescope is to gather more light than the human eye can collect on its own, allowing distant or faint celestial objects to be viewed more clearly and in greater detail.
2. How do refracting telescopes differ from reflecting telescopes? Answer: Refracting telescopes use lenses to bend (refract) and focus light, while reflecting telescopes use mirrors to reflect and focus light. The primary optical element in a refractor is a lens, while in a reflector, it’s a mirror.
3. Why do most modern observatories prefer reflecting telescopes? Answer: Reflecting telescopes have several advantages over refractors: they can be made much larger, they don’t suffer from chromatic aberration (where different colors don’t come to the same focus), and they’re typically more compact for a given focal length because they can use multiple mirrors.
4. What is chromatic aberration, and how does it affect telescopic observations? Answer: Chromatic aberration is a type of optical distortion where different colors of light are focused at slightly different distances due to the variation in the refractive index of glass with wavelength. This can cause rainbow-like halos around observed objects. Reflecting telescopes avoid this issue because mirrors reflect all colors of light equally, without bending them differently like lenses do.
5. Why is aperture size important in telescopes? Answer: The aperture, or the diameter of the primary lens or mirror, determines how much light the telescope can gather. A larger aperture allows for the observation of fainter objects and provides higher resolution, making distant objects appear sharper.
6. What is the difference between magnification and resolving power in telescopes? Answer: Magnification refers to the factor by which a telescope can enlarge the appearance of an object. Resolving power, on the other hand, refers to the telescope’s ability to distinguish between two closely spaced objects. A telescope might magnify an image a lot, but without good resolving power, the image might still appear blurry.
7. Why are many large observatories located on mountaintops or in space? Answer: High altitudes reduce the amount of Earth’s atmosphere the light has to travel through, minimizing atmospheric distortion and absorption. Space telescopes, like the Hubble, avoid atmospheric interference entirely, allowing for much clearer and more detailed observations.
8. What is adaptive optics, and why is it beneficial for ground-based telescopes? Answer: Adaptive optics is a technology used to correct the distortions caused by Earth’s atmosphere in real-time. It typically involves a deformable mirror that can change shape rapidly to counteract atmospheric effects, resulting in much clearer images.
9. How does a radio telescope differ from an optical one? Answer: Radio telescopes detect radio waves rather than visible light. They often have large parabolic dishes to collect and focus radio waves onto a receiver. While optical telescopes provide “pictures” of space, radio telescopes capture data that is typically visualized in different ways or used for spectral analysis.

10. Why is interferometry used in astronomy, and how does it benefit telescopic observations? Answer: Interferometry involves combining the data from multiple telescopes to simulate a telescope with a much larger aperture. This technique enhances the resolving power, allowing astronomers to see finer details in celestial objects than with a single telescope alone.