The apparent size is how large an object appears when viewed by an observer.  For larger astronomical objects the apparent size is often measured in degrees. For example, the apparent diameter of the Moon is roughly 0.5 degrees. A telescope makes the apparent size larger.

galileofs-125dx reflectortelescope

These Adhesive Sheets are designed to be used with our Sorbothane mounting feet or sheets. The SB12D sheet, which has two adhesive surfaces, is ideal for semi-permanent applications where the sorbothane surface will not have to be moved often. Our SB12E sheet, which has one adhesive and one felt surface, prevents the sorbothane from marking or marring the table surface that they are placed on.

Telescopes are instruments which use multiple lenses to produce magnified images of distant objects. It is unclear who invented the first telescope: lenses had been widely used in Europe to correct poor eyesight since the fourteenth century and I expect that, over time, the telescope was actually invented many times by different individuals, who discovered that combining different lenses could produce a magnified image.

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Are you quite sure that the Galilean telescope design is used in low power binoculars today? Their apparent fields of view are much larger than the “drinking straw” effect of the Galilean telescope design, however, because they are actually Keplerian telescopes that have either Porro or “roof” prisms to rotate the image 180 degrees. There is absolutely no way that modern binoculars are of the Galilean type.

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Keplerian and Galilean telescopes are both example of refractors where lenses are used to collect and focus light. Nowadays all large telescopes are reflectors where curved mirrors, rather than lenses, are used.  Reflectors have a number of advantages. One of them is that reflectors don’t suffer from chromatic aberration. This happens in refractors because different colours of light are bent very slightly differently as they pass through the lens, which results in a blurred image.  Chromatic aberration can be overcome by using achromatic lenses, which consist of two or more lenses made out of different types of glass joined together to form a compound lens, but this is expensive and technically difficult when constructing larger lenses. The main advantage of reflectors is that it is much easier to produce a large mirror than a large lens. A large lens many metres in diameters would be very thick, very heavy and difficult to manufacture to the quality needed in a telescope. It would also tend to sag, becoming deformed under its own weight,  producing a blurred image.

These pliable Sorbothane Sheets are ideal for isolating mechanical noise or vibrations. The sheets come in three thicknesses and can be placed under a breadboard in single or stacked layers to counter the effects of uneven work surfaces or to isolate the breadboard from vibrations. For objects over 5 lbs (approx. 2.2 kg), the thicker 1/4" (SB12B) or 1/2" (SB12C) sheets are recommended. For information on the isolation efficiency of these sheets at specific load capacities, please see the Sheet Cutting Guide tab above.

These Sorbothane mounting feet provide a passive isolation solution for workbench-mounted breadboards, effectively isolating noisy equipment from the optical table or breadboard surface. Unlike our pneumatic benchtop isolation solutions, these solid Sorbothane feet do not require inflation.

The tables below show the different sizes that a Sorbothane sheet should be cut down to for isolating certain frequencies. Within each table are minimum frequency values, meaning that at a specific size and load the isolator will effectively damp any frequency equal to or greater than what is given. Orange cells indicate areas where the specific isolator size and load should not be used. N/A indicates that the load is too great, whereas >100 Hz indicates that a better option is available (i.e., to isolate a frequency of 150 Hz, an isolator size that is effective from 50 Hz and up is a better choice than one that is effective from 100 Hz and up).

Thorlabs’ Sorbothane Feet and Sheets offer excellent vibration and acoustic isolation for laboratory needs. Our Sorbothane feet offer internal 1/4"-20 (M6) threads or an adhesive surface, which can be used to attach the feet to the bases of test equipment or breadboards. For a more versatile option, Thorlabs also offers 12" × 12" (305 mm x 305 mm) Sorbothane sheets with 1/8" (3.2 mm), 1/4" (6.4 mm), or 1/2" (12.7 mm) thickness. These sheets are easily cut and can be adapted to suit a variety of custom applications.

There are various combinations of lenses which can be used to magnify distant objects, but the simplest is the one used by Galileo.  Telescopes of this design are called Galilean telescopes and to understand how they work it is necessary to understand a little about lenses.

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He studied the way that the Moon was lit and how this changed over time and correctly deduced that this was due to shadows of lunar mountains and craters. Galileo turned his telescope to the Milky Way and discovered that it consisted of a vast number of stars, each too faint to be seen individually with the naked eye. When viewed from Earth these stars are so closely packed together they appear to be clouds. However, his discovery which had the greatest impact on his life was the phases of Venus.

These sheets are sized to fit directly under our 12" x 12" (305 mm x 305 mm) sorbothane sheets, but can also be cut down to fit under our sorbothane mounting feet.

[…] S (2018) Galileo and the telescope. Explaining Science. [Online]. https://explainingscience.org/2018/03/13/galileo-and-the-telescope/ [Accessed 21st March […]

A microscope objective is composed of a complex set of lenses and optics, and different objectives are designed for different imaging tasks.

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galileofs-125dx reflectortelescopemanual

There is now a video on the Explaining Science YouTube Channel which describes Venus’s orbit and how Galileo’s observation of its phases disproved the geocentric theory. To view it, please click on the link below.

Based on the values given above, the calculated load per isolator is 13.5 lbs. This value should then be looked up on each isolation graph for the round isolator feet below. Sorbothane feet with a calculated load per isolator that exceeds the maximum load are not suitable for the application. Without a known problem frequency, the isolator that effectively isolates at the lowest cut-on frequency is recommended.

GalileoReflectorTelescope

However, the phases of Venus which Galileo had seen can only be explained by Venus orbiting the Sun. Therefore, Galileo concluded that the geocentric theory was incorrect.   Unfortunately for Galileo, in 1616 the Catholic church declared heliocentrism to be heresy. Heliocentric books were banned and Galileo was ordered to refrain from holding, teaching or defending heliocentric ideas.

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The diagram below (which if you’ve studied physics at high school you may recall is called a ray diagram) shows that when the rays of light from a distant object pass through a converging lens, they form an inverted image, which is reduced in size compared to the object.

In the diagram above, the blue line shows a ray of light from the top of a distant object. The red line shows a ray of light from the bottom of the object. The apparent size is the angle between the two rays.

Hi I am Steve Hurley. I work in the IT industry. I studied for a PhD in astronomy in the 1980s. Outside work my real passion is explaining scientific concepts to a non-scientific audience. My blog (explainingscience.org) covers various scientific topics, but primarily astronomy. It is written in a style that it is easily understandable to the non scientist. Publications and videos For links to my books and videos please visit www.explainingscience.org View all posts by Steve Hurley

Galileantelescopedesign

For this example, the AV4(/M) or AV5(/M) sorbothane feet would both be acceptable solutions. The AV4 Ø27 mm isolator feet provide better isolation performance at lower frequencies but are near the load limit, so if the total load were higher than anticipated the isolator would be outside of the recommended load capacity. Our AV5 Ø38.1 mm isolator feet will have worse isolation performance at lower frequencies, but are well within the load range which may be preferable.

Galileo telescopeinvention

As you can see from the diagram above. the apparent size of the distant object is increased. The magnification of the telescope (M) is defined as:

[…] Galileu tenha melhorado o telescópio, ele não foi creditado por realmente tê-lo inventado (por Explicando a Ciência). Essa honra foi dada a outro europeu, que pode ter inventado este dispositivo de observação de […]

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To calculate the magnification of a Galilean telescope, we divide the focal length of the objective by the focal length of the eyepiece. So, if the focal length of the objective is 200 cm and the focal length of the eyepiece is 10 cm, the magnification of the telescope would be 20.

If we put a converging lens in front of the distant object then it will focus the light rays and produce an inverted image, which will be positioned as shown below.

If a sorbothane sheet is preferred, it would need to be cut to an appropriate size as shown in the Sheet Cutting Guide tab. For a 13.5 lb (6.1 kg) load, a 0.5" (12.7 mm) thick sheet cut into 1.5" x 0.5" (38.1 mm x 12.7 mm) pieces would provide a good isolation solution.

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The AV4(/M), AV5(/M), and AV6(/M) mounting feet each contain internal 1/4"-20 (M6) threading and include four 1/4"-20 (M6) threaded setscrews. In contrast, the AV3 mounting feet are not threaded, and are attached to equipment or breadboards using the included double-sided tape. See the table below for the load capacities and dimensions of each isolator. When choosing an isolator, we recommend picking the isolator that offers the largest range of damped frequencies for the specific load being used. For further assistance in choosing the proper sorbothane isolator, please see the Feet Selection Guide tab above.

An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes.

For these reasons the largest refractor used in professional astronomy is the one at Yerkes Observatory. It has an objective lens which is 1 metre in diameter. All telescopes larger than this are reflectors. It  is based at Williams Bay, Wisconsin and was operated by the University of Chicago until its closure in 2018

Despite this ruling Galileo continued to defend heliocentrism, and in 1633 the Roman Inquisition found him ‘vehemently suspect of heresy’, sentencing him to indefinite imprisonment. Galileo was kept under house arrest until his death in 1642.

For assistance in choosing the proper sorbothane isolator, please see the Feet Selection Guide and Sheet Cutting Guide tabs above.

The round sorbothane feet's isolation graphs, shown below, use load per isolator (m) in lbs, which is given by the following equation:

As seen from the Earth,  Venus goes through a full set of phases in a similar way to the Moon.  However, because Venus appears so small, these are only visible through a telescope and Galileo was the first person to see them.

The ray diagram below shows that when rays of light from a distant object pass through a diverging lens they spread out, so that they appear to come from an image which is closer to the lens and reduced in size compared to the object. This is called a virtual image, because the rays of light don’t actually form an image.

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Galileo telescopemodels

Sorbothane sheets can be cut to size using scissors or a utility knife. Please contact Technical Support to request Sorbothane sheets with a lower hardness.

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At point A in the diagram above, when Venus is between the Earth and the Sun, the sunlit part of Venus faces away from us making the planet almost invisible. The amount of the sunlit part of Venus we can see gets larger or waxes through to a crescent phase (B), to a half Venus (C)  and then to a full Venus at point D, when the whole sunlit side facing the Earth is illuminated.  It then gets smaller or wanes back to a half Venus (E) , then to a crescent (F) and then finally back to being almost invisible back at point A.

Please note that these feet may have silicon residue on their surface from the molding process. To remove the residue, wipe the feet down with an alcohol-based solvent such as isopropyl alcohol (IPA). To protect the work surface from this residue, please see our SB12E Adhesive Felt Sheets below.

Galileo telescopeInstructions

Using his telescope, Galileo made a number of important discoveries which revolutionised astronomy. He discovered the four brightest moons of Jupiter which are now called the Galilean moons.

A Galilean telescope consists of two lenses: a large converging lens of long focal length  (the objective) and the eyepiece – a diverging lens of a short focal length. Interestingly,  both of these lenses on their own produce a smaller image of a distant object, but when combined the produce a magnified image.

If we put a diverging lens with a short focal length in a position where it intercepts the light rays before they are brought to a focus, then the light rays are bent by the diverging lens and follow the path below.

In 1608 a spectacle maker called Hans Lippershey applied to the Dutch government  for a patent for a device for seeing at a distance. His application was refused and, in the resulting publicity, the Italian astronomer Galileo Galilei (1564-1642) became aware of the device. Galileo refined the early telescopes to produce instruments with better magnification and in 1609 he took the first recorded astronomical observations with a telescope.  Indeed, the first use of the word telescope, which is constructed from the Greek words ‘tele’ meaning ‘far’ and ‘skopos’ meaning ‘seeing’, is associated with Galileo’s instrument.

Galileo’s telescope could only magnify objects 30 times before the image became distorted. It also had a narrow field of view. In 1610 Johannes Kepler began investigations into the way that different combinations of lenses could work together to produce a magnified image. He invented a new type of telescope with a converging lens as the eyepiece This new design became known as the Keplerian telescope and  enables a higher magnification with less distortion than the Galilean telescope, although it produces an upside down image,  this doesn’t  matter for astronomy!.  Nowadays the Galilean telescope design is only used in  low power binoculars.

As readers of a previous post will know, in 1543, just before his death, Nicolas Copernicus (1473-1543) had published the theory of heliocentrism which states that the planets orbit the Sun. However, in Galileo’s time, the teaching of the Catholic church favoured geocentrism, the widely held view that the Earth was the centre of the Universe and the stars, planets, the Sun and the Moon were in orbit around it. Indeed certain verses of the bible could be interpreted as supporting that viewpoint, such as Psalm 104:5:

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The example presented here details the steps needed to ensure the proper selection of round sorbothane isolator feet to match the requirements of a particular load and problem frequency. Following the example are plots showing the amount of isolation achieved for our isolator feet. For specific isolation recommendations, please contact Tech Support.

Oh, alright, you have a point there, obviously. Granted, there are many types of binoculars. Even eyeglasses could be considered a form of binocular. For the record, I meant standard “field binoculars” or whatever it is most people normally think of as binoculars, not opera glasses, binocular microscopes, or head-mounted magnifiers. And of course there are always exceptions and specialty products, as with everything. Taking all of this into consideration, the Galilean telescope design is only used in *some* types of “binocular” today. You said “low power”, and I get what you meant by that now (low power for binoculars), but I consider virtually all field binoculars as being low power (for telescopes, which they also are), so I misunderstood.