Mathematics of Telescopes

Mathematics of Telescopes

Length: 1229 words (3.5 double-spaced pages)

Rating: Excellent

Open Document

Essay Preview

More ↓
Missing Figures
A Brief History of Telescopes

Although telescopes has been around for several hundreds of years, there has been great discrepancy as to who invented it first. Here is one authors opinion. Lippershey was a Dutch spectacle marker during the early 17th century (approximately 1600). He was one of the first who created the "looker" (now called telescope) by placing two pieces of lenses together. The discovery that placing lenses together can magnify images were made by children who took Lippershey's spectacles and looked at a distant church tower.

One of the most influential scientist associated with the telescope has to be Galileo. He took the design and reinvented the telescope into one of the first refractive telescopes we use to this day.

Galileo used this great invention to report astronomical facts such as the moon is cover with craters instead of being smooth, the Milky Way is composed of millions of stars, and Jupiter have four moons. Perhaps the most famous discovery is the Earth revolves around the Sun and the Earth is not the center of the universe (even though he was discredited at the time).

Newton was also involved with telescopes. After his growing interest with light bending, he applied his knowledge of the reflecting and refracting properties of light and invented the first reflective telescopes. Newton's reflective telescopes vastly improve the clarity of images as well as escaping from chromatic abberration. In order to fully understand the concepts and ideas of how a telescopes work, some knowledge of simple optics are required.

Some Simple Optics

Refraction
Refraction occurs when light travels from one medium crosses a boundary and enters another medium of different properties. For example, light traveling from air to water. The amount of refraction (or bending) can be calculated using Snell's Law.

Refractor

How Refractor Telescopes Work
The principle behind the refractive telescopes is the use of two glass lenses (objective lens and eyepiece lens) to gather and bend parallel light rays in a certain way so that the image fits the size of the eye's pupil. Light rays is gather through the opening of the telescope called the aperture and passes through the objective lens and refracts onto a single point called the focal point. From there the light rays continue the same direction until it hits the eyepiece lens which also refract the light back into parallel rays. During the process, the image that enters our eyes is actually reverse of the original image and magnified because the size in which we preceive the image.

How to Cite this Page

MLA Citation:
"Mathematics of Telescopes." 123HelpMe.com. 21 Jan 2020
    <https://www.123helpme.com/view.asp?id=153813>.

Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »

Essay about Women 's Impact On The Advancement Of The Sciences

- Women have contributed and will continue to contribute to the sciences. Whether the subject is astronomy, mathematics, medicine, biology, or education, women have always been a key contributor to the sciences. During the 18th century there were a few women that contributed immeasurable efforts in the advancement of the sciences, many of them working their way up from apprenticeships and teaching themselves at home. Even though society made it hard on these women, their passion and determination fueled them to accomplish great scientific accomplishments that we still benefit from today....   [tags: Science, Scientific method, Mathematics, Bologna]

Research Papers
1510 words (4.3 pages)

The Magic Of Mathematics And Mathematics Essay

- Yihao Hu Statement of Background & Goals John Hopkins University Department of Applied Mathematics & Statistics Degree Objective: Ph.D. in Applied Mathematics In the realm of mathematics and applied mathematics, I am especially interested in numerical methods for partial differential equations, fluid dynamics, dynamical systems, scientific computing and Optimization. The magic of mathematics that attracts me most is solving the most sophisticated problems in the real world through different applied methods which are based on the rigorous theoretical analysis....   [tags: Mathematics, Applied mathematics]

Research Papers
952 words (2.7 pages)

How the Telescope Opened the Universe Essay

- Telescopes were one of the most important inventions in the science of astronomy. They opened up the sky, allowing people to see things previously invisible. With telescopes, scientists could look beyond the visible sky and learn about what exists past the night sky. From the earliest telescopes of Galileo’s age to the incredible telescopes used today, they have allowed people to see just how large the universe is and what makes up that universe. How the Telescope Opened the Universe When Galileo created his telescope and aimed it towards Jupiter, not only did he have the first view of something beyond the Earth, but his discovery proved that there was more to the night sky than the small p...   [tags: astronomy, telescopes, galileo]

Research Papers
931 words (2.7 pages)

Essay on Ontology of Mathematics

- An ontological theorist generally begins his discussion with a preconceived notion of what kind of thing an object will turn out to be. Instead, we will here begin with a Thomassonian approach to the ontology of mathematics. First, let us consider what happens when we rst come to determine a mathematical proposition (which I will use synonymously with 'mathematical entitty'). A mathematician does not feel as though he creates mathematical theories. Pythagoras can hardly be thought to have created the claim that a2 + b2 = c2....   [tags: Mathematics]

Research Papers
1511 words (4.3 pages)

Introduction to Mathematics Glossary of Terms Essay

- Introduction to mathematics glossary of terms: In glossary all intend mathematical terms can be substantiate in plain language. In this mathematics glossary of terms is formulated in response to requests from teachers and others during the national curriculum consultation. . Mathematics glossary of terms is always incomprehensible even before they get heavy into the Greek symbols. Now we are learned in this topic about mathematics glossary of terms. Some terms of mathematics glossary of terms: * Absolute value * Acute angle * Acute triangle * Additive identity * Additive inverse * Adjacent angles * A...   [tags: Mathematics ]

Research Papers
944 words (2.7 pages)

Essay about Mathematics in Neuropsychology

- “Neuropsychology is a specialty that applies the principles of assessment and intervention based upon the scientific study of human behavior as it relates to normal and abnormal functioning of the central nervous system.” (The American Psychological Association) In more basic terms, the field of neuropsychology relies heavily on the study of the central nervous system combined with the study of the behavior of an individual. A type of psychology career, it involves using computational methods and mathematics, “particularly statistics, as a professional tool to quantify and analyze their scientific findings.” Neuropsychologists also work towards diagnosing any potential mental impairments...   [tags: Mathematics]

Research Papers
1304 words (3.7 pages)

Why Is Mathematics Important For Mathematics? Essay examples

- S. Gudder once wisely stated, “The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” Many people have different views of mathematics and the role it plays in their life. There are some students who believe that learning mathematics is useless and is not a necessity for their major, and there are others who find math, arithmetic, and numbers easier to process. I find Gudder’s thoughts to be true based on my upbringings and recent experience in my Math 110 course....   [tags: Mathematics, Algebra, Pythagorean theorem]

Research Papers
976 words (2.8 pages)

Essay on Developing Mathematics Learning Skills

- Mathematics is a subject that many people fear and complain is too difficult to learn. The truth, however, is everyone is capable of learning mathematics, even complicated mathematics. They simply need to know the proper method of learning. Mathematics is different from other subjects. It is more than rote memorization. Developing learning skills is vital to learning mathematics. Study skills specific to the subject are required, as is developing problem solving skills and learning to properly deal with learning stresses....   [tags: Mathematics]

Research Papers
914 words (2.6 pages)

Essay on Mathematics in Everyday Life

- Mathematics is possibly one of the most underappreciated sciences. It everywhere in our lives, mathematics runs our computers, flies our aircraft, and protects our information. But for such a major part of our lives, very few people can say that they know how it is done, how the RSA encryption protects their e-mail, or even that 21 squared is 441 without going into tedious mental calculations or reaching for their calculator. Contrary to popular belief, mathematics has a wide range of useful applications....   [tags: Mathematics]

Research Papers
1449 words (4.1 pages)

Essay on Egyptian Mathematics

- The Egyptians are one of the earliest known and most well documented people to inhabit the Earth. They were one of the first people to respond to practical needs within agriculture, business, and industry. Moreover, archaeological and historical artifacts suggest that the Egyptians were among the first to develop the study of mathematics. This paper will discuss the development of mathematics in ancient Egypt, focusing on the use of hieroglyphs, the decimal system, and hieratic writing and numerals to demonstrate that the Egyptians made notable contributions to modern day understandings of mathematics....   [tags: Mathematics]

Research Papers
656 words (1.9 pages)

Related Searches

The following diagram will show the components and the process of light rays traveling through a refractor telescope.



Magnification of a refractor telescope mainly depends on the distance of the eyepiece lens with regard to the focal point because the focal length determines how large the image get scale by. Typically a long focal length of the objective lens combine with a short focal length of the eyepiece lens will yield greater magnification. However, magnification is not the most important optical property for viewing astronomical phenomenon. The aperture size is more important because it accounts for the amount of light the telescope receives and the more light, the brighter the image. The size of aperture also accounts for the resolution power of the telescope. Larger aperture size will yield high quality of image, more crisp and detail image, and increase clarity of the image.

Advantages/Disadvantages
Advantages of a refractor telescopes

* After initial setup, refractor telescopes are less likely to be misalign than reflector telescopes.
* No cleaning is necessary inside the telescope because the tube is sealed off from contact with air.
* Temperature and air current cannot effect the refractor as much as a reflector because of the isolation from outside atmosphere.

Disadvantages of a refractor telescopes

* Refractor suffers from chromatic aberration due to the different index of refraction for different wavelengths.
* Quality of transmission of light through the lens depends on the wavelength.
* Quality of transmission of light decreases as the thickness of lens increase.
* Difficult to construct a perfect lens in terms of curvature and purity inside the lens.
* The objective lens will sag due to its own weight because the lens is only supported at the edge.
* The cost of a objective lens increases as the diameter of the lens increase, so cost efficiency verse quality of image, reflectors is better than refractors.
* The limitation of diameter size of the objective lens because the larger the lens, more problems such as chromatic aberration will occur.

Ray Tracing Through Refractor Telescope
The following is a sample trace of a ray through the refractor telescope lens system. Several assumption is made such as the radius of curvature for the lenses and index of refraction.

Reflector

How Reflector Telescopes Work
The main difference between a refractor and a reflector is the latter telescope involves both refraction and reflection of light rays. Reflector telescopes uses two mirrors (primary and secondary mirror) as well as a glass lens (eyepiece lens) in their lens system. Similar to refractors, light rays are gather through the aperture. However instead of bending the rays through a glass lens immediately, rays are to travel to the back of the telescope where the primary mirror is located. The primary mirror is shaped parabolically so that all incoming parallel rays will reflect off the mirror at their own specific angle and hit the surface of the secondary mirror. Once again a reflection will occur and all the rays will converge to a single point call the focal point. It is from that point where optics of refractors and reflectors are common. Light rays will continue to travel and refracts at the eyepiece lens and forms an image that is magnified to people's perception. However this image is also in reverse to the original image. Refer to the following diagram to understand the components and processes in which light rays travel through a reflector telescope.

Magnification of a reflector telescope mainly depends on the distance of the eyepiece lens with regard to the focal point because the focal length determines how large the image get scale by. Typically a long objective focal length combine with a short focal length of the eyepiece lens will yield greater magnification. However, magnification is not the most important optical property for viewing astronomical phenomenon. The aperture size is more important because it accounts for the amount of light the telescope receives and the more light, the brighter the image. The size of aperture also accounts for the resolution power of the telescope. Larger aperture size will yield high quality of image, more crisp and detail image, and increase clarity of the image.

Advantages/Disadvantages
Advantages of a reflector telescopes

* The main advantage is reflector telescope can escape from chromatic aberration because wavelength does not effect reflection.
* The primary mirror is very stable because it is located at the back of the telescope and can be support in the back.
* More cost effective than refractor of similar size.
* Easier to make a high quality mirror than lens because mirror need to only concern with one side of the curvature.

Disadvantages of a reflector telescopes

* Optical misalignment can occur quite easily.
* Require frequent cleaning because the inside is expose to the atmosphere.
* Secondary mirror can cause diffraction of original incoming light rays causing the "christmas star effect" where a bright object have spikes.


Return to 123HelpMe.com