# 26.5 Telescopes

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• Outline the invention of a telescope.
• Describe the working of a telescope.

Telescopes are meant for viewing distant objects, producing an image that is larger than the image that can be seen with the unaided eye. Telescopes gather far more light than the eye, allowing dim objects to be observed with greater magnification and better resolution. Although Galileo is often credited with inventing the telescope, he actually did not. What he did was more important. He constructed several early telescopes, was the first to study the heavens with them, and made monumental discoveries using them. Among these are the moons of Jupiter, the craters and mountains on the Moon, the details of sunspots, and the fact that the Milky Way is composed of vast numbers of individual stars.

[link] (a) shows a telescope made of two lenses, the convex objective and the concave eyepiece, the same construction used by Galileo. Such an arrangement produces an upright image and is used in spyglasses and opera glasses.

The most common two-lens telescope, like the simple microscope, uses two convex lenses and is shown in [link] (b). The object is so far away from the telescope that it is essentially at infinity compared with the focal lengths of the lenses ( ${d}_{\text{o}}\approx \infty$ ). The first image is thus produced at ${d}_{\text{i}}={f}_{\text{o}}$ , as shown in the figure. To prove this, note that

$\frac{1}{{d}_{\text{i}}}=\frac{1}{{f}_{\text{o}}}-\frac{1}{{d}_{\text{o}}}=\frac{1}{{f}_{\text{o}}}-\frac{1}{\infty }\text{.}$

Because $1/\infty =0$ , this simplifies to

$\frac{1}{{d}_{\text{i}}}=\frac{1}{{f}_{\text{o}}}\text{,}$

which implies that ${d}_{\text{i}}={f}_{\text{o}}$ , as claimed. It is true that for any distant object and any lens or mirror, the image is at the focal length.

The first image formed by a telescope objective as seen in [link] (b) will not be large compared with what you might see by looking at the object directly. For example, the spot formed by sunlight focused on a piece of paper by a magnifying glass is the image of the Sun, and it is small. The telescope eyepiece (like the microscope eyepiece) magnifies this first image. The distance between the eyepiece and the objective lens is made slightly less than the sum of their focal lengths so that the first image is closer to the eyepiece than its focal length. That is, ${d}_{\text{o}}\prime$ is less than ${f}_{\text{e}}$ , and so the eyepiece forms a case 2 image that is large and to the left for easy viewing. If the angle subtended by an object as viewed by the unaided eye is $\theta$ , and the angle subtended by the telescope image is $\theta \prime$ , then the angular magnification     $M$ is defined to be their ratio. That is, $M=\theta \prime /\theta$ . It can be shown that the angular magnification of a telescope is related to the focal lengths of the objective and eyepiece; and is given by

$M=\frac{\theta \prime }{\theta }=-\frac{{f}_{\text{o}}}{{f}_{\text{e}}}\text{.}$

The minus sign indicates the image is inverted. To obtain the greatest angular magnification, it is best to have a long focal length objective and a short focal length eyepiece. The greater the angular magnification $M$ , the larger an object will appear when viewed through a telescope, making more details visible. Limits to observable details are imposed by many factors, including lens quality and atmospheric disturbance.

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Dancan
hello
are you an elementary student too?
benedict
no bro
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Che
hi
Miranwa
yes
Miranwa
welcome
Miranwa
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what is strain?
SAMUEL
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
ABHIJIT
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
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most possible as it is for you to drink your wine from your straw
Selina
state the law of conservation of energy
energy can neither be destroy or created,but can be change from one form to another
dare
yeah
Toheeb
it can neither be created nor destroyed
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its so sample question dude
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what is the difference between a principle and a law?
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philippines
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why?
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you are beautiful
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are you physics student
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laws are ment to be broken
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hehe ghulam where r u from?
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yes
dare
principle are meant to be followed
dare
south Africa
dare
here Nigeria
Toheeb
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
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Rules are meant to be broken while principals to be followed
Karanja
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
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it is the product of mass and velocity of an object.
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yes
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remains constant
taha
mass of an object is always constant. and that is universally applied.
Shii
mass of a body never changes but the weight can change due to variance of gravity at different points of the world
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mass of an object does not change
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Ahsan
ty
Denise
weight is the earth pull of the body
Ugbesia
why does weight change but not mass?
Theo
Theo, the mass of an object can change but it depends on how you define that object. First, you need to know that mass is the amount of matter an object has, and weight is mass*gravity (the "force" that attracts object A to the object B mass).
Nicolas
So if you face object A with object B, you will get a different result than facing object A with object C, so the weight of object A changes but not its mass.
Nicolas
Now, if you have an object and you take a part away from it, you are changing it mass. Lets use the human body and fat loss process as an example.
Nicolas
When you lose weight by doing exercise, you are being attracted by the same object before and after losing weight so the change of weight is related to a change of mass not a change of gravity.
Nicolas
The explanation of this is simple, we are composed of smaller particles, which are itself objects, so the loose of mass of an object actually is the separation of one object is two different ones.
Nicolas
But if you define an object because of its form and characteristics and not the amount of mass, then the object is the same but you have taken a part of it mass away.
Nicolas
Theo, weight =mass. gravity, here mass is fixed everywhere but gravity change in different places so weight change not mass.
ABHIJIT
yup weight changes and mass does not. That's why we're 1/3 our weight on the moon
clifford
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mass is fixed always while weight is dynamic
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thanks guys
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Yusuf Shuaibu, for water the Adhessive force between water molecules and glass is greater than the cohessive force between it's own molecules but for Mercury the cohessive force will be greater in comparison with adhessive force. For this water wet glass but Mercury does not.
ABHIJIT
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esther
wieght is the vector
ghulam
yes
Mohet
Yes
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what is specific heat capacity of watee
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Siyanbola
@siyanbola Resistance to acceleration
Dillon
The specific heat capacity of water is 1 calorie/1C°/ for 1 gram of water . it means that number of calories required to raise the temperature of 1g of water from 15 to 16C° is 1.
Khalil
understood?
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I think it's 1 in joules/kgC
Dillon
Anderson where are you from?. . &. what is your qualification
Khalil
Anderson i think you are right
Khalil
Micheal
lawrence
what is acceleration
lawrence
rate of change of velocity is acceleration
Khalil
its amount of heat to raise the temlrature through one kelvin of substance .
ghulam
The amount of heat energy required to raise the température of water by 1K
Cffrrcvccgg
infact a it must be a unit mass of water
Cffrrcvccgg
approximately equal to 4184J/Kg/K
Cffrrcvccgg
Just got through thermodynamics last semester. Also a change in 1 degree in celcius is equivalent to a change in 1 degree kelvin
Dillon
Also it's 1J/kgK or 4.184 cal/gK or /gC
Dillon
I think, at least
Dillon
Anderson are you good in physics numerical problems . if yes... . then plz help me. i am good in physics theory but nill in numericals
Khalil
I can try, what's the problem? I may be busy soon but I will reply today or tomorrow
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Numericals 🙄
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4200kJ/kgk...
Trevor
J
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SHM and uniform circular motion
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Thank God
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How do we begin sir
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i need help
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yes
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Am a Ghanaian
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But am in Nigeria
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Me too
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Nigeria too
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ok
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physics professor 'Where are from you' lol
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elucidate
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