# 26.5 Telescopes  (Page 2/4)

 Page 2 / 4

The image in most telescopes is inverted, which is unimportant for observing the stars but a real problem for other applications, such as telescopes on ships or telescopic gun sights. If an upright image is needed, Galileo’s arrangement in [link] (a) can be used. But a more common arrangement is to use a third convex lens as an eyepiece, increasing the distance between the first two and inverting the image once again as seen in [link] .

A telescope can also be made with a concave mirror as its first element or objective, since a concave mirror acts like a convex lens as seen in [link] . Flat mirrors are often employed in optical instruments to make them more compact or to send light to cameras and other sensing devices. There are many advantages to using mirrors rather than lenses for telescope objectives. Mirrors can be constructed much larger than lenses and can, thus, gather large amounts of light, as needed to view distant galaxies, for example. Large and relatively flat mirrors have very long focal lengths, so that great angular magnification is possible.

Telescopes, like microscopes, can utilize a range of frequencies from the electromagnetic spectrum. [link] (a) shows the Australia Telescope Compact Array, which uses six 22-m antennas for mapping the southern skies using radio waves. [link] (b) shows the focusing of x rays on the Chandra X-ray Observatory—a satellite orbiting earth since 1999 and looking at high temperature events as exploding stars, quasars, and black holes. X rays, with much more energy and shorter wavelengths than RF and light, are mainly absorbed and not reflected when incident perpendicular to the medium. But they can be reflected when incident at small glancing angles, much like a rock will skip on a lake if thrown at a small angle. The mirrors for the Chandra consist of a long barrelled pathway and 4 pairs of mirrors to focus the rays at a point 10 meters away from the entrance. The mirrors are extremely smooth and consist of a glass ceramic base with a thin coating of metal (iridium). Four pairs of precision manufactured mirrors are exquisitely shaped and aligned so that x rays ricochet off the mirrors like bullets off a wall, focusing on a spot.

A current exciting development is a collaborative effort involving 17 countries to construct a Square Kilometre Array (SKA) of telescopes capable of covering from 80 MHz to 2 GHz. The initial stage of the project is the construction of the Australian Square Kilometre Array Pathfinder in Western Australia (see [link] ). The project will use cutting-edge technologies such as adaptive optics    in which the lens or mirror is constructed from lots of carefully aligned tiny lenses and mirrors that can be manipulated using computers. A range of rapidly changing distortions can be minimized by deforming or tilting the tiny lenses and mirrors. The use of adaptive optics in vision correction is a current area of research.

## Section summary

• Simple telescopes can be made with two lenses. They are used for viewing objects at large distances and utilize the entire range of the electromagnetic spectrum.
• The angular magnification M for a telescope is given by
$M=\frac{\theta \prime }{\theta }=-\frac{{f}_{\text{o}}}{{f}_{\text{e}}}\text{,}$
where $\theta$ is the angle subtended by an object viewed by the unaided eye, $\theta \prime$ is the angle subtended by a magnified image, and ${f}_{\text{o}}$ and ${f}_{\text{e}}$ are the focal lengths of the objective and the eyepiece.

## Conceptual questions

If you want your microscope or telescope to project a real image onto a screen, how would you change the placement of the eyepiece relative to the objective?

## Problem exercises

Unless otherwise stated, the lens-to-retina distance is 2.00 cm.

What is the angular magnification of a telescope that has a 100 cm focal length objective and a 2.50 cm focal length eyepiece?

$-\text{40}\text{.}0$

Find the distance between the objective and eyepiece lenses in the telescope in the above problem needed to produce a final image very far from the observer, where vision is most relaxed. Note that a telescope is normally used to view very distant objects.

A large reflecting telescope has an objective mirror with a $\text{10}\text{.}0 m$ radius of curvature. What angular magnification does it produce when a $3\text{.}\text{00 m}$ focal length eyepiece is used?

$-1\text{.}\text{67}$

A small telescope has a concave mirror with a 2.00 m radius of curvature for its objective. Its eyepiece is a 4.00 cm focal length lens. (a) What is the telescope’s angular magnification? (b) What angle is subtended by a 25,000 km diameter sunspot? (c) What is the angle of its telescopic image?

A $7.5×$ binocular produces an angular magnification of $-7\text{.}\text{50}$ , acting like a telescope. (Mirrors are used to make the image upright.) If the binoculars have objective lenses with a 75.0 cm focal length, what is the focal length of the eyepiece lenses?

$+\text{10.0 cm}$

Consider a telescope of the type used by Galileo, having a convex objective and a concave eyepiece as illustrated in [link] (a). Construct a problem in which you calculate the location and size of the image produced. Among the things to be considered are the focal lengths of the lenses and their relative placements as well as the size and location of the object. Verify that the angular magnification is greater than one. That is, the angle subtended at the eye by the image is greater than the angle subtended by the object.

What is conductivity
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
Cffrrcvccgg
how to find magnitude and direction
how to caclculate for speed
Arjune
derivation of ohms law
derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
is there really flow of electrons exist?
babar
Yes It exists
Cffrrcvccgg
explain plz how electrons flow
babar
if electron flows from where first come and end the first one
babar
an electron will flow accross a conductor because or when it posseses kinectic energy
Cffrrcvccgg
electron can not flow jist trasmit electrical energy
ghulam
free electrons of conductor
ankita
electric means the flow heat current.
electric means the flow of heat current in a circuit.
Serah
What is electric
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
why we cannot use DC instead of AC in a transformer
becuse the d .c cannot travel for long distance trnsmission
ghulam
what is physics
branch of science which deals with matter energy and their relationship between them
ghulam
Life science
the
what is heat and temperature
how does sound affect temperature
sound is directly proportional to the temperature.
juny
how to solve wave question
I would like to know how I am not at all smart when it comes to math. please explain so I can understand. sincerly
Emma
Just know d relationship btw 1)wave length 2)frequency and velocity
Talhatu
First of all, you are smart and you will get it👍🏽... v = f × wavelength see my youtube channel: "mathwithmrv" if you want to know how to rearrange equations using the balance method
PhysicswithMrV
nice self promotion though xD
Beatrax
thanks dear
Chuks
hi pls help me with this question A ball is projected vertically upwards from the top of a tower 60m high with a velocity of 30ms1.what is the maximum height above the ground level?how long does it take to reach the ground level?
mahmoud
what is scalar quantities
babatunde
scaler quantity are quanties that have only direction and no magnitude
Natsu
ice Point
babatunde
please guys help, what is the difference between concave lens and convex lens
convex lens brings rays of light to a focus while concave diverges rays of light
Christian
for mmHg to kPa yes
Matthew
it depends on the size
Vincent
a lens which diverge the ray of light
rinzuala
concave diverges light
Matthew
thank you guys
Vincent
A diverging lens
Yusuf
What is isotope
Yusuf
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
Karthi
what is wire wound resistors?