3.2OPTICS

Optical Telescopes•Astronomers use telescopes to

gather more light from astronomical bodies.

•The larger the telescope, the more light it gathers.

•Optical telescopes can focus light into an image using either a lens or a mirror.

Refracting Telescopes• In a refracting telescope, the primary (objective) lens bends, or refracts,

light as it passes through the glass and brings it to a focus to form a small inverted image.

Reflecting Telescopes• In a reflecting telescope, the primary (objective) mirror – a concave piece

of glass with a reflective surface – forms an image by reflecting the light.▫ Almost all modern telescopes are reflecting.

Optical Telescopes• In either case, the focal

length is the distance from the lens or mirror to the focal point (intersection).▫Short-focal length lenses

and mirrors must be strongly curved.

▫ Long-focal length lenses and mirrors are less strongly curved.

Focal Length

Focal Length

Optical Telescopes• The image formed by

the primary lens or primary mirror of a telescope is small, inverted, and difficult to view directly.

• Astronomers use a small lens called the eyepiece to magnify the image and make it convenient to view.

Lenses

• Convex lenses are converging lenses; thicker across the middle and thinner at the edges.

• Concave lenses are diverging lenses; thinner across the middle and thicker at the edges.

Converging LensesConvex

Diverging LensesConcave

Lenses Double Convex

Plano Convex

Concavo

Convex

Double Concav

e

Plano Concav

e

Convexo

Concave

Double Convex

Double Concave

Plano ConvexConcavo Convex

Plano Concave Convexo Concave

Eye Conditions• Farsightedness is the difficulty

in seeing objects nearby.▫ Hyperopia

▫ Corrected through the use of convex (converging) lenses.

• Nearsightedness is the difficulty in seeing objects far away.▫ Myopia

▫ Corrected through the use of concave (diverging) lenses.

Converging LensesObject-Image Relations – Case 1

• THE OBJECT IS LOCATED BEYOND 2F

▫ Located between 2F and F point on other side▫ Inverted (upside-down)▫ Smaller

Magnification < 1▫ Real Image (side of lens opposite the object)

Converging LensesObject-Image Relations – Case 2

• THE OBJECT IS LOCATED AT 2F

▫ Located at 2F on other side▫ Inverted (upside-down)▫Same size

Magnification = 1▫Real image (side of lens opposite the object)

Converging LensesObject-Image Relations – Case 3

• THE OBJECT IS LOCATED BETWEEN 2F AND F

▫ Located beyond 2F on other side▫ Inverted (upside-down)▫ Larger

Magnification > 1▫ Real image (side of lens opposite the object)

Converging LensesObject-Image Relations – Case 4

• THE OBJECT IS LOCATED AT F

▫No image formed

Converging LensesObject-Image Relations – Case 5

• THE OBJECT IS LOCATED IN FRONT OF F

▫ Located somewhere on the same side of the lens as the object further from the lens

▫Upright▫ Larger

Magnification > 1▫Virtual image (object side of lens)

Diverging LensesObject-Image Relations

• IN EACH CASE

▫ Located somewhere on the same side of the lens as the object closer to the lens

▫ Upright▫ Smaller

Magnification < 1▫ Virtual image (object side of lens)

Equations

• F is + for a converging lens (convex)

• F is – for a diverging lens (concave)

• di is + for an image located on the opposite side of the lens as the object (real)

• di is – for an image located on the object’s side of the lens (virtual)

• hi is + for an upright image

• hi is – for an inverted image

F = focal length, distance from the lens to the focal point

do = distance from the lens to the object

di = distance from the lens to the image

hi = height of the image

ho = height of the object

Lens Equation

1/F = 1/do + 1/di

Magnification Equation

M = hi/ho = -di/do

Lens Example Problem 1• A 4.00 cm tall light bulb is placed a distance of 45.7 cm from a

double convex lens having a focal length of 15.2 cm. Determine the image distance and the image size.

di = 22.8 cm

hi = -1.99 cm

Lens Example Problem 2• A 4.00 cm tall light bulb is placed a distance of 35.5 cm from a

diverging lens having a focal length of -12.2 cm. Determine the image distance and the image size.

di = -9.08 cm

hi = 1.02 cm

Refracting Telescope Disadvantages• Refracting telescopes suffer from a distortion, limiting their

usefulness.

▫ When light is refracted (bent) through glass, shorter wavelengths bend more than longer wavelengths. Blue light (shorter λ) comes to focus closer to the lens than does red light

(longer λ).

▫ This color separation is known as chromatic aberration.

Chromatic Aberration Example

Correcting Chromatic Aberration• This problem can be improved, yet not entirely corrected.

▫ An achromatic lens, is a lens made in two pieces of two different kinds of glass that can bring any two colors to the same focus, but other colors remain slightly out of focus. Difficult, expensive to produce.

The Powers of a Telescope• Astronomers build large telescopes because a telescope can

aid your eyes in 3 ways:▫ The 3 Powers of a Telescope

• The first two are the most important of these powers because they depend on the diameter of the telescope.

1. LIGHT GATHERING POWER2. RESOLVING POWER

3. MAGNIFYING POWER

Light-Gathering Power• Light-gathering power (LGP) refers to

the ability of a telescope to collect light.▫ Catching light in a telescope is like

catching rain in a bucket – the bigger the bucket, the more rain it catches.

• LGP is proportional to the area of the telescope objective.▫ Lens or mirror with a large area gathers

a large amount of light.

▫ Area of a circular lens or mirror:

A = πr2 = π (D/2)2

Light-Gathering Power

•To compare the relative LGP of two telescopes, A and B for example, you can calculate the ratio of the areas of their objectives, which reduces the ratio of their diameters (D) squared:

LGP Equation

LGPA/LGPB = (DA/DB)2

LGP Example Problem

•Suppose you compared a telescope 24 cm in diameter with a telescope 4 cm in diameter. How much more light does the larger telescope gather?

36 times more light

Resolving Power• The second power, resolving power,

refers to the ability of a telescope to reveal fine detail.

• Because light acts as a wave, it produces a small diffraction fringe around every point of light in the image can’t see detail smaller than fringe.

• Can estimate resolving power by calculating the angular distance between two stars.▫ “ Resolved” = “Separated”

Resolving Power

Details become clearer in the

Andromeda galaxy as the resolving power (angular resolution)

is improved :

a) 10’b) 1’c) 5”d) 1”

Resolving Power

•The resolving power (α) in arc seconds, equals 11.6 divided by the diameter of the telescope in centimeters:

Resolving Power Equation

α = 11.6/D

Resolving Power Example• What is the resolving power of a 25.0

cm telescope?

• This is the best possible resolving power for this particular telescope, however other factors can influence it:▫ Lens quality▫ Atmospheric conditions

0.464” (arc seconds)

Magnifying Power of a Telescope• The magnifying power of a telescope is its ability to make

the image bigger.▫ Least important of the 3 powers.

• You can change the magnification by changing the eyepiece.

• Calculated by dividing the focal length of the objective (telescope) by the focal length of the eyepiece:

Magnifying Power Equation

M = Fo/Fe

Magnifying Power Example Problem

•What is the magnification of a telescope having an objective with a focal length of 80 cm using an eyepiece whose focal length is 0.5 cm?

160 times

6.4 mm 9.7 mm 12.4 mm 15 mm 20 mm

26 mm 32 mm 40 mm 56 mm

Meade Series 4000 Super Plossl Telescope

Eyepieces

Light Pollution• The quest for light-gathering power

and high resolution explains why nearly all major observatories are located far from big cities and usually on high mountains.

• Astronomers avoid cities because light pollution, the brightening of the night sky by light scattered from artificial outdoor lighting, can make it impossible to see faint objects.

Paranal Observatory

Location: Chile

Altitude: 2635 m (8660 ft)

Nearest city: 75 miles

Buying Telescopes• Important things to consider when purchasing a

telescope, assuming you have a fixed budget:

1. Highest-quality optics▫Using plastic lenses won’t help you see much.

2. Large diameter▫You want to maximize light-gathering power.

3. Reflecting rather than refracting▫Refracting telescopes suffer optical distortions.

4. Solid mounting device▫Needs to be steady so you can easily point at objects.

Observing Beyond the Visible Spectrum• Beyond the red end (700 nm) of

the visible spectrum, some infrared radiation leaks through atmospheric windows ranging from wavelengths of 1200 nm to 20,000 nm.

• Most infrared radiation gets absorbed in the atmosphere (water vapor, CO2, ozone).▫ Infrared telescopes on the summit

(13,800 ft) of Mauna Kea in Hawaii are above most of the atmospheric components. Mauna Kea Telescope

Observing Beyond the Visible Spectrum• NASA is currently testing the

Stratospheric Observatory for Infrared Astronomy (SOFIA), a Boeing 747SP that will carry a 2.5 m telescope, control systems, and a team of astronomers, technicians, and educators in the dry fringes of the atmosphere.

• Once at a designated altitude (>40,000 ft), they can open a door above the telescope and make infrared observations for hours as the plane flies a precisely calculated path.

Observing Beyond the Visible Spectrum• To reduce internal noise, the light-sensitive

detectors in astronomical telescopes are cooled to very low temperatures, usually with liquid nitrogen.▫ Detectors usually consist of HgCdTe (Mercury

Cadmium Telluride).

• Especially necessary for a telescope observing infrared wavelengths.▫ Infrared radiation is emitted by heated objects,

and if the detectors are warm, they will emit many times more infrared radiation than what is coming from a distant object.

Observing Beyond the Visible Spectrum

• Beyond the other end of the visible spectrum, astronomers can observe in the near-ultraviolet at wavelengths of about 290 to 400 nm.▫ Your eyes cannot detect this radiation, but it

can be recorded by special detectors.

▫ Wavelengths shorter than 290 nm, the far-ultraviolet, are completely absorbed by the ozone layer extending from about 15 km. to 30 km. above Earth’s surface. To observe in the far-UV or beyond at X-rays and

gamma rays requires telescopes to be positioned in space.

Modern Astronomical Telescopes•Traditional telescopes use

large, solid, heavy mirrors to focus starlight to a prime focus, or by using a secondary mirror, to a Cassegrain focus.

▫Some small telescopes may have a Newtonian focus or a Schmidt-Cassegrain focus.

Cassegrain focus

Primary mirror

Secondary mirror

Prime focus

Mayall Telescope

• 4 meters

• Kitt Peak National Observatory, Arizona

• Can be used at the prime focus or the Cassegrain focus

Modern Astronomical Telescopes• Telescopes must have a sidereal

drive, to follow the stars an equatorial mounting with easy motion around a polar axis (23.5°) is the traditional way.

• Today, astronomers can build simpler, lighter-weight telescopes on alt-azimuth mountings that depend on computers to follow the motion of the stars.

Active Optics• Active Optics involves computer

control of the shape of telescope mirrors, allowing them to be thin and lightweight – either floppy mirrors or segmented mirrors.▫ Reducing the weight of the

mirror reduces the weight of the rest of the telescope makes it stronger and less expensive. Thin mirrors also cool faster at

nightfall and produce better images less distortion from uneven expansion and contraction.

SEGMENTED MIRROR

FLOPPY MIRROR

Gran Telescopio Canarias

• Actuators mechanical devices for moving or controlling a

system

• Keeps mirrors in their optimal shape

Adaptive Optics• Adaptive Optics uses high-speed computers to monitor the

distortion produced by turbulence in Earth’s atmosphere and to correct the telescope image and sharpen a fuzzy blob into a crisp picture.

▫ Don’t confuse adaptive optics with the slower-speed active optics that controls the overall shape of a telescope mirror.

Adaptive Optics• In the image below, a laser produces an artificial star allowing astronomers to gauge

atmospheric conditions and pass that information to a computer that modifies the telescope mirror thousands of times per second to compensate for poor seeing.

Examples of Modern Telescope Design

VLTParanal Observatory - Chile

Gran Telescopio Canarias Canary Islands – NW coast of Africa

Large Binocular Telescope Arizona

Examples of Modern Telescope Design

Giant Magellan Telescope Planned location: Andes Mountains

Thirty Meter Telescope Planned location: Mauna Kea

E-ELTPlanned location: TBD

Interferometry• Astronomers have been

able to achieve very high resolution by connecting multiple telescopes together to work as if they were a single telescope.

• This method of synthesizing a larger telescope is known as interferometry.▫ Light from separate

telescopes must be combined as if it had been collected by a single large mirror.

Imaging Systems• The original imaging device in astronomy was the

photographic plate.▫ Have been replaced by electronic imaging systems.

• Charged-coupled devices (CCDs), which are specialized computer chips containing millions of microscopic light detectors arranged in an array about the size of a postage stamp, are common.▫ Images are stored as numbers in computer memory.

▫ Astronomers can manipulate images to bring out otherwise invisible details by producing false-color images. Different colors represent different levels of intensity and

are not necessarily the true colors of the object.