3.23.2OPTICSOPTICS

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

• When a lens is converging, the focal length (f) will be positive +

• When a lens is diverging, the focal length (f) will be negative -

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 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.

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.

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.

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:

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 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?

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

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

Resolving Power Example Problem•What is the resolving power

of a 25.0 cm telescope?

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

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 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?

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 now 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.

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

heated objects, and if the telescope is warm it will emit many times more infrared radiation than that 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.

▫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 such wavelengths requires

telescopes to be 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, and an equatorial mounting with easy motion around a polar axis 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, computer

control of the shape of telescope mirrors, allows the use of thin, lightweight mirrors – 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 the correct the telescope image to 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.

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.