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TELESCOPESTELESCOPESINCREASE THE ANGLE

THAT AN OBJECT SUBTENDS AT THE EYE

REFRACTORS REFLECTORSTHE OBJECTIVE IS A LENS

THE OBJECTIVE IS A MIRROR

• NEWTONIAN• CASSEGRAIN

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MAGNIFYING POWERMAGNIFYING POWERMMDEFINITION

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eyethetoobjectfarthebysubtendedanglethe

eyethetoatformedimagefinalthebysubtendedangleTheM

The telescope is said to be in normal adjustment when the final image is formed at infinity

This allows a fair comparison of performance to be made between the telescope and the naked eye - which has to look at an object, which itself is at infinity.

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EXAMPLE

A telescope with a magnifying power of 40 is used to view the Moon which subtends an angle of 0.50 to the eye.What will the angle subtended to the eye by the final image, if the telescope is in normal adjustment?

The angle will be

40 x 0.50

= 200

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FORMATION OF THE FINAL IMAGE

Objective Eye Piece

Rays from bottom of object

Rays from top of object

Intermediate Image where focal points coincide

Fo & Fe

Rays emerge parallel because final image is at infinity

To top of final image at

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Objective Lens Eye Piece lens

MAGNIFYING POWER FORMULA

fo fe

h = height of intermediate image

For small angles in radiansofh

Guide ray

/

/

efh/

oe f

h

f

hM

/

h

f

f

hM o

e

/

e

o

ff

M When the telescope is in normal adjustment

h

and

TELESCOPE LENGTH = fTELESCOPE LENGTH = foo + f + fee

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The Eye Ring or Exit The Eye Ring or Exit PupilPupilThis is the image of the Objective Aperture in the Eyepiece Lens

Objective lens Eyepiece lens

object

Fe

EYE RING

RAY DIAGRAM CONSTRUCTION

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Objective lens Eyepiece lens

Guide line

Eye Ring

FORMATION OF THE EYE RINGFORMATION OF THE EYE RING

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Objective lens Eyepiece lens

Fe

u = fo + fe v

vffvuf eoe

11111

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eoe

o

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eeo

eoe ffff

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fffv

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Do

Do = Diameter of Objective Lens

DER

DER = Diameter of the Eye Ring

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eoe

fff

fff

u

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o

ER

o

e

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heightobjectheightimage

ff

m

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M BUT

Magnifying power MRingEyeofDiameter

ObjectiveofDiameterM

EYE RING EYE RING FORMULAFORMULA

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EXAMPLE 1EXAMPLE 1

A telescope consists of two convex lenses, one of focal length 500mm, the other of focal length 50mm. The telescope is in normal adjustment.

(a) What is the focal length of the eyepiece?

(b) What is the separation of the lenses?

(c) Where is the final image located?

(d) Is this image erect or inverted?

(e) What is the magnifying power?

(f) Where should the pupil of the eye be placed to obtain the best view through the telescope?

fe = 50 mm; fo = 500 mm

fe + fo = 50 + 500 = 550 mm

At infinity in normal adjustment

It is inverted

M = fo / fe = 500 50 = 10

u = 550 mm, fe = 50 mm , find v

55010

550111

5501

501111

ufv v = 55 mm

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EXAMPLE 2EXAMPLE 2

A small telescope, of length 330 mm, is rated as 10 x 50

(a) What does this mean?

(b) What is the focal length of the eyepiece?

(c) What is the focal length of the objective?

(d) What is diameter of its eye ring?

(e) What is the instrument’s relative light gathering potential?

M = 10 & the Diameter of the Objective is 50 mm

So fo= 11 fe. Then 11 fe = 330; fe = 30 mm33010 eo

e

o ffandff

fo = 300 mm

M = Do / DER ; so 10 = 50 DER ; Eye Ring Diameter = 10 mm

Diameter of Objective Diameter of Eye Ring = 50 10 = 5 times

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CHROMATIC CHROMATIC ABERRATIONABERRATIONLENSES ACT LIKE PRISMS AND DISPERSE LIGHT

A lens has a shorter focal length for blue light than it does for red

This causes image to be blurred and to have coloured edges

FBFB

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SPHERICAL SPHERICAL ABERRATIONABERRATIONOnly rays of light parallel and close to the principal axis pass through the focal point, F, of the lens.

Principal axis

F

Rays farther from the axis strike the lens with a greater angle of incidence and consequently have a greater angle of refraction.

USING A LENS WITH A WIDE APERTURE BLURS THE IMAGE SPHERICAL ABERRATION

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SPHERICAL MIRRORS ALSO SUFFER FROM SPHERICICAL ABERRATION

Ff

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PARABOLIC MIRRORS ELIMINATE SPHERICICAL ABERRATION

Ff

IN ADDITION MIRRORS DO NOT SUFFER FROM

CHROMATIC ABERRATION

ALL LARGE TELESCOPES ARE PARABOLIC REFLECTORS

i.e. There objective is a parabolic mirror

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NEWTONIAN NEWTONIAN REFLECTORREFLECTOR

Convex Eyepiece

Parabolic Concave Mirror

Plane Mirror at 450 to the axis

F

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CASSEGRAIN CASSEGRAIN REFLECTORREFLECTOR

Fsite of 1st intermediate image

Auxiliary convex mirror - in practice very much smaller than the objective

Parabolic Concave Objective

2nd intermediate image

Convex lens eyepiece, acts like a magnifying glass

The Final Image is at Infinity

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Advantages of ReflectorsAdvantages of Reflectors

• Less loss of light in reflection compared with refraction

• Do not suffer from chromatic aberration

• Parabolic reflectors do not suffer from spherical aberration

• Diameter can be much greater because a mirror - can it be supported

from behind - “glass sags” *• There is only one surface to be ground• No worry about trapped air bubbles in the glass

*Telescopes have large apertures

1. To gather more light

2. To increase their Resolving Power