5A1 Astrophysics Telescopes

1
5A-1 AstrophysicsTelescopes

• Astrophysics booklet pages 1 to 27

2
AQA A2 Specification
3
Lenses

• Lenses use the process of refraction to change
  the direction of light at their two surfaces.
• There are two types of lenses
• 1. CONVERGING - These make a parallel beam of
  light converge to a focus.
• 2. DIVERGING - These make a parallel beam of
  light spread out so that they appear to come
  fromconverge a focus.

4
Converging lens
5
Converging lens
With glass a converging lens has a convex shape.
6
Converging lens
With glass a converging lens has a convex shape.
centre of the lens
O
principal axis
converging lens
7
Converging lens
With glass a converging lens has a convex shape.
centre of the lens
O
principal axis
converging lens
8
Converging lens
With glass a converging lens has a convex shape.
Converging lens with a parallel beam of light
centre of the lens
O
principal axis
converging lens
9
Converging lens
With glass a converging lens has a convex shape.
Converging lens with a parallel beam of light
principal focus
centre of the lens
O
F
principal axis
converging lens
10
Converging lens
With glass a converging lens has a convex shape.
Converging lens with a parallel beam of light
principal focus
centre of the lens
O
F
principal axis
converging lens
focal length, f
11
Some definitions
The principal axis is a construction line that is
perpendicular to and passes through the centre of
the lens. The principal focus, F is the point
through which all rays travelling parallel to the
principal axis before refraction pass through
after refraction. The focal length, f is the
distance from the centre of the lens, O to the
principal focus, F.

12
Some definitions
The principal axis is a construction line that is
perpendicular to and passes through the centre of
the lens. The principal focus, F is the point
through which all rays travelling parallel to the
principal axis before refraction pass through
after refraction. The focal length, f is the
distance from the centre of the lens, O to the
principal focus, F.

13
Some definitions
The principal axis is a construction line that is
perpendicular to and passes through the centre of
the lens. The principal focus, F is the point
through which all rays travelling parallel to the
principal axis before refraction pass through
after refraction. The focal length, f is the
distance from the centre of the lens, O to the
principal focus, F.

14
Some definitions
The principal axis is a construction line that is
perpendicular to and passes through the centre of
the lens. The principal focus, F is the point
through which all rays travelling parallel to the
principal axis before refraction pass through
after refraction. The focal length, f is the
distance from the centre of the lens, O to the
principal focus, F.

15
Standard rays converging lens
(a) Rays incident parallel to the principal axis
pass through the principal focus after refraction.
principal focus
F
principal axis
16
Standard rays converging lens
(a) Rays incident parallel to the principal axis
pass through the principal focus after refraction.
principal focus
F
principal axis
17
Standard rays converging lens
(b) Rays passing through the centre of the lens
are not deviated.
centre of the lens
O
18
Standard rays converging lens
(b) Rays passing through the centre of the lens
are not deviated.
centre of the lens
O
19
Standard rays converging lens
(c) Rays passing through the principal focus
before refraction are refracted parallel to the
principal axis.
F
F
principal axis
20
Standard rays converging lens
(c) Rays passing through the principal focus
before refraction are refracted parallel to the
principal axis.
F
F
principal axis
21
Converging lens images
22
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
23
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
24
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
25
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
26
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
27
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
28
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
29
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
30
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
image
Uses Camera and Eye The image formed
is Smaller than the object (diminished) Betwe
en the F and 2F Inverted (upside down) Real
31
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
image
Uses Camera and Eye The image formed
is Smaller than the object (diminished) Betwe
en the F and 2F Inverted (upside down) Real
32
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
image
Uses Camera and Eye The image formed
is Smaller than the object (diminished) Betwe
en the F and 2F Inverted (upside down) Real
33
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
image
Uses Camera and Eye The image formed
is Smaller than the object (diminished) Betwe
en the F and 2F Inverted (upside down) Real
34
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
image
Uses Camera and Eye The image formed
is Smaller than the object (diminished) Betwe
en the F and 2F Inverted (upside down) Real
35
Converging lens images
1. Object more than twice the focal length
distant from a converging lens
object
2F
O
F
2F
F
image
Uses Camera and Eye The image formed
is Smaller than the object (diminished) Betwe
en the F and 2F Inverted (upside down) Real
(light rays travel to the image)
36
Converging lens images
2. Object between F and 2F
object
2F
F
2F
F
37
Converging lens images
2. Object between F and 2F
object
2F
F
2F
F
38
Converging lens images
2. Object between F and 2F
object
2F
F
2F
F
39
Converging lens images
2. Object between F and 2F
object
2F
F
2F
F
40
Converging lens images
2. Object between F and 2F
object
2F
F
2F
F
image
Use Projector The image formed is Larger
than the object (magnified) Beyond
2F Inverted Real
41
Converging lens images
2. Object between F and 2F
object
2F
F
2F
F
image
Use Projector The image formed is Larger
than the object (magnified) Beyond
2F Inverted Real
42
Converging lens images
2. Object between F and 2F
object
2F
F
2F
F
image
Use Projector The image formed is Larger
than the object (magnified) Beyond
2F Inverted Real (light rays travel to the
image)
43
Converging lens images
3. Object nearer than the principal focus
F
object
F
44
Converging lens images
3. Object nearer than the principal focus
F
object
F
45
Converging lens images
3. Object nearer than the principal focus
F
object
F
46
Converging lens images
3. Object nearer than the principal focus
F
object
F
47
Converging lens images
3. Object nearer than the principal focus
image
F
object
F
Uses Magnifying glass The image formed
is Larger than the object On the same side
of the lens as the object Upright Virtual
48
Converging lens images
3. Object nearer than the principal focus
image
F
object
F
Uses Magnifying glass The image formed
is Larger than the object On the same side
of the lens as the object Upright Virtual
49
Converging lens images
3. Object nearer than the principal focus
image
F
object
F
Uses Magnifying glass The image formed
is Larger than the object On the same side
of the lens as the object Upright Virtual
(light rays only appear to come from the image)
50
Real and virtual images
REAL images are formed where light rays cross
after refraction by a lens. Real images can be
cast onto a screen. Example A projector
image VIRTUAL images are formed where light
rays only appear to come from. A virtual image
cannot be cast onto a screen. Example The image
formed by a plane mirror or a magnifying glass
51
Real and virtual images
REAL images are formed where light rays cross
after refraction by a lens. Real images can be
cast onto a screen. Example A projector
image VIRTUAL images are formed where light
rays only appear to come from. A virtual image
cannot be cast onto a screen. Example The image
formed by a plane mirror or a magnifying glass
52
Real and virtual images
REAL images are formed where light rays cross
after refraction by a lens. Real images can be
cast onto a screen. Example A projector
image VIRTUAL images are formed where light
rays only appear to come from. A virtual image
cannot be cast onto a screen. Example The image
formed by a plane mirror or a magnifying glass
53
Real and virtual images
REAL images are formed where light rays cross
after refraction by a lens. Real images can be
cast onto a screen. Example A projector
image VIRTUAL images are formed where light
rays only appear to come from. A virtual image
cannot be cast onto a screen. Example The image
formed by a plane mirror or a magnifying glass
54
Real and virtual images
REAL images are formed where light rays cross
after refraction by a lens. Real images can be
cast onto a screen. Example A projector
image VIRTUAL images are formed where light
rays only appear to come from. A virtual image
cannot be cast onto a screen. Example The image
formed by a plane mirror or a magnifying glass
55
Scale diagram questions

• Draw scale ray diagrams to determine the position
  size, orientation and nature of the images formed
  by a converging lens
• (a) of focal length 20 cm of an object size 12 cm
  placed 60 cm from this lens.
• position 30 cm size 6 cm
• orientation inverted nature real
• (b) of focal length 12 cm of an object size 4 cm
  placed 8 cm from this lens.
• position 24 cm size 12 cm
• orientation upright nature virtual

56
The lens formula

• where
• u distance of an object along the principal
  axis from the centre of the lens
• v distance of the image along the principal
  axis from the centre of the lens
• f the focal length of a thin lens

57
Real is positive sign convention

• When using the lens formula
• Converging lens focal lengths and real image
  distances are POSITIVE numbers.
• Diverging lens focal lengths and virtual image
  distances are NEGATIVE numbers.

58
Question 1

• (1 / 30 ) (1 / v ) (1 / 10)
• 0.03333 (1 / v ) 0.1000
• (1 / v ) 0.1000 - 0.03333
• (1 / v ) 0.06667
• v 15.00
• Image distance 15 cm
• The image is also real as the value of v is
  positive.

• Calculate the image distance when an object is
  placed 30 cm away from a converging lens of focal
  length 10 cm.

59
Question 2

• (1 / 20 ) (1 / v ) (1 / 40)
• 0.05000 (1 / v ) 0.02500
• (1 / v ) 0.02500 - 0.05000
• (1 / v ) - 0.02500
• v - 40.00
• Image distance - 40 cm
• The image is also virtual as the value of v is
  negative.

• Calculate the image distance when an object is
  placed 20 cm away from a converging lens of focal
  length 40 cm.

60
Question 3

• A diverging lens has a negative focal length.
• (1 / u ) (1 / - 10 ) (1 / - 25)
• (1 / u ) - 0.1000 - 0.04000
• (1 / u ) - 0.04000 0.1000
• (1 / u ) 0.06000
• u 16.67
• Object distance 17 cm
• The object is REAL hence u is POSITIVE

• Calculate the object distance required for a
  diverging lens of focal length 25 cm to produce a
  virtual image at a distance of 10 cm.

61
Complete
62
Answers
Note It is possible in some circumtances to
have a virtual object
63
Magnification

• magnification (m) image size
• object size
• It can also be shown that m v
• u

64
Magnification question

• Calculate the magnification produced and the
  image size when an object of size 35 mm is placed
  6 cm away from a lens of focal length 5 cm.

Applying the lens formula (1 / u ) (1 / v )
(1 / f ) (1 / 6 ) (1 / v ) (1 / 5 ) (1 / v )
(1 / 5 ) ( 1 / 6) (1 / v ) 0.2000
0.1667 (1 / v ) 0.0333 v 30 cm

• m v / u
• 30 / 6
• magnification 5 x
• Therefore the image size
• 5 x 35 mm
• 175 mm

65
The power of a lens

• The power of a lens is a measure of how quickly
  it causes an initial parallel beam of light to
  converge to a focus.
• lens power 1 / focal length
• If the focal length is measured in metres then
  lens power is measured in dioptres (D)
• Converging lenses have positive powers, diverging
  lenses have negative powers.

66
Lens power questions

• Calculate
• (a) the power of a converging lens of focal
  length 20 cm.
• (b) the power of a diverging lens of focal length
  50 cm.
• (c) the foacl length of a lens of power 4.0 D

• lens power 1 / focal length
• (a) power 1 / 0.20m
• 5.0 dioptres
• (b) power 1 / - 0.50m
• - 2.0 dioptres
• (c) 4.0 1 / f
• f 1 / 4.0
• focal length 0.25 m (25 cm)

67
The refracting telescope
The refracting telescope consists of two
converging lenses. Light is collected by a wide,
long focal length objective lens. The image
formed by this lens is viewed through, and
further magnified by, a short focal length
eyepiece lens. When in normal adjustment the
distance between the two lenses is equal to the
sum of their focal lengths (fo fe ).
68
Ray diagram for a refracting telescope in normal
adjustment
69
The objective lens forms an inverted real image
between the lenses at their common focal planes.
The eyepiece lens acts like a magnifying glass
with this image. The final image, viewed by the
observer, is virtual, inverted and formed at
infinity. Once through the eyepiece lens, all the
light originally from the distant object passes
through a circular area called the eyering. This
is the best position for the pupil of the
observers eye.
70
Angular magnification
71
Magnifying power of a telescope
72
Reflecting telescopes
73
Newtonian reflecting telescope
74
Cassegrain reflecting telescope
75
Comparison of refracting and reflecting telescopes
76
Spherical aberation
77
Chromatic aberation
78
Diffraction of star light
79
Resolving power
80
Resolving power of a telescope
81
Rayleigh criterion
82
Charge coupled device
83
CCD Structure
84
CCD Operation
85
Quantum efficiency
86
Radio telescopes
87
I-R telescopes
88
U-V telescopes
89
X-ray telescopes
90
Internet Links

• Tiger image formation by a plane or curved mirror
  - NTNU
• Mirage of pig formed by a concave mirror -
  includes UTube clip - NTNU
• Geometric Optics with Lenses - PhET - How does a
  lens form an image? See how light rays are
  refracted by a lens. Watch how the image changes
  when you adjust the focal length of the lens,
  move the object, move the lens, or move the
  screen.
• Prism/Lens - no dispersive refraction and
  reflections - NTNU
• Lens images / ray diagrams - NTNU
• How an image is formed by a convex lens / effect
  of stopping down lens - NTNU
• Lens / mirror effect on a beam of light - NTNU
• Curved mirror images / ray diagrams - NTNU
• Resolution from two circular apertures - NTNU

91
Core Notes from the Student Guide pages 1 to 27
92
Notes from the Student Guide pages 1 to 61.1
Lenses

• xxx
• Try the summary questions on pages 5 6

93
Notes from the Student Guide pages 7 to 131.2
The Refracting Telescope

• xxx
• Try the summary questions on page 13

94
Notes from the Student Guide pages 14 to 171.3
Reflecting Telescopes

• xxx
• Try the summary questions on pages 16 17

95
Notes from the Student Guide pages 18 to 211.4
Resolving Power

• xxx
• Try the summary questions on page 21

96
Notes from the Student Guide pages 22 to 271.5
Telescopes Technology

• xxx
• Try the summary questions on page 27