Wave Interference and Diffraction
Part 3: Telescopes and Interferometry
PHY 2049
Physics 2 with Calculus
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Telescopes: Purpose is Light Collection
ÎPupil
of eye D ≈ 8mm (in very dim light)
ÎLargest
ÎRatio
telescope (Keck) has D = 10m
of areas = (10/0.008)2 = 1.5 × 106
‹ Can
collect light for hours rather than 0.1 sec
‹ More sensitive light collectors (CCD arrays)
‹ Thus telescopes are several billion times more sensitive
ÎCan
see near the end of the known universe
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Telescope Construction
ÎAll
large telescopes are reflectors: Why?
‹ Mirror
only needs single high quality surface
(lens needs perfect volume since light passes through it)
‹ No chromatic aberration (no lens for refracting)
‹ Full support for mirror, no distortion from moving
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Keck Telescope (D = 10 m)
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Keck Hexagonal Mirror (36 Segments)
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Keck Primary Mirror (Each segment 1.8 m)
Hole
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Main Limitation on Earth: Atmosphere
ÎAir
cells in atmosphere
‹ Air
cells above telescope mirror cause distortion of light
‹ Best performance is ≈ 0.25 – 0.5″ resolution on the ground
‹ This is why telescopes are sited on high mountains
ΓAdaptive
optics” just beginning to offset this distortion
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Diffraction Through Circular Opening
Intensity of light after passing
through a circular opening.
Spreading caused by diffraction.
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Theoretical Performance Limit: Diffraction
ÎLight
rays hitting mirror spread due to diffraction
‹ These
rays interfere, just like for single slit
‹ Calculation a little different because of circular shape
‹ Angle of spread Δθ = 1.22λ/D (D = diameter)
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Example: Optical Telescopes
ÎKeck
telescope: D = 10m, λ = 550nm
‹ Δθ
= 1.22 × 550 × 10-9 / 10 = 6.7 × 10-8 rad = 0.014”
‹ Compare this to 0.25” – 0.5” from atmosphere
ÎHubble
space telescope: D = 2.4m, λ = 550nm
‹ Δθ
= 1.22 × 550 × 10-9 / 2.4 = 2.8 × 10-7 rad = 0.058”
‹ But actually can achieve this resolution!
ÎRayleigh
criterion
objects separated by Δθ < 1.22λ/D cannot be distinguished
‹ An approximate rule, shows roughly what is possible
‹ Two
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Single Star
Units in multiples of λ/D
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Two Stars: Separation = 2.0
Units in multiples of λ/D
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Two Stars: Separation = 1.5
Units in multiples of λ/D
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Two Stars: Separation = 1.22
Units in multiples of λ/D
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Two Stars: Separation = 1.0
Units in multiples of λ/D
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Two Stars: Separation = 0.8
Units in multiples of λ/D
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Two Stars: Separation = 0.6
Units in multiples of λ/D
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Two Stars: Separation = 0.4
Units in multiples of λ/D
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Single Star
Units in multiples of λ/D
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