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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
College Physics B - PHY2054C
Diffraction
Optical Instruments
11/03/2014
My Office Hours:Tuesday 10:00 AM - Noon
206 Keen Building
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Suggested Topics
Announcement: Test 3 on Wednesday, November 5th.
• Thin-lens equation; construction of images for lenses.
• Reflection, Refraction (Snell’s Law) & diffraction
• Interference (thin films & double slits)
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Outline
1 DiffractionDouble-Slit ExperimentDiffraction Grating
2 Normal EyeFar-Sighted VisionNear-Sighted Vision
3 Magnifying Glass
4 TelescopesOptical TelescopesTelescope SizeResolving PowerLight-Gathering PowerRadio Astronomy
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Double-Slit Analysis
Determine the path length between each slit and the screen.
Assume W is very large. If the slits are separated by a distanced , then the difference in length between the paths of the tworays is:
∆L = d sin θ
Bright fringe:
d sin θ = m λ
m = 0, ± 1, ± 2, ...
Dark fringe:
d sin θ = (m +12)λ
m = 0, ± 1, ± 2, ...
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Diffraction Grating
An arrangement of many slits is called a diffraction grating.
Assumptions:
1 The slits are narrow.
2 The screen is very faraway.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Diffraction Grating
An arrangement of many slits is called a diffraction grating.
Assumptions:
1 The slits are narrow.
2 The screen is very faraway.
Since the screen is so faraway, the rays striking thescreen are approximatelyparallel making an angle θwith the horizontal axis:
∆L = d sin θ = m λ
Bright fringes:
m = 0, ± 1, ± 2, ...
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Diffraction Grating
The condition for bright fringes from a diffraction grating isidentical to the condition for constructive inteference from adouble slit:
• Overall intensity patterndepends on the numberof slits.
• The larger the numberof slits, the narrowerthe peaks.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Diffraction Grating
A diffraction grating will produce an intensity pattern on thescreen for each color:
• The different colors will have different angles anddifferent places on the screen.
• Diffraction gratings are widely used to analyze the colorsin a beam of light.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Diffraction and CDs
Light reflected from the arcs in a CD actsas sources of Huygens waves:
• The reflected waves exhibitconstructive interference atcertain angles.
• Light reflected from a CD hasthe colors “separated”.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Outline
1 DiffractionDouble-Slit ExperimentDiffraction Grating
2 Normal EyeFar-Sighted VisionNear-Sighted Vision
3 Magnifying Glass
4 TelescopesOptical TelescopesTelescope SizeResolving PowerLight-Gathering PowerRadio Astronomy
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Normal Eye
Light emanating from a pointon the object is focused toa corresponding point on theretina:
• Near-point distance, sN ,is the closest distance anobject can be that youcan focus (so ≈ 25 cm):
f eye, near ≈ 2.3 cm
• Objects nearer than thenear-point cannot befocused on the retina.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Normal Eye
Light emanating from a pointon the object is focused toa corresponding point on theretina:
• The normal eye can alsofocus on objects that arevery far away (so ∼ ∞):
f eye, distant ≈ 2.5 cm
• Eye must adjust its focallength to values betweensN and ∞. It does this byusing those muscles thatdeform and change theshape of the eye’s lens.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Far-Sighted Vision
The near-point distance is greater than for a normal eye:
• Objects located closer than the near-point distancecannot be focused.
➜ To compensate, a lenscan be placed in frontof the eye.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Far-Sighted Correction
The contact (or glasses) lens isthe first lens in the system.
For example, if a person’snear-point distance is 75 cm,then the corrective lens needsto be a converging lens withf lens = 38 cm:
1f lens
=1so
+1si
=1
+25 cm+
1−75 cm
f lens = 38 cm
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Refractive Power
The contact (or glasses) lens isthe first lens in the system.
In case a person’s near-pointdistance is greater than 75 cm,then the focal length of thecorrective lens needs to beshorter.
Refractive Power:
D =1
f lens[m−1]
For example:
1/f lens = 1/(0.38 m)
= 2.7 diopters
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Near-Sighted Vision
A near-sighted person is unable to focus light from distant ob-jects on the retina:
• The incoming rays from an object very far away areapproximately parallel to the axis (at infinity).
• A near-sighted eyeproduces an imagein front of the retina.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Near-Sighted Correction
The object at ∞ needs to focus onthe retina.
For example, if a person can focusobjects within 2.0 m, the correctivelens needs to be a diverging lenswith f lens = −2.0 m:
1f lens
=1so
+1si
=1∞
+1
−2 m
f lens = − 2 m
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Glasses
The eyeglass lens is a shortdistance in front of the eye,instead of touching it as withthe contact lens:
• The distance must betaken into account.
• This generally makesthe focal length of theeyeglasses about 10 %shorter than a contactlens.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Review Question 1The figures below show ray diagrams for different types ofcontact lenses. Which of the following statements correctlydescribes the images formed by these contact lenses?
A A contact lens always forms a real image.
B A contact lens always forms a virtual image.
C A contact lens can form a real or virtual image,depending on the type of lens.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Review Question 1The figures below show ray diagrams for different types ofcontact lenses. Which of the following statements correctlydescribes the images formed by these contact lenses?
A A contact lens always forms a real image.
B A contact lens always forms a virtual image.
C A contact lens can form a real or virtual image,depending on the type of lens.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Outline
1 DiffractionDouble-Slit ExperimentDiffraction Grating
2 Normal EyeFar-Sighted VisionNear-Sighted Vision
3 Magnifying Glass
4 TelescopesOptical TelescopesTelescope SizeResolving PowerLight-Gathering PowerRadio Astronomy
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Magnifying Glass
The goal is to produce a greatlymagnified image at the retina.
The largest clearly focused imagefor the unaided eye results whenthe object is at the near point:
• The object’s apparent sizewhen it is located at the nearpoint can be measured usingthe angle θ.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Magnifying Glass
The goal is to produce a greatlymagnified image at the retina.
The largest clearly focused imagefor the unaided eye results whenthe object is at the near point.
A magnifying glass produces amagnified (enlarged) image at thenear point of the eye:
• Object is positioned insidethe focal length of this lens.
• Angular magnification:
mθ =θM
θ=
hi
ho=
sN
so
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Magnifying Glass: Analysis
A magnifying glass produces amagnified (enlarged) image at thenear point of the eye:
1so
+1si
=1f
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Magnifying Glass: Analysis
A magnifying glass produces amagnified (enlarged) image at thenear point of the eye:
1so
−1
sN=
1f
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Magnifying Glass: Analysis
A magnifying glass produces amagnified (enlarged) image at thenear point of the eye:
1so
−1
sN=
1f
1so
=1f
+1
sN=
sN + ff sN
so =f sN
sN + f
mθ =sN
so=
sN
(sN f )/(sN + f )
=sN
f+ 1 ≈
sN
f
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Review Question 2A lens is used as a magnifier. Which of the following statementsis INCORRECT?
A The lens is convex.
B The refractive power of the lens is positive.
C The magnification is greatest when the eye focuses at thenear point.
D The focal length of the lens must be negative.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Review Question 2A lens is used as a magnifier. Which of the following statementsis INCORRECT?
A The lens is convex.
B The refractive power of the lens is positive.
C The magnification is greatest when the eye focuses at thenear point.
D The focal length of the lens must be negative.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Outline
1 DiffractionDouble-Slit ExperimentDiffraction Grating
2 Normal EyeFar-Sighted VisionNear-Sighted Vision
3 Magnifying Glass
4 TelescopesOptical TelescopesTelescope SizeResolving PowerLight-Gathering PowerRadio Astronomy
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Telescopes
Analogously to a bucket that collects only the rainfalling into it, a telescope’s mirror intercepts only thelight falling into it.
Telescopes intercept electromagnetic radiation.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Optical Telescopes
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Question 3
What is the resolution of a telescope?
A Its ability to see very faint objects
B Its ability to distinguish two adjacent objects close togetherin the sky
C Its ability to make distant objects appear much closer to us
D Its ability to separate light into its component colors foranalysis
E Its ability to focus more than just visible light for imaging
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Question 3
What is the resolution of a telescope?
A Its ability to see very faint objects
B Its ability to distinguish two adjacent objects close togetherin the sky
C Its ability to make distant objects appear much closer to us
D Its ability to separate light into its component colors foranalysis
E Its ability to focus more than just visible light for imaging
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Reflecting Mirror
Images can be formed through reflection or refraction.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Refracting Lens
Images can be formed through reflection or refraction.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Image Formation
Image can be formed by a mirroras rays of light coming from differentpoints on a distant object are focusedto slightly different locations.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Reflectors and Refractors
Both gather/focus electromagnetic radiation to be observedby human eyes or recorded on photographs or in computers.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Optical Telescopes
All large modern optical telescopes are reflectors
• Light travelling through lens is refracted differentlydepending on wavelength (chromatic aberration)
• Some light travelling through lens is absorbed
• Large lens can be very heavy, and can only besupported at edge.
• Lens needs two optically acceptable surfaces(accurately machined and polished); mirror onlyhas one surface.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Types of Reflecting Telescopes
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Keck TelescopeThe twin 10-m-diameteroptical and infraredtelescopes on MaunaKea in Hawai
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
The Hubble Space Telescope
The Hubble Space Telescope has several instruments:
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
The Hubble Space Telescope
Cassegrain design• Telescope reflects light
from a 2.4-m-diameterprimary mirror
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
The Hubble Space Telescope
The current detectors spanthe visible, near-infrared,and near ultraviolet regionsfrom about 100 nm (UV) to2200 nm (IR):
• Literally revolutionizedour view of the sky
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Telescope Size
To count as many as possibleof all the available photons,increase
1 exposure time.2 collection area.
Light-gathering power• Improves detail• Brightness proportional to
square of radius of mirror
⇐ (b) taken with telescopetwice the size of (a)
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Various Telescopes: Mauna Kea
To the right of Keck domes: 8.3-m Subaru telescope⇒ Largest single mirror yet built
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
VLT Observatory
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
VLT Observatory
European Southern Observatory, Atacama, Chile• World’s largest optical telescope• Comprises four 8.2-m reflecting telescopes
➜ In tandem, create the effective area of a single16-m mirror
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Resolving Power
Resolution:Ability of any device, such as a camera or a telescope,to form distinct, separate images of objects lying closetogether in the field of view.
Limiting Factor:Diffraction➜ Fuzziness(loss of resolution)
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Resolving Power
resolution (arc seconds) = 0.25 ·wavelength (µm)
diameter (m)
ExampleBest possible angular resolution of blue light (0.4 µm)using a 1-m telescope:
resolution (arc seconds) = 0.25 ·0.4 µm
1 m= 0.1
′′
Resolution:Ability of any device, such as a camera or a telescope,to form distinct, separate images of objects lying closetogether in the field of view.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Resolving Power
resolution (arc seconds) = 0.25 ·wavelength (µm)
diameter (m)
Another exampleBest possible angular resolution of infrared light(10 µm) using the same 1-m telescope:
resolution (arc seconds) = 0.25 ·10 µm
1 m= 2.5
′′
Resolution:Ability of any device, such as a camera or a telescope,to form distinct, separate images of objects lying closetogether in the field of view.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Resolution
(a) 10′
(c) 5′′
(b) 1′
(d) 1′′
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Light-Gathering Power
ExampleA 5-m telescope produces an image 25 times brighterthan a 1-m instrument because it has 52 = 25 timesthe collecting area.or in other words:A 5-m telescope produces an image 25 times fasterthan a 1-m device because it gathers energy at a rate25 times greater.
Increasing the collecting area:The observed brightness of an astronomical object isdirectly proportional to the area of the telescope’s mirrorand hence to the square of the mirror diameter.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Radio Telescopes
• Similar to optical reflecting telescopes➜ Prime Focus
• Less sensitive to imperfections (longer wavelengths)➜ Can be made very large
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Radio Telescopes
• Similar to optical reflecting telescopes➜ Prime Focus
• Less sensitive to imperfections (longer wavelengths)➜ Must be made very large
(radio sources extremly faint, photons don’t carrymuch energy, sources often very distant)
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Radio Telescopes
• Similar to optical reflecting telescopes➜ Prime Focus
• Less sensitive to imperfections (longer wavelengths)➜ Must be made very large
World’s largest fully steerable radio telescope(105-m-diameter, National Radio Astronomy Observatory, WV)
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Arecibo Observatory
300-m-diameter dish at the National Astronomy andIonospheric Center near Arecibo, Puerto Rico
• Receivers suspended nearly 150 m above center
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Resolving Power
resolution (arc seconds) = 0.25 ·wavelength (µm)
diameter (m)
ExampleBest possible angular resolution of blue light (0.4 µm)using a 1-m telescope:
resolution (arc seconds) = 0.25 ·0.4 (µm)
1 (m)= 0.1
′′
Resolution:Ability of any device, such as a camera or a telescope,to form distinct, separate images of objects lying closetogether in the field of view.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Resolving Power
resolution (arc seconds) = 0.25 ·wavelength (µm)
diameter (m)
ExampleAngular resolution of radio radiation at a wavelengthof 3 cm using the 105-m telescope in West Virginia:
resolution (arc seconds) = 0.25 ·30, 000 (µm)
105 (m)≈ 71
′′
Resolution:Ability of any device, such as a camera or a telescope,to form distinct, separate images of objects lying closetogether in the field of view.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Radio Astronomy
Longer wavelength means poor angular resolution.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Radio Astronomy
Longer wavelength means poor angular resolution.However:
• Can observe 24 hours a day• Clouds, rain, and snow don’t interfere• Observations possible at entire different frequency
➜ Totally different information
Radio Galaxy Centaurus AResolution of the
• optical image is ≈ 1′′
• superimposed radiomap is 12
′′
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Interferometry
InterferometryInformation from severalwidely-spread telescopescombined as if they camefrom a single dish
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Interference
• Identical waves that overlap can interfere
• Interference is when the fields add or cancel• Adding fields ➜ Constructive Interference• Canceling fields ➜ Destructive Interference
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Interferometer
Complex interferencepattern as our Earthrotates and antennaetrack their target
A central computercombines and storesdata
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Interferometry
InterferometryInformation from severalwidely-spread telescopescombined as if they camefrom a single dish
Resolutionwill be that of a large effective dishwhose diameter corresponds tolargest separation between dishes.
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CollegePhysics B
DiffractionDouble-SlitExperiment
Diffraction Grating
Normal EyeFar-Sighted Vision
Near-Sighted Vision
MagnifyingGlass
TelescopesOptical Telescopes
Telescope Size
Resolving Power
Light-GatheringPower
Radio Astronomy
Interferometry
InterferometryInformation from severalwidely-spread telescopescombined as if they camefrom a single dish
VLA Interferometer• Located on the Plain of San
Augustin, New Mexico• Comprises 27 dishes spread
along a Y-shaped pattern about30 km across(resolution of few arc seconds)