diffraction magnifying optical instrumentscrede/files/fall2014/optical...magnifying glass the goal...

$: Diffraction Magnifying Optical Instrumentscrede/FILES/FALL2014/Optical...Magnifying Glass The goal is to produce a greatly magniﬁed image at the retina. The largest clearly focused$
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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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)

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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, ...

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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, ...

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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”.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Outline



3 Magnifying Glass


CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Outline



3 Magnifying Glass


CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Magnifying Glass: Analysis


1so

+1si

=1f

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy



1so

−1

sN=

1f

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy



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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Outline



3 Magnifying Glass


CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Optical Telescopes

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Reflecting Mirror

Images can be formed through reflection or refraction.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Refracting Lens

Images can be formed through reflection or refraction.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Reflectors and Refractors

Both gather/focus electromagnetic radiation to be observedby human eyes or recorded on photographs or in computers.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Types of Reflecting Telescopes

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Keck TelescopeThe twin 10-m-diameteroptical and infraredtelescopes on MaunaKea in Hawai

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

The Hubble Space Telescope

The Hubble Space Telescope has several instruments:

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy


Cassegrain design• Telescope reflects light

from a 2.4-m-diameterprimary mirror

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy


The current detectors spanthe visible, near-infrared,and near ultraviolet regionsfrom about 100 nm (UV) to2200 nm (IR):

• Literally revolutionizedour view of the sky

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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)

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Various Telescopes: Mauna Kea

To the right of Keck domes: 8.3-m Subaru telescope⇒ Largest single mirror yet built

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

VLT Observatory

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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)

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

′′


CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Resolving Power


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

′′


CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Resolution

(a) 10′

(c) 5′′

(b) 1′

(d) 1′′

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Radio Telescopes

• Similar to optical reflecting telescopes➜ Prime Focus

• Less sensitive to imperfections (longer wavelengths)➜ Can be made very large

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Radio Telescopes


• Less sensitive to imperfections (longer wavelengths)➜ Must be made very large

(radio sources extremly faint, photons don’t carrymuch energy, sources often very distant)

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Radio Telescopes


• 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)

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Resolving Power


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

′′


CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Resolving Power


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

′′


CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Radio Astronomy

Longer wavelength means poor angular resolution.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

′′

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Interferometry

InterferometryInformation from severalwidely-spread telescopescombined as if they camefrom a single dish

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


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

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Interferometer

Complex interferencepattern as our Earthrotates and antennaetrack their target

A central computercombines and storesdata

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Interferometry


Resolutionwill be that of a large effective dishwhose diameter corresponds tolargest separation between dishes.

CollegePhysics B


Diffraction Grating


Near-Sighted Vision

MagnifyingGlass


Telescope Size

Resolving Power


Radio Astronomy

Interferometry


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)

diffraction magnifying optical instrumentscrede/files/fall2014/optical...magnifying glass the goal...

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