The Limits of Sight The WorldView-4 satellite is a commercial - - PowerPoint PPT Presentation

▶
the limits of sight
SMART_READER_LITE
LIVE PREVIEW

The Limits of Sight The WorldView-4 satellite is a commercial - - PowerPoint PPT Presentation

Mar 22, 2023 424 likes •1.1k views

The Limits of Sight The WorldView-4 satellite is a commercial satellite designed to take surveillance photographs for sale and has been active since 2014. The cost for photos from the satellite archive is as low $14. The aperture of the camera on

slide-1
SLIDE 1

The Limits of Sight

The WorldView-4 satellite is a commercial satellite designed to take surveillance photographs for sale and has been active since 2014. The cost for photos from the satellite archive is as low $14. The aperture of the camera on the satellite is a = 1.1 m and the satellite operates L = 620 km above the Earth. What is the size of the smallest object visible to the camera? Visible light covers a range of wavelengths of λ ≈ 400 − 700 nm. What is the size of the smallest object visible to human eyes?

Jerry Gilfoyle Limits of Sight 1 / 59

slide-2
SLIDE 2

The Limits of Sight

The WorldView-4 satellite is a commercial satellite designed to take surveillance photographs for sale and has been active since 2014. The cost for photos from the satellite archive is as low $14. The aperture of the camera on the satellite is a = 1.1 m and the satellite operates L = 620 km above the Earth. What is the size of the smallest object visible to the camera? Visible light covers a range of wavelengths of λ ≈ 400 − 700 nm. What is the size of the smallest object visible to human eyes?

Jerry Gilfoyle Limits of Sight 1 / 59

slide-3
SLIDE 3

Waves

y = A sin (kx − ωt + φ0) Demo is here.

Jerry Gilfoyle Limits of Sight 2 / 59

slide-4
SLIDE 4

Electromagnetic Induction

Jerry Gilfoyle Limits of Sight 3 / 59

slide-5
SLIDE 5

Electromagnetic Induction

What happens when a static B field is near a coil? Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-6
SLIDE 6

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-7
SLIDE 7

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-8
SLIDE 8

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Current Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-9
SLIDE 9

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Current Is there an E field? Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-10
SLIDE 10

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Current Is there an E field? Yes Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-11
SLIDE 11

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Current Is there an E field? Yes A changing B field creates and E field. Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-12
SLIDE 12

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Current Is there an E field? Yes A changing B field creates and E field. How do you create a B field? Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-13
SLIDE 13

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Current Is there an E field? Yes A changing B field creates and E field. How do you create a B field? A current Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-14
SLIDE 14

Electromagnetic Induction

What happens when a static B field is near a coil? Nothing What happens when the magnet is pulled away? Current Is there an E field? Yes A changing B field creates and E field. How do you create a B field? A current A changing E field can create a changing B field. Lenz’s Law demo is here.

Jerry Gilfoyle Limits of Sight 3 / 59

slide-15
SLIDE 15

Electromagnetic Plane Waves - Lab 27, Act 3

1 Install Java if it is not already on your computer. See here. 2 Download a simulation of electromagnetic plane waves from here. To run ejs waves emwave.jar navigate to where you installed it and double-click on the icon. If that fails and you don’t get an interface like the one in the figure, consult your instructor. 3 The red lines in the window represent the electric field at different points in space and time. Configure the simulation by using the slider under Ey to set the y-component of the electric field to zero. Leave the z-component at the default value of 10. Click the check-box next to the B to turn on the simulation of the magnetic field (blue lines). 4 Click the start button at bottom-right to watch the wave move. Test the effect of changing the δ (phase shift), λ (wavelength), and ∆t (essentially the speed of the simulation). 5 Describe what happens to the electric and mag- netic fields and how they are related (i.e. When the E is large, what is the B field doing?). 6 What is the orientation of the E field? What is the orientation of the B field? Does E × B point in the direction of energy flow, as it did in the previous activity? 7 Consider two points on the electric field wave that are one-half wavelength apart. How are the E and

  • B vectors at the first point related to their part-

ners at the second point.. What will be the total electric and magnetic fields if two waves are added that are out of phase by one-half wavelength? 8 The electromagnetic wave in this simulation is called a “plane wave” because its wavefronts are shaped like planes. What is the orientation of these planes? (Perpendicular to E? Perpendicu- lar to the z axis? Something else?) Jerry Gilfoyle Limits of Sight 4 / 59

slide-16
SLIDE 16

Lenz’s Law

Jerry Gilfoyle Limits of Sight 5 / 59

slide-17
SLIDE 17

Electromagnetic Waves

Jerry Gilfoyle Limits of Sight 6 / 59

slide-18
SLIDE 18

Electromagnetic Spectrum

Jerry Gilfoyle Limits of Sight 7 / 59

slide-19
SLIDE 19

The Electric Field of Sunlight

The intensity of sunlight reaching the Earth is called the solar constant (which is not really constant) and has a value of Is = 1366 J/s − m2. What is the size of the electric field in sunlight? How does this compare with the typical fields we use in lab (| E| ≈ 10 N/C)?

Jerry Gilfoyle Limits of Sight 8 / 59

slide-20
SLIDE 20

Lab Results

Video is here

Jerry Gilfoyle Limits of Sight 12 / 59

slide-21
SLIDE 21

Water Waves

The videos are here and here. The simulation is here.

Jerry Gilfoyle Limits of Sight 13 / 59

slide-22
SLIDE 22

Double Slit Interference

Jerry Gilfoyle Limits of Sight 14 / 59

slide-23
SLIDE 23

d P r r D

1 2

y Incident Wavefronts Screen

Double Slit Interference

Jerry Gilfoyle Limits of Sight 15 / 59

slide-24
SLIDE 24

r

1

r2 d

Double Slit Interference

D Screen P α α θ δ y

Jerry Gilfoyle Limits of Sight 16 / 59

slide-25
SLIDE 25

r

1

r2 d

Double Slit Interference

θ δ θ

Jerry Gilfoyle Limits of Sight 17 / 59

slide-26
SLIDE 26

X-Ray Interference

A beam of X-rays with a wavelength λ = 2.10 × 10−11 m is incident on a thin slab of NaCl, a crystalline solid. A detector is located on a track D = 1.70 m downstream from the target and the first peak in the interference pattern is at a perpendicular distance y1 = 0.12 m from the central axis. What is the interatomic spacing of NaCl?

peaks α (λ=1.54

0.1 0.2 0.3 0.4 0.5 0.6

Intensity (counts/10 sec) Position (m) angstroms)

Jerry Gilfoyle Limits of Sight 18 / 59

slide-27
SLIDE 27

Rapidly Time-Varying Intensity Pattern

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time sin2(kr - ω t + ϕ 2 ) ω ϕ

Jerry Gilfoyle Limits of Sight 19 / 59

slide-28
SLIDE 28

Rapidly Time-Varying Intensity Pattern

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time sin2(kr - ω t + ϕ 2 )

Time Average

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time sin2(kr - ω t + ϕ 2 )

Jerry Gilfoyle Limits of Sight 19 / 59

slide-29
SLIDE 29

Predicted Double Slit Interference Intensity Pattern

Angular Position Intensity

Jerry Gilfoyle Limits of Sight 20 / 59

slide-30
SLIDE 30

Measured Double Slit Interference Intensity Pattern

slit width = 0.08 mm separation = 0.25 mm

Jerry Gilfoyle Limits of Sight 21 / 59

slide-31
SLIDE 31

Double Slit Interference Intensity Pattern

Angular Position Intensity

Jerry Gilfoyle Limits of Sight 22 / 59

slide-32
SLIDE 32

Double Slit Interference

A laser beam is passed through two narrow slits and an interference pattern is thrown on a screen a distance D = 1.7 m away from the slits. The bright spots are ∆y = 0.1 m apart. What is the separation d of the slits? The light has a wavelength λ = 6.5 × 10−7 m.

x y d Intensity L Incoming Waves

∆y Jerry Gilfoyle Limits of Sight 23 / 59

slide-33
SLIDE 33

Interference

Angular Position Intensity

Diffraction

Angular Position Intensity

Jerry Gilfoyle Limits of Sight 24 / 59

slide-34
SLIDE 34

Guidance for the Diffraction Lab (Lab 29)

1 For Activity 1 of Lab 29 you will need the same interference data you

had in Lab 28. Just download the Excel data file for Lab 28 from the lab schedule page at the following address

https://facultystaff.richmond.edu/~ggilfoyl/genphys/132/132introS20/ introS20.html#labs

and use that to fill in the table in Activity 1 for Lab 29.

2 For Activity 2 of Lab 29 use the Excel data set available at the Lab

29 listing on the lab schedule.

Jerry Gilfoyle Limits of Sight 25 / 59

slide-35
SLIDE 35

Diffraction

a = 0.16 mm

Jerry Gilfoyle Limits of Sight 26 / 59

slide-36
SLIDE 36

Diffraction

a Incident Waves

Jerry Gilfoyle Limits of Sight 27 / 59

slide-37
SLIDE 37

a Incident Waves θ θ a 2 sin δ= θ a 2

Jerry Gilfoyle Limits of Sight 28 / 59

slide-38
SLIDE 38

Diffraction

a Incident Waves a 2 sin δ= θ a 2

Jerry Gilfoyle Limits of Sight 29 / 59

slide-39
SLIDE 39

Diffraction

a Incident Waves a 2 sin δ= θ a 2

Jerry Gilfoyle Limits of Sight 30 / 59

slide-40
SLIDE 40

Diffraction

a 3 sin δ= θ a Incident Waves θ θ θ θ a/3

Jerry Gilfoyle Limits of Sight 31 / 59

slide-41
SLIDE 41

Diffraction

a 3 sin δ= θ a Incident Waves a/3

Jerry Gilfoyle Limits of Sight 32 / 59

slide-42
SLIDE 42

Diffraction

a Incident Waves a 4 sin δ= θ θ θ θ θ a/4

Jerry Gilfoyle Limits of Sight 33 / 59

slide-43
SLIDE 43

Diffraction

a Incident Waves a 4 sin δ= θ a/4

Jerry Gilfoyle Limits of Sight 34 / 59

slide-44
SLIDE 44

Diffraction

A laser beam of wavelength λ = 6328 ˚ A is shone on a single slit of width a = 1.0 mm. If a screen is placed a distance L = 0.40 m away, then how far from the central maximum are the first two dark spots on each side of the central maximum?

x y a Intensity L Incoming Waves

Jerry Gilfoyle Limits of Sight 35 / 59

slide-45
SLIDE 45

Diffraction Equation

I = Im sin α α 2 = Im

  • sin

πa

λ sin θ

  • πa

λ sin θ

2 α = πa λ sin θ θ ≡ angular position

Jerry Gilfoyle Limits of Sight 36 / 59

slide-46
SLIDE 46

L’Hopital’s Rule

If f (a) = g(a) = 0 and lim

x→a+

f ′(x) g′(x) = A then lim

x→a+

f (x) g(x) = A

Jerry Gilfoyle Limits of Sight 37 / 59

slide-47
SLIDE 47

The Diffraction Function

x 1 2 3 4 5 6 7 8 9 f(x)

  • 1
  • 0.5

0.5 1 1.5 2

green - 1/x red - sin(x) blue - sin(x)/x

Jerry Gilfoyle Limits of Sight 38 / 59

slide-48
SLIDE 48

Interference

Angular Position Intensity

Diffraction

Angular Position Intensity

Jerry Gilfoyle Limits of Sight 39 / 59

slide-49
SLIDE 49

Interference and Diffraction

Angular Position Intensity Angular Position Intensity

Jerry Gilfoyle Limits of Sight 42 / 59

slide-50
SLIDE 50

Defining the Limits of Sight-1

Demo is here

Jerry Gilfoyle Limits of Sight 43 / 59

slide-51
SLIDE 51

Defining the Limits of Sight-2

See more here.

Jerry Gilfoyle Limits of Sight 44 / 59

slide-52
SLIDE 52

Defining the Limits of Sight-2

See more here.

Jerry Gilfoyle Limits of Sight 44 / 59

slide-53
SLIDE 53

The Limits of Sight

The WorldView-4 satellite is a commercial satellite designed to take surveillance photographs for sale and has been active since 2014. The cost for photos from the satellite archive is as low $14. The aperture of the camera on the satellite is a = 1.1 m and the satellite operates L = 620 km above the Earth. What is the size of the smallest object visible to the camera? Visible light covers a range of wavelengths of λ ≈ 400 − 700 nm. What is the size of the smallest object visible to human eyes?

Jerry Gilfoyle Limits of Sight 45 / 59

slide-54
SLIDE 54

The Limits of Sight

The image below is the first picture ever taken by humans showing the event horizon of a black hole. The black hole has a mass of 6.5 billion Solar masses and resides at the center of the M87 galaxy in the Virgo galaxy cluster 55 million light-years from Earth (L = 5 × 1022 m. The image was made with radio waves with wavelengths that range from λl = 10−3 m to λh = 107 m. The angular size of the image is ∆θ ≈ 3 × 10−9deg. What is the best wavelength to use to make the image (high or low)? What is the size of the aperture on the ‘camera’?

Jerry Gilfoyle Limits of Sight 46 / 59

slide-55
SLIDE 55

The Limits of Sight

Intensity camera aperture L a focal plane screen

Jerry Gilfoyle Limits of Sight 50 / 59

slide-56
SLIDE 56

The Limits of Sight

R

θ

R

θ h Intensity camera aperture L a focal plane screen

Jerry Gilfoyle Limits of Sight 51 / 59

slide-57
SLIDE 57

The Diffraction Lab

a = 0.04 mm d = 0.125 mm

Jerry Gilfoyle Limits of Sight 52 / 59

slide-58
SLIDE 58

The Diffraction Lab

a = 0.04 mm d = 0.125 mm a = 0.04 mm

Jerry Gilfoyle Limits of Sight 52 / 59

slide-59
SLIDE 59

The Diffraction Lab

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 2 4 6 8 10 12 14 Position (m) Intensity Double-slit Interference, a = 0.04mm, d = 0.125 mm 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 1 2 3 4 5 Position (m) Intensity Single-slit Diffraction, a = 0.04 mm

Jerry Gilfoyle Limits of Sight 53 / 59

slide-60
SLIDE 60

The Diffraction Lab

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Double-slit Interference, a = 0.04mm, d = 0.125 mm

θ = arctan y

L

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Single-slit Diffraction, a = 0.04 mm

θ = arctan y

L

  • θ

Jerry Gilfoyle Limits of Sight 54 / 59

slide-61
SLIDE 61

The Diffraction Lab

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Double-slit Interference, a = 0.04mm, d = 0.125 mm

θ = arctan y

L

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Single-slit Diffraction, a = 0.04 mm

θ = arctan y

L

  • Green - single-slit diffraction

Blue - double-slit interference a = 0.04 mm d = 0.125 mm

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity

Jerry Gilfoyle Limits of Sight 54 / 59

slide-62
SLIDE 62

The Diffraction Lab

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Double-slit Interference, a = 0.04mm, d = 0.125 mm

θ = arctan y

L

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Single-slit Diffraction, a = 0.04 mm

θ = arctan y

L

  • Green - single-slit diffraction

Blue - double-slit interference a = 0.04 mm d = 0.125 mm

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity

Jerry Gilfoyle Limits of Sight 55 / 59

slide-63
SLIDE 63

The Diffraction Lab

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Double-slit Interference, a = 0.04mm, d = 0.125 mm

θ = arctan y

L

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity Single-slit Diffraction, a = 0.04 mm

θ = arctan y

L

  • a = 0.04 mm

d = 0.125 mm 2θp

  • 4
  • 2

2 4 2 4 6 8 10 12 14 θ (deg) Intensity

ame =

λ sin θp Jerry Gilfoyle Limits of Sight 56 / 59

slide-64
SLIDE 64

Atomic Spectroscopy -1

Light of wavelength λ = 600 nm is incident normally on a diffraction grating in a spectrometer. Two adjacent maxima occur at angles given by sin θ1 = 0.2 and sin θ2 = 0.3. The fourth-order maxima are missing. What is the separation between adjacent slits?

Jerry Gilfoyle Limits of Sight 57 / 59

slide-65
SLIDE 65

The Diffraction Grating

Jerry Gilfoyle Limits of Sight 58 / 59

slide-66
SLIDE 66

What You See.

Visible emission spectrum of helium.

Jerry Gilfoyle Limits of Sight 59 / 59