Electromagnetic (EM) spectrum
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Electromagnetic (EM) spectrum. non-ionizing radiation. ionizing radiation. 1 EHz 10 18. 1 Hz. 1 kHz 10 3. 1 MHz 10 6. 1 GHz 10 9. 1 THz 10 12. 1 PHz 10 15. 300 Mm. 300 km. 300 m. 0.3 m. 0.3 mm. 300 nm. 0.3 nm. electric power supply. cellular phone.

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Electromagnetic (EM) spectrum

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Electromagnetic em spectrum

Electromagnetic (EM) spectrum

non-ionizing radiation

ionizing radiation

1 EHz

1018

1 Hz

1 kHz

103

1 MHz

106

1 GHz

109

1 THz

1012

1 PHz

1015

300 Mm

300 km

300 m

0.3 m

0.3 mm

300 nm

0.3 nm

electric

power supply

cellular

phone

750 nm

400 nm

g-rays

X-RAY/CT

MRI

PET

ULTRASOUND — not EM radiation


Blackbody radiation

0

0

1

2

3

4

5

6

7

8

9

x 1014

BLACKBODY RADIATION

4000 K

spectral energy density

3000 K

2000 K

1000 K

frequency (Hz)


Electromagnetic em spectrum

FUNCTIONAL FORMS OF EM RADIATION

IT COULD BE A DIRAC DELTA PULSE: d (t-t1)

IT COULD BE A HARMONIC WAVE: sin (w t)

ARBITRARY FUNCTION OF t


Electromagnetic em spectrum

HARMONIC WAVES

sin (wt) = sin (w (t-r/c)) =

sin (wt-wr/c)=

sin (wt –kr)

Temporal frequency in rad/s

w

Spatial frequency in rad/m

k = w/c

frequency in cycles/sec

n = w/2p

Wave number (m-1)

k = k/2p

Period in time in s

T =1/n =2p/w

Period in space in m

l = 1/k = 2p/k


Electromagnetic em spectrum

EM RADIATION

fixed temporal coordinate

fixed spatial coordinate

Period in time

T=1/n

Period in space

l=2p/k


Superposition of waves same w

0

0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

4

5

6

7

8

9

10

Superposition of waves (same w)

U(t)

t/p

t/p

constructive interference

destructive interference


Superposition of waves same w1

Superposition of waves (same w)

  • frequency stays constant

  • amplitude and phase may be different

U1 ~ U2

interferometric measurement: (assume initial Dfi = 0)

Df = 2p/l (x1 – x2)


Superposition of waves different w

0

0

5

10

15

20

25

0

10

20

30

40

50

60

70

80

90

100

Superposition of waves (different w)

U(t)

t/p

t/p

beat frequency

U1 = cos(w1t)

U2 = cos(w2t)

w = w1 – w2


Superposition of harmonic waves arbitrary waveforms

Superposition of harmonic waves“ARBITRARY WAVEFORMS”

0

0

0.5

1

1.5

2

2.5

3

t/p


Time vs frequency

0

50

100

150

200

250

300

0

-0.1

-0.05

0

0.05

0.1

0.15

Time vs. frequency

Gaussian

Spectrum

Gaussian Decay

Frequency

Time

Lorentzian Spectrum

Exponential Decay

Dirac Delta Function

?


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