Download Electromagnetic waves

Biophysics I. 2015/2016
Lecture 2.
Related literature:
Related multimedia material:
__________________________________________________________________________________
Topics of the lecture:
1. Definition of wave
2. Categorization of waves
3. Characteristic quantities of wave motion
4. The speed of electromagnetic waves
5. Generation and propagation of electromagnetic waves
6. The electromagnetic spectrum
7. Wave nature of light (diffraction, interference, polarization)
__________________________________________________________________________________
Electromagnetic waves
(1) Definition of waves
Wave: repeating and periodic disturbance that moves through a medium from one location to
another. Waves are energy transport phenomenon that transports energy along a medium without
transporting matter
(2) Categorization of waves
1. According to the direction of the vibration:
a. Longitudinal waves are always characterized by particle motion being parallel to wave
motion.
b. Transverse waves are always characterized by particle motion being perpendicular to
wave motion.
2. According to the nature of the disturbance:
a. A mechanical wave is a wave that is not capable of transmitting its energy through a
vacuum. Mechanical waves require a medium in order to transport their energy from
one location to another.
b. An electromagnetic wave is a wave that is capable of transmitting its energy through a
vacuum (i.e., empty space).
(3) Characteristic quantities of wave motion
Biophysics I. 2015/2016
Amplitude: the distance from rest to crest of from rest to trough
Wavelength (λ): the distance from a point on a wave to the corresponding point on the next cycle of
the wave
Frequency (f) of a wave: the number of the crests that pass through a given point within one second.
One wave or cycle per second is called the Hertz (Hz) (1 Hz is equivalent to 1 cycle/second)
Period (T) of a wave: the time for a particle on a medium to make one complete vibrational cycle.
Period is the reciprocal of the frequency and vice versa
Problem (1)
The wavelength of the wave in the diagram above is given by letter ______. (A)
The amplitude of the wave in the diagram above is given by letter _____. (D)
(4) The speed of electromagnetic waves
𝑐 = 𝜆𝑓
EM waves travel through at the vacuum of space at the constant speed of light (c = 3x108 m/s).In a
medium it depends on the refractive index of the medium. Wave speed is dependent upon medium
properties and independent of wave properties.
Problem (2)
If the frequency of a radio station 2 FM is 92.2 MHz and its wavelength is 3.254 metres, find the
velocity of radio waves.
𝞴=3.254 m
Biophysics I. 2015/2016
f = 92.2 MHz = 92.2x106 Hz
𝑚
c=𝞴f=(3.254)(92.2x106)=3x108 𝑠
(5) Generation and propagation of electromagnetic waves
EM waves are produced by the vibration of charged particles, and have electrical and magnetic
properties. A vertical wire carries an alternating current generates an electric field. The electric field,
in turn, generates a magnetic field whose change generates an electric field. This succession of
induced fields (electric [E] to magnetic [B] to electric to magnetic, etc.) results in the generation of
the electromagnetic wave (James Clerk Maxwell and Heinrich Hertz).
The vectors of the electric field E and the
magnetic field B are perpendicular to each other
and to the direction of the wave propagation. In
the running wave the vectors E and B oscillate in
phase (achieve the maximum value in the same
points of the space).
(6) The electromagnetic spectrum
Electromagnetic waves exist with an enormous range of frequencies = electromagnetic spectrum:
radio waves, microwaves, infrared waves, visible light waves, UV rays, X-rays, gamma rays
The wavelength and the frequency of the waves are inversely proportional to each other.
Radio waves:
• emitted by radio stations, during transmission or by TV stations etc. , also emitted by stars.
• range from few millimeters to large wavelength.
• used by antennas.
• used for data transmission via modulation, majorly used for communication.
Micro waves:
• emitted by the microwave oven (heating the food).
• initial use: in long range communication.
• used by astronomers to study the structures of galaxies.
• two types: super high frequency and extremely high frequency.
• used by Wi-fi.
Infrared rays:
• are emitted by everything that is warm and hot.
• have three types:
- Far infrared rays (15 - 1000 μm wavelength range)
- Mid infrared rays
- Near infrared rays (0.75-1.4 μm wavelength range)
• infrared spectrometers are generally used to study the vibrational spectra of
Biophysics I. 2015/2016
molecules
Visible light :
• are emitted by everything from a bulb to particle striking other particles
• are detected by human eye
• wavelength lies between ~ 400 nm to 700 nm (from violet to red)
• are used in optical fiber communication medium
Ultraviolet :
• are emitted by sun
• harmful for human body, cause skin burn, can cause skin cancer
• can ionize atoms → mutagen
• are absorbed by ozone layer mostly
X-rays :
• are used by doctors
• can interact with matter
• are produced by the sudden stoppage of the high speed charged particle by
the use of metal target which absorbs these particles and the x-rays are emitted
by such particles.
• have two types:
- hard ray
- soft X-ray
Gamma rays :
• are emitted by radioactive substances (produced by the radioactive decay of the radioactive
atoms)
• are used in treatment of many diseases
Problem (3)
The wavelength of visible light varies from 370 nm to 700 nm. Find the lowest frequency that an
electromagnetic wave can have still be in the visible range.
c= 𝞴f when 𝞴 is biggest: f is smallest.the required frequency is the one corresponding to a
wavelength of 700 nm (7x10-7 m)
fmin=𝜆
𝑐
𝑚𝑎𝑥
3𝑥108
= 7𝑥10−7 = 4.3𝑥1014 𝐻𝑧
(7) Wave properties of light
light: has wave and particle nature
wave because of
-reflection (change in direction when bounce off a barrier)
-refraction (change in the direction when pass from a medium to another)
-diffraction (change in the direction when pass through an opening or around
an obstacle /sideways spreading of waves into the region beyond a slit or
around an obstacle)
-interference (waves from two sources meet, a new wave is produced)
-polarization (vibrations occur in a single plane)
in detail…
DIFFRACTION
Biophysics I. 2015/2016
d>>λ : no diffraction
(most of the waves
pass straight through
the slit)
d<λ:
diffraction
(the waves spread
into the region
beyond the slit)
d<λ: diffraction (the
waves spread into
the whole region
beyond the slit)
Explanation: Huygens-Fresnel principle
Every unobstructed point on a wave-front emanates secondary spherical waves in all directions.
These wavelets have the same frequency as the front they were emitted from.
Problem (4)
A fine diffraction grating has 400 lines per mm ruled on it. Find the grating constant d.
slit slit
__ __ __
d d
It is obvious that if the grating has 400 lines per mm it also has 400 slits per mm. Thus one line and
1
1
one slit take up 400 𝑚𝑚𝑑 = 400 𝑚𝑚 = 0.0025 𝑚𝑚 = 2.5𝑥10−6 𝑚
1
In general, if a grating has n lines per mm then 𝑑 = 𝑛 𝑚𝑚.
Young’s double slit experiment
demonstration wave-like properties of light (1801): light from a laser beam is passed through two
narrowly spaced slits. The light diffracts through the slits and interferes in the space beyond the slits.
The interference pattern is then projected onto a screen located several meters away.
Biophysics I. 2015/2016
𝝀=
𝒚𝒅
𝒎𝑳
and 𝒅 𝒔𝒊𝒏 𝜽 = 𝒏𝝀
Problem (5)
Red light falls normally onto (i.e. at right angles to) a diffraction grating. The grating has 400lines per
mm engraved on it and the second order diffracted image is at 30°from the straight through position.
Find the wavelength of the light.
1
400 lines/mm 𝑑 = 400 𝑚𝑚 = 0.0025 𝑚𝑚 = 2.5𝑥10−6 𝑚
𝑑 𝑠𝑖𝑛 𝜃 = 𝑛𝜆𝜆 =
𝑑𝑠𝑖𝑛𝜃
𝑛
=
(2.5𝑥10)(sin 30°)
2
= 6.25𝑥10−7 𝑚
Problem (6)
A diffraction grating has 350 lines per mm ruled on it. Monochromatic light of wavelength 5.2x10-7
m incident normally on it. What is the highest order diffracted image formed?
𝑑
𝑑 𝑠𝑖𝑛 𝜃 = 𝑛𝜆. Maximum value of n occurs when sin Θ is maximum, i.e. when 𝑠𝑖𝑛𝜃 = 1. 𝑛𝑚𝑎𝑥 = 𝜆 .
𝑑=
1
𝑚𝑚 = 2.857𝑥10−6 𝑚
350
𝑛𝑚𝑎𝑥 =
2.857𝑥10−6
5.2𝑥10−7
= 5.49max value of n is 5, i.e. the 5th order is the highest.
Problem (7)
A diffraction grating having 100 lines per mm is placed between monochromatic light source (which
gives out parallel light) and a screen as can be seen in the figure. The distance from the grating to the
screen is 2 m. Bright spots are seen on the screen at the points A, B, C, D, E, F, G, H and I. If the
distance |𝐴𝐼| = 80 𝑐𝑚, calculate the wavelength of the source.
1
100 lines per mm𝑑 = 100 𝑚𝑚 = 1𝑥10−5 𝑚
𝑠𝑖𝑛𝜃 =
|𝐴𝐸|
0.4
=
= 0.1961
|𝑂𝐴| √22 + 0.42
𝑛𝜆 = 𝑑𝑠𝑖𝑛𝜃𝜆 =
𝑑𝑠𝑖𝑛𝜃
𝑛
=
1𝑥10−5 (0.1961)
4
INTERFERENCE
Overlapping of waves from two
different sources produce a new
wave
Two types: 1. constructive
2. destructive
= 4.9𝑥10−7 𝑚
Biophysics I. 2015/2016
POLARIZATION
A light wave that is vibrating in more than one plane is referred to as unpolarized light. In polarized
waves vibrations (of the electric field strength vector) occur in a single (well defined) plane. The
process of transforming unpolarized light into polarized light is known as polarization. Only
transverse waves can be polarized.