PHYSICS
CHAThe PTstudy ER of 2 interference, diffraction and polarization of light.. Light is treated as light waves rather than as rays.
CHAPTER 2: Physical optics (9 Hours)
PHYSICS CHAPTER 2 Learning Outcome: s c i s y h p / y m . .. u d e . . ki r t a m . . h p m . .k w w w
2.1 Huy Huygen gen’s ’s pri princi ncipl ple e (1 (1 hour hour)) At the end of this cchapter, hapter, students should be able to: this chapter, Explain Huygen’s principle governing the propagation of wave fronts.
Include spherical and plane wavefronts.
Explain diffraction patterns by using Huygen’s principle.
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2.1 Huygen’s principle 2.1.1 Wavefronts
is defined as a line or surface, in the path of a wave motion, on which the disturbances at every point have the same phase.. phase Figure 2.1 shows the wavefront of the sinusoidal waves. wavefront A D
Figure 2.1
B
E
C
F
v
λ
Line joining all point of adjacent wave, e.g. A, B and C or D,E and F are in phase Wavefront always perpendicular to the direction of wave
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Type of wavefronts Circular wavefronts as shown in Figure 2.2 are produced by a point source generates two-dimensional waves. circular wavefront
λ ray
point source
Figure 2.2
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Spherical wavefronts as shown in Figure Figure 2.3 are produced by a point source generates three-dimensional waves. spherical wavefronts
point source
rays Figure 2.3
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Plane wavefronts as shown in Figures 2.4a and 2.4b are produced by a point source generates three-dimensional waves at large distance from the source.
plane wavefront rays
plane wavefront
Figure 2.4a : (3-D)
rays
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Ray is defined as a line represents the direction of travel of a wave.. wave It is at right angle to the wavefronts as shown in Figure 2.5.
ray
wavefront
λ Figure 2.5
Beam of light is a collection of rays or a column light.. column of of light
parallel beam, e.g. a laser beam (shown in Figure 2.6a) Source of light from infinity Figure 2.6a
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divergent beam, e.g. a lamp near you (shown in Figure 2.6b)
Figure 2.6b
convergent beam as shown in Figure 2.6c.
Figure 2.6c
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2.1 .1.2 .2 Huy uyg gen en’s ’s pr prin inci cip ple
states that every point on a wavefront can be considered as a source of secondary wavelets that spread out in the forward direction at the speed of the wave. The new wavefront is the envelope of all the secondary wavelets i.e. the tangent to all of them. them . secondary wavefront
wavelets
Figure 2.7
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Application of Huygen’s principle a. Constructio Construction n of new wavefront wavefront for a plane plane wave
P1
A
A’ Q
Q2
P3
Q3
s B
If the wave speed is v, hence in time t the distance travels by the wavelet is s = vt .
From Huygens’ Principle, points P1, P2, P3 and P4 on the wavefront AB are the sources of secondary wavelets.
From the points, draw curves of radius s.
Then draw a straight line A’B’ which is tangent to the curves at points Q1,Q2,Q3 and Q4
Hence, line A’B’ is the new wavefront after t second.
1
P2
P4
Q4 B’
Figure 2.8
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b. Constructio Construction n of new wavefront wavefront for a circular circular wave A’
Q1
A
s
P1
Q2
Explanation as in the construction of new wavefront for a plane wavefront.
But the wavefront A’B’ is a curve touching points Q1,Q2,Q3 and Q4.
The curve A’B’ is the new (circular) wavefront after t second.
P2 source P3 B
B’
P4
Q3 Q4
ray Figure 2.9
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c. Diffra Diffracti ction on of of wave wave at at a sing single le slit slit
Figure 2.10
Huygens’ principle can be used to explain the diffraction of wave.
Each of the point in Figure 2.10, acts as a secondary source of wavelets (red circular arc)
The tangent to the wavelets from points 2, 3 and 4 is a plane wavefront.
But at the edges, points 1 and 5 are the last points that produce wavelets.
Huygens’ principle suggest that in conforming c onforming to the curved shape of the wavelets near the edges, the new wavefront bends or diffracts around the edges - applied to all kinds of waves. Stimulation 2.1
PHYSICS CHAPTER 2 Learning Outcome: s c i s y h p / y m . .. u d e . . ki r t a m . . h p m . .k w w w
2.2 Constructi Constructive ve inte interferen rference ce and destr destructiv uctive e interference (1 hour) At the end of this cchapter, hapter, students should be able to: this chapter, Define coherence.
State the conditions to observe interference of light.
State the conditions of constructive and destructive interference.
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2.2 Constructive interference and destructive interference 2.2. 2. 2.1 1 In Inte terrfe ferren enc ce of of lig light ht
Light wave is an electromagnet waves (emw).
It consists of varying electric field E and varying magnetic field B which are perpendicular to each other as other as shown in Figure 2.11.
Figure 2.11 Electric field:
E = E 0 sin (ωt-kx)
Magnetic field: B = B sin (ωt-kx)
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Interference is defined as the effect of interaction between two or more waves which overlaps or superposed at a point and at a particular time from the sources sources.. For light the Interference is occurred when two light waves meet at a point, a bright or a dark region will be produced in accordance to the Principle of superposition. Principle of superposition states the resultant displacement at any point is the vector v ector sum of the displacements due to the two light waves. waves . Constructive interference is defined as a reinforcement of amplitudes of light waves that will produce a bright fringe (maximum).. (maximum) Destructive interference is defined as a total cancellation of amplitudes of light waves that will produce a dark fringe (minimum).. (minimum)
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2.2. 2. 2.2 2 Co Cond ndit itio ions ns for for per perma mane nent nt inte interf rfer eren ence ce
Permanent interference between two sources of light only take place if they are coherent sources. It means
the sources must have the same wavelength or frequency (monochromatic).
the sources must have a constant phase difference between them.
The light waves that are interfering must have the same or approximately of amplitude to obtain total cancellation at minimum or to obtain a good contrast at maximum.
The distance between the coherent sources should be as small as possible of the light wavelength ( ).
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2.2.3 Path di diffe ferrence,
L
is defined as the difference in distance from each source to a particular point. point .
P
x1 S1
x2
Figure 2.12
S2
screen
∆ L
Path difference, ∆ L = |S2P − S1P|
= |x
|
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Interference of two coherent sources in phase Path difference for constructive interference S and S are two coherent sources in phase 1 2
S1
x1 P (maximum)
S2
x2
+
=
