1. PART 3
Wave Optics
1. Huygen’s Principle
2. Young’s Two Slits Experiment
3. Air Wedge
4. Interference of Thin Film
5. Diffraction by a Single Slit
6. Diffraction Grating
7. Spectrometer and Spectroscopy
8. Polarization

2. Christian Huygens
• 1629 – 1695
• Best known for
contributions to fields of
optics and dynamics

3. Huygen’s Principle

4. Huygen’s Principle, Cont.
• All points on a given wave front are taken as
point sources for the production of spherical
secondary waves, called wavelets, which
propagate in the forward direction with
speeds characteristic of waves in that
medium.

5. Wave Optics
• The wave nature of light is needed to explain
various phenomena.
– Interference
– Diffraction
– Polarization

6. Conditions for Interference
• For sustained interference between two
sources of light to be observed, there are two
conditions which must be met.
– The sources must be coherent.
• The waves they emit must maintain a constant phase
with respect to each other.
– The waves must have identical wavelengths.

7. Resulting Interference Pattern
• The light from the two slits form a visible pattern on
a screen.
• The pattern consists of a series of bright and dark
parallel bands called fringes.
• Constructive interference occurs where a bright
fringe appears.
• Destructive interference results in a dark fringe.

8. Fringe Pattern
Young’s Double Experiment
• The bright areas represent
constructive interference.
• The dark areas represent
destructive interference.

9. Interference Patterns
• Constructive
interference occurs at
the center point.
• The two waves travel
the same distance.
– Therefore, they arrive in
phase.

10. Interference Patterns, 3
• The upper wave travels
one-half of a wavelength
farther than the lower
wave.
• The trough of the bottom
wave overlaps the crest of
the upper wave.
• This is destructive
interference.
– A dark fringe occurs.

11. Geometry of Young’s Double Slit Experiment
x

12. Interference Equations, 2
• For a bright fringe
• d sin θbright = m λ
– m = 0, 1, 2, …
– m is called the order number.
• When m = 0, it is the zeroth order maximum.
• When m = 1, it is called the first order maximum.

13. Interference Equations, 3
• When destructive interference occurs, a dark
fringe is observed.
• This needs a path difference of an odd half
wavelength.
• d sin θdark = (m + ½) λ
m = 0, 1, 2, …

14. Interference Equations, Final
• For bright fringes
λL
x = m , m = 0,1,2...
d
bright
• For dark fringes
λL 1
x = ( m + ), m = 0,1,2...
d 2
dark

15. Interference Equations, Final
• For fringe separation
λL
y =
d
separation

16. Interference Equations, Final

17. Example 1
A screen is separated from a double-slit
source by 1.2m. The distance between the
two slits is 0.030 mm. The second order
bright fringe is measure to be 4.50 cm from
the centerline. Determine:
a) the wavelength of the light
b) the fringe separation

18. Example 2
In a young’s double slits experiment, an
interference pattern is formed on a screen
1.0 m away from the double slits. The double
slits are separated by 0.25 mm and the
wavelength of light used is 550 nm.
Determine the distance from the central
bright fringe the distance of
a) the 5th bright fringe
b) the 3rd dark fringe

19. Air Wedge

20. Air Wedge

21. Air Wedge
Separation between bright fringes
1 L λ L ≅ ny
y=  
2H  n is number of bright fringe
Angular size of air wedge
H 
tan θ =  
L
1λ
=
2y

22. Example 3
Air wedge is formed by placing a piece of thin paper
at the edges of a pair of glass plates. Light of
wavelength 600 nm is incident normally onto the
plates. Fringes are observed with fringe separation of
0.25 mm. The length of the air wedge is 5.0 cm.
a)Determine of the thickness of the piece of paper.
b)Estimate the number of bright fringes that are
formed on the plate.

23. Example 4
Figure below shows how a piece of material of
thickness 5μm forms an air wedge between a pair of
a glass plates A and B. Light of wavelength 500 nm
is incident normally onto the plates. Estimate the
number of bright fringes produced.

24. Interference in Thin Films
• Interference effects are commonly
observed in thin films.
– Examples are soap bubbles and oil on water
• Varied colours observed when incoherent
light is incident on the water.
• The interference is due to the interaction of
the waves reflected from both surfaces of
the film.

25. Interference in Thin Films
1 Phase Reversal 0 or 2 Phase Reversal

26. Problem Solving with Thin Films
Equation 1 phase 0 or 2 phase
m = 0, 1, 2, … reversal reversals
2nt = (m + ½) λ constructive destructive
2nt = m λ
destructive constructive

27. Interference in Thin Films
• Identify interference in the
film(constructive/destructive)
• Starts the number of order (m) with m=0 (otherwise)
• Find the refraction index of thin film.
• Determine the number of phase reversals. (0,1 or 2)
• Using table, use correct formula and column

28. Example 5
a) Calculate the minimum thickness of a soap-
bubble film (n=1.33) that will result in
constructive interference in the reflected
light if the film is illuminated by light with
wavelength 602 nm.
b) In (a), if the soap-bubble is on top of a glass
slide with n=1.50, find the minimum
thickness (nonzero thickness) for
constructive interference?

29. Example 6
Nearly normal incident light of wavelength
600 nm falls onto a thin uniform transparent
film in air. The refractive index of the film is
1.34. A very bright ray reflected by the surface
of the film is observed. Determine the
minimum thickness of the film.

30. Example 7
Refer the figure, find the
minimum thickness of the
film that will produce at
least reflection at a
wavelength of 552 nm.
Hint: minimum thickness is refer to destructive
interference

31. Diffraction
• This spreading out of light
from its initial line of travel is
called diffraction.
– In general, diffraction occurs
when waves pass through
small openings, around
obstacles or by sharp edges.

32. Fraunhofer Diffraction
• Fraunhofer Diffraction
occurs when the rays leave
the diffracting object in
parallel directions.
– Screen very far from the slit
– Converging lens (shown)
• A bright fringe is seen along
the axis (θ = 0) with
alternating bright and dark
fringes on each side.

33. Single Slit Diffraction, 3
• In general, destructive interference occurs for
a single slit of width a is given by:
a sin θdark = mλ
m = ±1, ±2, ±3, …

34. Example 8
The angular separation between the two first
order minima diffraction pattern produced by
single slit is 200. The incident light has wavelength
600 nm. Determine the width of the slit.

35. Example 9
Parallel light of wavelength 550 nm is incident
normally upon a single slit, thus forming a
diffraction pattern on a screen. The first order
minimum is at angular position of 10. Determine
the width of the slit.

36. Diffraction Grating, Cont.
• The condition for maxima is
– d sin θbright = m λ
• m = 0, ±1, ±2, …
• The integer m is the order
number of the diffraction
pattern.
• Number per lines per cm =
1/d

37. Diffraction Grating, Final
• All the wavelengths are
focused at m = 0
– This is called the zeroth order
maximum
• The first order maximum
corresponds to m = 1

38. Example 10
A parallel light beam of wavelength 600 nm is
incident normally onto a diffraction. The angle
between the two first order maxima is 300.
Determine the number of lines per cm on the
diffraction grating.

39. Example 11
A parallel light beam of wavelength 540 nm is
incident normally onto a diffraction grating which
has 5000 lines per cm. Determine the maximum
number of orders of maxima which can be formed
on both sides of the central maximum.

40. Polarization of Light Waves
• This is an unpolarized
wave.

41. Polarization

42. Selective Absorption
• The intensity of the polarized beam transmitted
through the second polarizing sheet (the analyzer)
varies as
– I = Io cos2 θ
• Io is the intensity of the polarized wave incident on the analyzer.
• This is known as Malus’ Law and applies to any two polarizing
materials whose transmission axes are at an angle of θ to each
other.

43. Polarization by Reflection
• Brewster’s Law relates
the polarizing angle to
the index of refraction for
the material.
• θp may also be called
Brewster’s Angle.

44. Example 12
A plane-polarised light beam has intensity I0. It is
incident normally onto a polaroid. If the angle
between the transmission axis of the polaroid and
the plane of polarisation is 600, determine the
intensity of the light beam after it has passed
through the polaroid. (0.25I0)

45. Example 13
The index of refraction of a glass plate is 1.52.
What is the Brewster’s angle when the plate is
in air.