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Interference and Diffraction of Light Waves: Young's Experiment and Huygens' Principle, Study notes of Optics

University of Luxemburg (UL)Optics

The concepts of interference and diffraction of light waves through the famous Young's Experiment. the requirements for observing interference, the role of coherent light, and the observation of bright and dark fringes. Huygens' principle is also introduced to explain the formation of interference patterns. The document also touches upon the difference between constructive and destructive interference and provides examples to illustrate the concepts.

Typology: Study notes

2021/2022

Uploaded on 08/05/2022

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bg1
Physical or wave optics
In the last chapter, we have
been studying geometric
optics
◆light moves in straight lines
◆can summarize everything by
indicating direction of light
using a ray
◆light behaves essentially the
way a stream of particles
(photons) would
This has worked well for a
number of phenomena
◆reflection
◆refraction
…and has helped us to
understand the workings of
◆mirrors
◆thin lenses
But our particle theory of light
gives out when we try to
understand phenomena like
interference, diffraction and
polarization
◆just doesn’t work
Have to resort to wave or
physical optics (in this
chapter)
◆…and treat light like a wave
The first thing we’ll look at is
interference of light waves
◆not easy to observe because
of the short wavelengths of
light involved (4X10-7 m to
7X10-7 m)
Along the way we’ve going to
find out why the sky is blue
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Physical or wave optics

 In the last chapter, we have been studying geometric optics ◆ light moves in straight lines ◆ can summarize everything by indicating direction of light using a ray ◆ light behaves essentially the way a stream of particles (photons) would  This has worked well for a number of phenomena ◆ reflection ◆ refraction  …and has helped us to understand the workings of ◆ mirrors ◆ thin lenses  But our particle theory of light gives out when we try to understand phenomena like interference, diffraction and polarization ◆ just doesn’t work  Have to resort to wave or physical optics (in this chapter) ◆ …and treat light like a wave  The first thing we’ll look at is interference of light waves ◆ not easy to observe because of the short wavelengths of light involved (4X10-7^ m to 7X10-7^ m)  Along the way we’ve going to find out why the sky is blue

Electromagnetic waves

 Now we’re back to

thinking of light as

specifically being an

electromagnetic wave

◆ oscillating electric and magnetic fields perpendicular to each other propagating through space ◆ equal amounts of energy stored in the electric field and in the magnetic field ◆ in interactions with matter, it’s the electric component that does most of the work

Young’s Experiment

 In order to observe interference of 2 light waves, need to have 2 things present ◆ sources must be coherent (same phase with respect to each other) ◆ waves must have identical wavelength  Laser produces coherent light which can be split into two light beam which then can interfere with each other  But the first interference experiment was carried out in 1801 ◆ …no lasers then Sunlight shines through a narrow slit; the light then spreads (Huygen’s principle) and illuminates a second screen with 2 small slits The waves through S 1 and S 2 spread out and interfere with each other producing a series of bright and dark fringes

Interference fringes

Remember example

Constructive interference

When light arrives from S

1

and S

2

so that constructive interference

takes place, a bright fringe results

Interference patterns

Light from slit S

2

has to travel further then light from S

1

path length difference is d sin θ

if d sin θ is a multiple of the wavelength λ, then constructive

interference occurs

d sin θ = mλ m=0,+/-1, +/-2, …

y = L tan θ > L sin θ

ybright = (λL/d)m

Interference patterns

Light from slit S

2

has to travel further then light from S

1

path length difference is d sin θ

if d sin θ is an odd multiple of the wavelength λ/2, then destructive

interference occurs

d sin θ = (m+1/2)λ m=0,+/-1, +/-2, …

y = L tan θ > L sin θ

ydark = (λL/d)(m+1/2)

Diffraction

no

yes

Diffraction

 Diffraction occurs when a wave passes through a small opening not so different in size from the wavelength of the wave  The wave spreads out as we saw on the previous slide  So instead of a bright spot just in the middle we see a spread-out distribution of light ◆ but with some structure to it  Type of diffraction we’re studying is called Fraunhofer diffraction ◆ screen is far away from slit ◆ …or there’s a converging lens just after the slit ◆ Demo Don’t worry about the lens; Just think of the screen as far away

Dark spots

 So dark spots when ◆ a/2 sinθ = λ/ ◆ …or a/2 sinθ = 2λ/ ◆ …or a/2 sinθ = 3λ/  Corresponding to ◆ sinθ 1 = λ/a ◆ sinθ 2 = 2λ/a ◆ sinθ 3 = 3λ/a ◆ …  Everything is in phase at θ=0, so there’s a bright spot there ◆ and other bright spots roughly half-way between the dark spots

Let’s go crazy and put in lots of slits

Light diffracts

through each

of the slits

and we get

interference

between each of

the diffracted

waves

A device like

this is called a

diffraction grating

but there’s both

diffraction and

interference taking

place

Again, there’s a path

length difference

between light passing

through different slits

bright lines or spots

when d sinθ

bright

= mλ

m=0,1,2,…

Application of interference

 Laser is set up to reflect off of CD surface  Surface has a series of bumps and pits encoding information (i.e. the music) ◆ depth of depression is equal to 1/4 of the wavelength of the laser light  So when the laser light comes to an edge (leading or trailing), part of the light reflects from the top of the bump and part from the depression (with a path length difference then of 1/2 of a wavelength) ◆ this insures destructive interference  Bump edges interpreted as one’s and depressions as 0’s DVD^ player^ uses^ a^ shorter^ wavelength laser and smaller track separation, pit depth and length DVD can store 30X as much info

Intensity pattern

The more slits in the grating the sharper are the interference peaks; Can also make a diffraction grating by having finely etched lines on a reflective surface, i.e. a CD (or DVD)