PA2001: Time and Energy Waves and Interference Light as a wave Fermat’s principle Reflection Refraction Thin Film

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PA2001: Time and Energy

Waves and Interference

http://www.le.ac.uk/ph/mr6/lectures.html

• Light as a wave

• Fermat’s principle• Reflection• Refraction

• Thin Film interference

• Single slit diffraction• Young’s double slit experiment

Tipler Chapters 16,33,35


Dr Mervyn Roy, S6



The Electromagnetic Spectrum

400 nm

700 nm

500 nm

600 nm

Wa

vele

ng

th

0.1 nm

1 nm

100 nm

10 m

1 mm

10 cm

10 m

1000 m Long-waves

Radio, TV

Microwaves

Infra-red

Visible

X-rays

Gamma rays



Fermat’s principle

The path taken by light in travelling from one point to another is such that the time of travel is a minimum.

Explains the law of reflection:

Euclid



Phase changes

incident wave:

wave incident on a barrier



Phase changes

wave incident on a barrier

phase change of upon reflection(note: phase change of only for reflection at rare/dense interface)

reflected wave:

incident wave:



Refractionsome reflection

some reflection

Snell’s Law

- derived using Fermat’s principle – shortest path is not the fastest as v < c

note: phase change of only at rare / dense interface

rare medium (air)

dense medium (glass)



Refractionrare medium (air)

dense medium (glass)

some reflection

some reflection

Snell’s Law

- derived using Fermat’s principle – shortest path is not the fastest as v < c

note: phase change of only at rare / dense interface

phase change

no phase change



Refraction 2Or, why shooting fish in a barrel isn’t easy

Fish are always deeper than you think

nwater = 1.3



Dispersive media

- waves of different wavelength travel at different velocity and therefore refract differently

© The Exploratoriumwww.exploratorium.edu

Newton’s prism



Interference

Add coherent harmonic waves with phase difference

0, 2

/2



Interference


0, 2

/2



Interference


0, 2

/2



Interference


0, 2

/2



Interference 2


Intensity,

In general (Hecht, Optics 2nd Ed. 9.1),

With constant amplitude as before,



Interference 3

Phase difference is related to path difference

Add coherent harmonic waves with path difference,



Thin film interference 1

travels further thandifference in path length introduces phase difference

interferes with

type of interference depends on

To find type of interference:

Calculate path and phase difference, then:

Note: have to be careful with possible phase changes of at each interface




travels further thandifference in path length introduces phase difference

interferes with

type of interference depends on

At normal incidence:

Maximum in the intensity if




© The Exploratorium, www.exploratorium.edu

At normal incidence see interference fringes with films of varying thickness



A

B

CD

Thin film interference 4 B

AD

A

C

D

combine with Snell’s law



Thin film growth

At fixed, angle of incidence,

In-situ monitoring of film thickness



• aperture size ~ wavelength

screenslit width, a

Diffraction (single slit)

Water wave




Diffraction (single slit)

a aaa

Screen

Intensity

screenslit width, a

Laser light



Young’s slits

slit separation, d

Laser light

Interference fringes

Screen far away, rays ~ parallel

d Path difference, Constructive interference:



Diffraction gratings


Angle of maxima is wavelength dependent:

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PA2001: Time and Energy Waves and Interference Light as a wave Fermat’s principle Reflection Refraction Thin Film