Wave PhysicsPHYS 2023

Tim Freegarde

2

Continuity conditions

• various derivations and forms

• typically:

• one condition derived from balance of forces• conservation of

momentum• the two conditions combined• conservation of energy

• reduce to equations of the form

where are combinations of material properties

3

Continuity conditions• for a boundary at between regions A

and B:

• transverse waves on a string:

• electromagnetic waves:

non-normal incidence:

• sound waves:

• thermal waves:

4

Reflection at an interface

combine forward and reflected waves to give

total fields for each region

apply continuity conditions for separate

components

hence derive fractional transmission and

reflection

yx

A B

5

Impedance

• sound waves:

• thermal waves:

• transverse waves on a string:

• electromagnetic waves:

• at interface between two media:

6

Electromagnetic waves at a normal interface

combine forward and reflected waves to give

total fields for each region

apply continuity conditions for separate

components

hence derive fractional transmission and

reflection

yx

A B

• continuity conditions:

• parameters:

77

Newton’s rings

diffuser

beam-splitter

lens

plate

s

r

• apply to sinusoidal waves by taking into account the phase with which components arrive• combine by adding the amplitudes

• contributions may therefore interfere constructively or destructively

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8

Phase change upon reflection

• phase change if

• for electromagnetic waves

in non-magnetic media

99

Brewster’s angle

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ii

r

r

itan• reflected light fully (s-) polarized