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Major Concepts in Physics Lecture 3. . Prof Simon Catterall Office 309 Physics, x 5978 [email protected] http://physics/courses/PHY102.08Spring. Today …. Announcements Interference – why light is a wave! Phase difference, constructive and destructive interference

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Major concepts in physics lecture 3

Major Concepts in Physics Lecture 3.

Prof Simon Catterall

Office 309 Physics, x 5978

[email protected]

http://physics/courses/PHY102.08Spring

PHY102


Today
Today …

  • Announcements

  • Interference – why light is a wave!

  • Phase difference, constructive and destructive interference

  • Examples: sound, Young’s double slit experiment, thin films

PHY102


Clickers
Clickers

  • We will NOT be using clickers this semester

    • Registration costs

    • Unnecessary since do not plan to use for grading

  • If anyone has bought one for this semester you should return it to the bookstore.

  • Instead use flashcards

PHY102


Homeworks etc
Homeworks etc

  • Collect homework 1 in workshop this week.

    • Due 2 weeks from now in workshop

PHY102


Interference
Interference

  • Phenomena that results from applying principle of superposition to (usually) 2 coherent sources of waves

  • Typically waves originate from two different locations

PHY102


Coherence
Coherence

  • Two waves are coherent if they maintain a fixed phase relationship to each other

PHY102


Phase
Phase

  • Phase difference is the angle (in radians) between corresponding wave crests

  • If phase difference is

    • 0 or multiple of 2p – constructive interference

    • p or odd multiple – destructive interference

  • Typically independent sources are NOT coherent – eg. do NOT see interference from 2 light bulbs ….

PHY102




Example sound from speakers
Example: sound from speakers

  • Two loudspeakers powered from same source (coherent).

  • Swap polarity – phase difference now 180 degrees (p radians) – volume drops!

PHY102


When both waves travel in the same medium the interference conditions are:

For constructive interference

where m = an integer.

For destructive interference

where m = an integer.

PHY102


Example (text problem 25.1): A 60.0 kHz transmitter sends an EM wave to a receiver 21 km away. The signal also travels to the receiver by another path where it reflects from a helicopter. Assume that there is a 180 phase shift when the wave is reflected.

(a) What is the wavelength of this EM wave?

PHY102


Example continued: EM wave to a receiver 21 km away. The signal also travels to the receiver by another path where it reflects from a helicopter. Assume that there is a 180

(b) Will this situation give constructive interference, destructive inference, or something in between?

The path length difference is l = 10 km = 2, a whole number of wavelengths.

Subtlety: a wave reflecting off a dense medium suffers an additional 180 degree phase shift.

Since there is also a 180 phase shift there will be destructive interference.

PHY102


P EM wave to a receiver 21 km away. The signal also travels to the receiver by another path where it reflects from a helicopter. Assume that there is a 180

S1

d

S2

Coherent waves can become out of phase if they travel different distances to the point of observation.

This represents the extra path length (l) that the wave from S2 must travel to reach point P (P far away)

PHY102


Young s fringes
Young’s fringes EM wave to a receiver 21 km away. The signal also travels to the receiver by another path where it reflects from a helicopter. Assume that there is a 180

  • Single slit provides two independent coherent light sources

  • On distant screen see alternating bright and dark lines – corresponding to points where constructive and destructive interference takes place

  • Note how separation of slits affects fringe separation …

PHY102


The pattern seen on the screen EM wave to a receiver 21 km away. The signal also travels to the receiver by another path where it reflects from a helicopter. Assume that there is a 180

There are alternating bright/dark spots.

An intensity trace

PHY102


The bright spots occur where there is constructive interference:

where m is an integer and is called the “order”.

The dark spots occur where there is destructive interference:

PHY102


Fig 25 21
Fig. 25.21 interference:

PHY102


The screen is far away compared to the distance between the slits (D>>d) so tan  sin  . Here,

The distance between two adjacent minima is:

PHY102


Thin films
Thin Films slits (D>>d) so tan

  • When light hits eg thin layer of oil on surface of water – get air/oil reflected wave r1

  • Happens at oil/water interface too – r2

  • Can get interference from different waves from different path lengths

  • Depending on wavelength may get constructive or destructive interference – selects out certain colors …

PHY102



Water slits (D>>d) so tan

Oil

Air

Example (text problem 25.18): A thin film of oil (n=1.50) of thickness 0.40 m is spread over a puddle of water (n=1.33). For which wavelength in the visible spectrum do you expect constructive interference for reflection at normal incidence?

Consider the first two reflected rays. r1 is from the air-oil boundary and r2 is from the oil-water boundary.

Incident wave

r1 has a 180 phase shift (noil >nair), but r2 does not (noil<nwater).

PHY102


Example continued: slits (D>>d) so tan

To get constructive interference, the reflected waves must be in phase. For this situation, this means that the wave that travels in oil must travel an extra path equal to multiples of half the wavelength of light in oil.

The extra path distance traveled is 2d, where d is the thickness of the film. The condition for constructive interference here is:

Only the wavelengths that satisfy this condition will have constructive interference.

PHY102


Example continued: slits (D>>d) so tan

Make a table:

All of these wavelengths will show constructive interference, but it is only this one that is in the visible portion of the spectrum – color ??

PHY102


Butterfly wing
Butterfly wing slits (D>>d) so tan

  • Iridescent color because of same phenomena!

  • Path length depends on viewing angle – different colors at different angles …

PHY102


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