2 & 3D Waves

K Warne

CAPS Statements G11 At the end of this section you should be able to....

Diffraction · Define a wavefront as an imaginary line that connects waves that are in phase (e.g. all at the crest of their cycle).

  · State Huygen‘s principle.

  · Define diffraction as the ability of a wave to spread out in wavefronts as they pass through a small aperture or around a sharp edge.

  · Apply Huygen‘s principle to explain

  diffraction qualitatively. Light and dark areas can be described in terms of constructive and destructive interference of secondary wavelets.

  · Sketch the diffraction pattern for a single slit.

Wave Comparison

Direction of wave

Particles vibrate

Direction of wave

Particles vibrate

Transverse Waves

WavesA wave is a series of pulses or disturbances in a medium.A Transverse wave has the disturbance is at 90o to the direction of movement.The particles vibrate perpendicular to the wave's velocity.

Displacement - time Draw graphs of transverse position (y) vs time

vs t, for a particle of a string or spring as a pulse move past it.

Time (s)

Dis

plac

emen

t (m

)

+

-

y

Reflection Waves reflect

(bounce) off the surface of objects in their paths.

The angle that waves are incident (hit) the surface is the same as that with which they reflect off again.

Angle of incidence

Refraction of waves Waves slow

down on entering a more dense medium.

If the wave strikes this medium at an angle it then changes direction.

Normal line 90° to the surface

The wave bends towards the normal on entering a more dense medium at an angle.

The waves bend away from the normal when exiting a more dense medium.

Interference

c) The pulses continue on their original paths.

When two pulses arrive at the same point at the same time they …………………. on one another.

This is called interference – it can be constructive or destructive.

…………………. Interference

………………… Interference

Interference

c) The pulses continue on their original paths.

When two pulses arrive at the same point at the same time they superimpose on one another.

This is called interference – it can be constructive or destructive.

Constructive Interference

Destructive Interference

Single Slit Experiment

This experiment proves that light undergoes ……………………….., and hence LIGHT is a ……………...A thin rectangular piece of glass is painted with black paint, and a thin single slit is made on the paint with a razor blade.

White LightA beam of white light is shone through the slit.

Observation1) A broad …………………….. of bright white light is observed.2) This is flanked by alternate spectral ……………….. and black fringes.

What factors would affect the amount of diffraction?? How??

Single Slit Experiment

This experiment proves that light undergoes DIFFRACTION, and hence LIGHT is a WAVE.A thin rectangular piece of glass is painted with black paint, and a thin single slit is made on the paint with a razor blade.

White LightA beam of white light is shone through the slit.

Observation1) A broad central band of bright white light is observed.2) This is flanked by alternate spectral colour fringes and black fringes.

Slit width – smaller slit greater diffraction, wavelength

Single Slit - RED light

If RED light is used: 1) Fringes are more ………………….2) Broad central band of ……………. is observed3) Alternate bands of Red and ………………… are observed.

Red Light is MONOCHROMATIC.(light of single frequency)

Single Slit - RED light

If RED light is used: 1) Fringes are more distince.2) Broad central band of RED is observed3) Alternate bands of Red and BLACK are observed.

Red Light is MONOCHROMATIC.(light of single frequency)

Single Slit - BLUE light

If BLUE light is used: 1) Fringes are very distinct.2) Broad central band of ........... is observed3) Alternate bands of Blue and Black are observed.4) The bands are .................... than in the case of the RED.5) The DIFFRACTION is ………………….This shows that BLUE light has a ………….. WAVELENGTH than RED light.

Blue Light is MONOCHROMATIC(light of single frequency)

Single Slit - BLUE light

If BLUE light is used: 1) Fringes are very distinct.2) Broad central band of BLUE is observed3) Alternate bands of Blue and Black are observed.4) The bands are CLOSER than in the case of the RED.5) The DIFFRACTION is less – i.e the longer wavelength diffracts MORE.This shows that BLUE light has a SMALLER WAVELENGTH than RED light.

Blue Light is MONOCHROMATIC(light of single frequency)

Single Slit - IMPORTANT POINTS

1. What is the effect of the WIDTH of the slit on the amount of DIFFRACTION?

A narrower width produces ……………….. diffraction.

2. What does DIFFRACTION prove about light?

DIFFRACTION proves that LIGHT is a ………………….

3. For what TYPE of wave does diffraction occur?

Diffraction occurs for BOTH TRANSVERSE and ………………………… WAVES.

Single Slit - IMPORTANT POINTS

1. What is the effect of the WIDTH of the slit on the amount of DIFFRACTION?

A narrower width produces greater diffraction.

2. What does DIFFRACTION prove about light?

DIFFRACTION proves that LIGHT is a WAVE.

3. For what TYPE of wave does diffraction occur?

Diffraction occurs for BOTH TRANSVERSE and LONGITUDINAL WAVES.

Diffraction

…………… of waves around objects in their path.

…………. direction

………………. wave fronts

Diffraction

Bending of waves around objects in their path.

Original direction

Deflected wave fronts

Hygen’s Principle

Every ………………… on the wave front acts as the ……………….. of a new wave.

Huygen’s Principle Every point on the wave front acts as

the source of a new wave.

A wavefront is an imaginary line that connects waves that are in phase

Diffraction

…………… lines appear in the diffracted waves.

Diffraction

Nodal lines appear in the diffracted waves.

Light intensity

NODE

NODE

ANTINODE

Diffraction

= ……………………….. of the wave m = 1, 2, 3… called the ………...of the

dark bands m = 1 gives the ………………….. (Dark) band

Diffraction

The waves moving to the center of the screen travel the same distance so are still in phase when they arrive.

Wid

th =

a

Broad central band = waves in

phase .: constructive interferance!

Diffraction

Waves moving away from the centre of the screen travel different distances so are no longer in phase!

Wid

th =

a

FIRST DARK BAND = waves out of phase .:

destructive interference!

D

View this slide as a slide show to see animation.

Destructive interference – nodal line – dark

bandConstructive interference – antinode – broad central

band

Destructive interference – nodal line – dark

band

CAPS Statements G11You should now be able to....

Diffraction · Define a wavefront as an imaginary line that connects waves that are in phase (e.g. all at the crest of their cycle).

  · State Huygen‘s principle.

  · Define diffraction as the ability of a wave to spread out in wavefronts as they pass through a small aperture or around a sharp edge.

  · Apply Huygen‘s principle to explain

  diffraction qualitatively. Light and dark areas can be described in terms of constructive and destructive interference of secondary wavelets.

  · Sketch the diffraction pattern for a single slit.

Extension Work The slides following this one are no

longer stipulated in the CAPS document (2013 onwards) and so are included for EXTENTION (optional) work only.

Diffraction

…………… lines appear in the diffracted waves.

Diffraction

Nodal lines appear in the diffracted waves.

Light intensity

NODE

NODE

ANTINODE

Diffraction

= ……………………….. of the wave m = 1, 2, 3… called the ………...of the

dark bands m = 1 gives the ………………….. (Dark) band

Diffraction

= wavelength of the wave m = 1, 2, 3… called the order of the dark bands m = = 1 gives the first order dark band

A

B

CWid

th =

a

FIRST DARK BAND

D

A

C

D

Sin = (m)

aa

Diffraction

= wavelength of the wave m = 1, 2, 3… called the order of the dark bands m = 1 gives the first order dark band

A

B

CWid

th =

a

FIRST DARK BAND

D

A

C

D

Sin = (m)

aa

1 Red light:

2 Blue light:

Diffraction Questions Sin = m

a

1. Find the position of the first dark band formed on the screen when red light of wavelength 690 nm is passed through a slit of width 6.0 m.

2. Compare this with the position of the first order dark band when

blue light of wavelength 460 nm is used.

………..

………..

1 Red light: = 690 x 10-9 m a = 6.0 x 10-6 m and m = 1sin = (1)(690 x 10-9 )/(6.0 x 10-6) = sin-1 (0.115) = 6.60o

2 Blue light: = 460 x 10-9 m a = 6.0 x 10-6 m and m = 1sin = (1)(460 x 10-9 )/(6.0 x 10-6) = sin-1 (0.077) = 4.40o

Diffraction Questions Sin = m

a

1. Find the position of the first dark band formed on the screen when red light of wavelength 690 nm is passed through a slit of width 6.0 m.

2. Compare this with the position of the first order dark band when

blue light of wavelength 460 nm is used.

6.60o

4.40o

Single vs Double slit