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Light, Sound and Waves
26 January 2015

18:53

Reflection

Incident ray
Reflected ray
Angle of incidence

Angle of reflection

Normal

• Laws of reflection
○ Apply to all reflections
○ Demonstration
 Light box
 Plane mirror
○ Apply
 Curved mirrors
 Rough surfaces

Image formation
• Kinds
○ Real
○ Imaginary

Plane mirrors
• Image
○ Always virtual
○ Light rays entering eye
 Diverging
○ Brain assumes
 Light travels in straight line
○ Same
 Size as object
 Distance from mirror
○ Seems behind mirror

Image

Object

Eye

Plane mirror

Curved mirrors
• Concave
○ Shape
 Satellite dish
○ Image formation
 Light ray parallel to principal axis
□ Reflect through focal point
 Light ray through focal point
□ Reflects parallel to axis
 Light ray at the pole
□ Reflects according to laws of reflection

Light^J Sound and Waves Page 1

Focal point

Centre of curvature

Pole

Principal axis

• Centre of curvature
○ Centre of mirror
• Focal point
○ Half way between mirror and centre
• Image formation

Object
f

C

Pole

Axis

Image

Object outside of C
• Image
○ Real
○ Inverted
○ Diminished

Object
f

C

Pole

Axis

Image

Object at C
• Image
○ Real
○ Inverted
○ Same size

Object

f

C

Pole

Axis

Pole

Axis

Image

Object between C and f
• Image
○ Real
○ Inverted
○ Magnified

Object
C

Light^J Sound and Waves Page 2

f

Object at f
• Image
○ Infinity

Object
f

C

Pole

Image

Object inside f
• Image
○ Virtual
○ Upright
○ Magnified
• Convex mirrors
○ Focal point behind mirror
○ Incident beams
 Parallel to axis
 Not reflected through
 Originate there

Object

Image

• Image
○ Always
 Upright
 Virtual
 Diminished
• Formula
○ V is negative
○ F is negative
• STS
○ Concave
 Dentists mirrors
□ Mirror close to teeth
 Inside focal length
□ Image magnified
 Shaving mirrors
□ Bathrooms
□ Close
 Enlarged image
○ Convex
 Shops
□ Security devices
 Large area seen
 Country roads
□ Dangerous bends
 Wing mirrors
□ Cars
□ Large field of view
□ Image
 Diminished
 Car looks further than it really is

Refraction
• Car drives on different surface
○ Changes direction
○ One wheel on another surface
 Sand slows
 Tarmac still fast

Light^J Sound and Waves Page 3

Axis

○ Changes direction
○ One wheel on another surface
 Sand slows
 Tarmac still fast
Angle of incidence (i)

Angle of refraction (r)

• Refraction
○ Less dense to more dense
 Bends towards normal
○ Dense to less dense
 Bends away from normal
•

• STS
○ Pool
 Seems less deep
 Light rays bent outward
□ Leaving
□ Less dense air
 Light appears to be coming from a shallower point

Apparent depth

Real depth

•

Total internal reflection
• Light
○ Dense to less dense
 Bend away from normal
○ Angle of incidence
 Light skims along surface
□ Critical angle
 Bigger than critical angle
□ Cannot leave glass
□ Reflected like hitting a mirror
□ Total internal reflection
• STS
○ Optical fibres
 Light continuously strikes top and bottom
□ Angle
 Greater than critical
□ Light trapped
 Transmit information
□ Long distances
 Uses
□ Transatlantic telephone messages
□ Surgeons
 See in body
 Cables
□ Coated with dense glass
 Ensure total internal reflection
○ Mirages
 Road surface hot
 Ait above heats
 Cold air higher
 Hot air
□ Less dense
 Cold air
□ Dense

Light^J Sound and Waves Page 4

□ Dense
 Light enters hot air
□ Bends away from normal
□ Several times
 Hits angle greater than critical angle
◊ Hits driver
○ Prism reflectors
 Bicycles

Lenses
• Converging lenses
○ Convex lenses
○ Light
 Refracted inward
 Converging effect
 Hits head on
□ Passes through focal point

Focal point

• Real image on screen
○ Magnified/diminished
○ Cinema
• Converging lens diagrams

2f

f

f

2f

f

2f

f

2f

Object outside 2f
• Image
○ Real
○ Inverted
○ Diminished

2f

f

Object at 2f
• Image
○ Real
○ Inverted
○ Same size

2f

f

Object between 2f and f
• Image
○ Real

Light^J Sound and Waves Page 5

Object between 2f and f
• Image
○ Real
○ Inverted
○ Magnified

2f

f

f

2f

f

2f

Object at f
• Image
○ Infinity
○ Blurred

2f

f

Object inside f
• Image
○ Virtual
○ Upright
○ Magnified

• Diverging lenses
○ Image
 Always
□ Virtual
□ Upright
□ Diminished

• STS
○ Converging lens
 Magnifying glass
 Object inside focal length
○ Combination
 Microscopes
 Telescopes
○ Spectacles

The eye
• Image forms on retina
○ Light energy converted

Light^J Sound and Waves Page 6

○ Light energy converted
 Electrical
 Sent
□ Along optic nerve
□ Brain
• Light entering
○ Incident
 Retina
○ Through lens
• Lens shape
○ Controlled by muscle
○ Focus
 Near/distance
• Iris
○ Controls
 Amount of light
○ Hole

Retina

Cornea

 Pupil
□ Larger
 Dark
□ Smaller
 Light

Iris

• Image
○ Inverted
 Retina
○ Mentally correct
○ Image retention
 Image stays on retina for short period
 Used
□ Cinema film
• Optic nerve
○ Spot it leaves
 Not light sensitive
 Blind spot
• Defects

Long sighted
• Converging lens

Short sighted
• Diverging lens

• Long sighted
○ Unable
 Decrease focal length to see close objects
○ Converging lens
• Short sighted
○ Distant objects
○ Diverging lens

Waves
• Examples
○ Sound
○ Light
○ Radio
○ TV signals
○ Mobile phones
• Energy transferred through medium
○ No overall movement
• Structure
○ Wavelength
○ Amplitude
○ Frequency
○ Period

Wavelength (λ)

Light^J Sound and Waves Page 7

Lens

Pupil

Blind spot

Optic nerve

Wavelength (λ)

Amplitude (A)

Direction of movement of the wave

• Frequency
○ The frequency, f, is the number of cycles completed at any one point per second
• Period
○ The period, T, in the time taken to undergo one complete cycle
...
Adjust the eyepiece of the telescope so that the cross wires are sharply focused
...
Focus the telescope for parallel light using a distant object
...
Set up the apparatus as shown in the diagram
...

Method
1
...

2
...
Take the
reading ϴ from the scale on the turntable
...
Take the reading for this position
...

3
...


Conclusion
For each value of n, calculate the wavelength λ using

, and take an average
...
g
...

• The larger the angles of ϴ, the smaller the percentage error
...


Measurement of a focal length of a concave mirror
Apparatus

Light^J Sound and Waves Page 17

Eye

u
Mirror

Light box

Screen

v

Method
1
...

2
...

3
...

4
...

Conclusion
For each set of results find the focal length using:

Take an average value as the focal length, alternatively use the graph as shown
...

• The difficulty in deciding in which position the image is most clear is the main source of inaccuracy
...
Set up the apparatus as shown in the diagram
...
Place the light-box well outside the approximate focal length
...
Move the screen until a clear inverted image of the cross wires is obtained
...
Measure the distances, u and v, as shown in the diagram
...
Repeat this procedure for different values of u
...


1/f
1/u/m-1

1/v/m-1

Accuracy
• An approximate value can be found by locating the image of a distant object (through a window), which
will be formed at the focal point
...


Verification of Snell's law of refraction (and hence finding the refractive index of glass)
Apparatus

Light-box
Protractor
i
Angle of incidence, i

Light^J Sound and Waves Page 19

Glass block

Angle of incidence, i

Angle of refraction, r

r

Method
1
...

2
...

3
...

4
...

Conclusion
Plot a graph of sin i against sin r
...
e
...
The slope of the line is the refractive index
...

• Larger angles will lead to a smaller percentage error
...
Set up the apparatus as shown in the diagram
...

2
...

3
...
This is the apparent depth
...
This is the real depth
...
Repeat for different depths of water
...

The slope of the line will be the refractive index
...

• Using larger values of the real depth will reduce the percentage error
...
Set up the apparatus as shown in the diagram
...

2
...

3
...
Start with a small for l and slow increase it, until the paper rider moves, indicating that the string is
vibrating
...
Record l and f
...
Repeat for various tuning forks, and record the measurements in a table
...
Plot a graph of frequency f against the inverse length: 1/l
...


1/l/m-1

f/Hz

Accuracy
• It is difficult to determine when the strings vibrations are at their greatest, the paper rider helps with this
...


Investigation of the variation of the fundamental frequency of a stretched string with tension
...
Set up the apparatus as shown in the diagram
...
Select a wire length l (e
...
30cm) by suitable placement of the bridges
...

3
...
Start at low tension and slow begin to increase it until
the string begins to vibrate
...

4
...

5
...


f/Hz

Accuracy
• It is difficult to determine when the strings vibrations are at their greatest, the paper rider helps with this
...


Measurement of the speed of sound in air
Apparatus

Tuning fork

Resonance tube

l

Large graduated
cylinder

Retort stand
d

Method
1
...

Using a vernier callipers, measure the diameter of the tube, d
...
Striker the highest frequency, f, tuning fork on the wooden block, and hold it in a horizontal position just
above the mouth of the tube
...
Slide the tube slowly up until the note heard from the tube is at its loudest
...

4
...
Record the measurements in a table
...

Calculate the speed of sound from
, for each of the tuning forks
...

Accuracy
• It is difficult to determine when the resonance is at its peak
...


Light^J Sound and Waves Page 24

Demonstration Experiments
28 January 2015

19:55

To show that light is a wave (Young's double slit experiment)
Apparatus

Light
source

Lines of
light

Screen

Screen with 2 slits
Screen

Method
1
...

2
...

3
...

Observation
A pattern is formed on the screen as shown in the diagram
...

Conclusion
As diffraction and interference are wave characteristics, this demonstrates that light is a wave
...

Observation
Walking along the dotted line in the diagram we would hear the sound repetitively grow and fall in volume
...


Light^J Sound and Waves Page 26

Definitions
26 January 2015

18:53

The laws of reflection of light
The angle of incidence equals the angle of reflection
...


Laws of refraction
The incident ray, the normal at the point of incidence, and the refracted ray all lie in the
same plane
...
(Snell's Law)
...
It can be formed on a screen
...
It cannot be formed on
a screen
...


Critical angle
The critical angle is the angle of incidence for which the corresponding angle of refraction is
90o
...
Light is reflected at the meeting of the two materials
...


Transverse wave
In a transverse wave, the movement of the particles is perpendicular to the movement of
the wave
...


Light^J Sound and Waves Page 27

Diffraction
Diffraction is the ability of a wave to spread out after meeting an obstacle or passing
through a small gap
...
When this happens the total displacement will
be equal to the algebraic sum of the individual displacements
...


Polarisation
Polarisation is the restriction of a wave to vibrations in one plane
...


Harmonics
Harmonics are multiples of the natural frequency of vibration of a body
...


Intensity of sound
The intensity of sound at a point is defined as the rate at which energy is crossing a unit
area perpendicular to the direction in which the sound is travelling
...


Threshold of hearing
The threshold of hearing is the lowest sound intensity to which an average human ear can
respond
...


The frequency limits of audibility
The frequency limits of audibility are the lowest and highest frequency sound waves that
the average human ear can hear
...


Light^J Sound and Waves Page 28

Derivations
28 January 2015

21:33

• Consider a light beam shining through a diffraction grating
...

• For constructive interference to occur two of these light rays must meet
...


nλ

Light rays
d

ϴ

Grating

Screen

Light^J Sound and Waves Page 29



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