4.4 Waves Flashcards

1
Q

Define monochromatic.

A

All light waves have the same wavelength.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What conditions does there need to be to measure wavelength of light?

A
  • Light must be monochromatic
  • There must be an accurate method of producing very small path differences, and of measuring these.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What did Thomas Young do to establish the wave theory of light?

A

He was the first person to measure wavelength successfully and doing so established the wave theory of light- until them people thought of light as a stream of tiny particles called corpuscles. To demonstrate this, he used his double-split experiment.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What was the Young double-slit experiment?

A

Young used a monochromatic red light source, which he placed behind a single slit in apiece of black card. Light passes through the slit and spreads out by diffraction, until it reaches another obstacle, in which there are two narrow parallel slits. Waves from both slits that are in phase will interfere constructively. Alternate bright and dark vertical bands are seen on the other screen.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What do waves transfer?

A

Energy without any net transfer of matter.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What are the two types of waves?

A
  • Transverse
  • Longitudinal
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What are some examples of longitudinal waves?

A
  • Sound waves
  • Ultrasound
  • Types of seismic waves (P waves)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What are vibrations in waves called?

A

Oscillations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What causes longitudinal waves?

A

Vibrations/ oscillations parallel to the direction of the energy transfer.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What are some examples of transverse waves?

A

Anything on the electromagnetic spectrum. e.g. UV light, visible light, microwaves, X-rays, gamma rays.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What produces transverse waves?

A

Vibrations/ oscillations at right angles to the direction of energy transfer.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What speed do electromagnetic waves travel at?

A

The speed of light: 3 x 108

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What are progressive waves?

A

Waves that move away fro the source.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What way do particles oscillate in in terms of waves?

A

All particles oscillate vertically- they do not move forward or backwards although the waves move forwards.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What are the two graphs we can draw waves on? And on both, what does the space between the waves represent?

A

Displacement (y axis) against distance travelled (x axis)- the distance between two waves us the wavelength.

Displacement (y axis) against time (x axis)- the distance between two waves is a period.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is a wavelength?

A

The distance between two successive identical points that have the same pattern of oscillation/ the distance the wave travels before the wave repeats itself.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is a period?

A

The time it takes for one complete pattern of oscillation to take place.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the frequency of a wave?

A

The number of waves per unit time at any point and is related to the time period T by using the equation f=1/T.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What is displacement in terms of waves?

A

The distance of any part of the wave has moves from its mean position- it can be positive or negative.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What is amplitude?

A

The maximum displacement- the distance from a peak or trough to the mean (rest) position.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is phase difference?

A

Phase difference concerns the relationship between the pattern of vibrations between two points.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is meant if two waves are in phase?

A

They have exactly the same pattern of oscillations.- there is zero phase difference between them.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is an oscilloscope?

A

A device for viewing oscillations by a display on the screen of a cathode ray tube.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

what does an oscilloscope display?

A

It displays a voltage-time signal and can be used as a voltmeter to display and measure the output from a microphone or signal generator. The time-varying voltage trace represents displacement against time for longitudinal waves.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Define the principle of superposition.

A

When two or more waves of the same type meet, the resultant waves can be found be adding the displacements of the individual weaves.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

What is constructive interference?

A

If two waves, with the same amplitude exist at the same point and are travelling in phase, the amplitude of the resultant wave will be twice the individual weaves.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

What is destructive interference.

A

When two waves with the same amplitude exist at the same point and are travelling in antiphase, they will cancel each other out, and the resultant wave will have an amplitude of zero.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

What does it mean if two waves are coherent?

A

The two waves have a constant phase difference.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

What is path difference?

A

The distance between the distances travelled by two waves arriving at the same point.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

What is phase difference?

A

The difference in the phases of two waves of the same frequency.

Phase difference is measured in degrees, if its 180° difference, it’s completely out of phase (destructive interference), while if its 360° its completely in phase (constructive interference).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

What does the path difference for constructive interference look like?

A

For constructive interference, the path difference = nλ. The peak must arrive with another peak, this inly happens when the wave length is a whole number.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

What doers the path difference look like for destructive interference?

A

For destructive interference, the path difference= (n+½)λ. The peak must meet a trough- this only happens when the path difference is an odd number of wavelengths. e.g. ½, 3/2, 5/2 ect.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

What is the difference between longitudinal and transverse waves?

A

Longitudinal waves have vibrations that are parallel to their direction of energy transfer, whereas transverse waves have vibrations that are at right angles to their direction of energy transfer.

Longitudinal waves require a medium to travel through, whereas some transverse waves (electromagnetic waves) do not.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

How is an oscillation different from a wave? Give an example to explain this.

A

An oscillation describes the periodic motion of a particle about its mean position or equilibrium position, whereas a wave refers to the motion of the energy outwards from the initial disturbance.

When a stone is dropped into a pond, the individual water particles will oscillate up and down about their equilibrium positions in the pond, but the water wave will spread out across the surface of the pond, transferring energy as a transverse wave across the pond’s surface, and at right angles to the oscillating motion of the water particles.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

How can you demonstrate interference using sound?

A

Using two load speakers connected to the same generator, walk along in front of the speakers, you you go along, you should hear a loud sound where the waves reinforce each other and a quiet sound where the waves partially cancel each other out.

This variation is clearer if you cover up one ear.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

How does frequency affect the distance between maxima and minima waves?

A

The distance between the loud and quiet regions is longer at low frequencies.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

What equation relates frequency, wave speed and wave length?

A

wave speed= frequency x wavelength

v= fλ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

How can we work out frequency from time?

A

f= 1/T

where T is equal to one time period.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

What is the spectrum of visible light?

A

20Hz - 20,000Hz

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

What is the equation the relates area, intensity and power?

A

Intensity= power/ area

=(energy/time)/area

=Power/ 4πr2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

How is the energy of a wave related to it amplitude?

A

Energy of a wave is proportional to the square of it’s amplitude.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

How is the energy of a wave related to it amplitude?

A

Energy of a wave is proportional to the square of it’s amplitude.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

What happens to the amplitude of a wave the further you go away from a wave?

A

It decreases as the wave spreads away from it’s source.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
43
Q

What would happen to the intensity of a wave if it’s amplitude decreases by a factor of 2?

A

It’s intensity will decrease by a factor of 4 because it’s intensity is also proportional to the square of its amplitude.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
44
Q

What can polarization be used as evidence of?

A

The wave nature of light- all transverse waves can be polarized.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
45
Q

What sort of wave cannot be polarized?

A

Longitudinal waves

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
46
Q

What is ultrasound?

A

Ultrasound is a sound wave with a very high frequency- so we cannot hear it- above 20,000Hz.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
47
Q

How do u ultrasounds produce an image?

A

A transmitter produces an ultrasound pulse. The ultrasound reflects at each boundary it crosses. Time for reflected pulse to return to the detector is measured and used to calculate distance. A computer changes this information into a picture.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
48
Q

How do radio waves transmit information?

A

Radio waves can be used to transfer information as an alternating current is put through a transmitter, which causes electrons to oscillate up and down a wire in the transmitter. This causes the electromagnetic fields around the transmitter to oscillate and form electromagnetic waves. These wave travel from the transmitter to a receiver, causing the electrons in the receiver to oscillate. Data is transmitted as the frequency of the waves is the same from the transmitter then those in the receiver- the data is encrypted in the frequency.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
49
Q

What is a boundary for a wave?

A

A boundary is between two mediums where the wave travels at different speeds.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
50
Q

At a boundary, what will the wave do?

A

A mixture of reflection, absorption and transmission.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
51
Q

How many radians is 360 °?

A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
52
Q

How many radians is 180degrees

A

π

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
53
Q

What do waves transfer?

A

Energy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
54
Q

What is the power of a wave?

A

The energy transferred per second from a wave.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
55
Q

What are the units for intensity of a wave.

A

Wm2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
56
Q

How to work out the intensity of a wave?

A

Intensity= power/ area

I= P/A

I= P/ 4πr2 - waves radiate spherically from a source.

57
Q

What are electromagnetic waves made up of

A

A magnetic field and an electric field oscillating at right angles to one another.

58
Q

How can you define the plane of waves for elecromagnetic waves?

A

The of oscillation of the electric field.

59
Q

What are some examples of unpolarised waves?

A

Light from the sun or light bulbs.

60
Q

Describe unpolarised waves?

A

There is a mixture of waves with many different planes, with all waves oscillating perpendicular to the direction of energy travel.

61
Q

What is a polarising filter?

A

Some crystalline materials can cause the oscillating fields to happen in one plane only. e.g. Polaroid filters.

62
Q

What is a plane-polarised wave?

A

A wave that has fields only in one plane.

63
Q

What sort of waves can be polarised?

A

Transverse waves

64
Q

Why can’t longitudinal waves be polarised?

A

Longitudinal waves do not have right angles to their direction of travel. The oscillations of those waves are in line with the waves direction of travel.

65
Q

Define plane-polarised light.

A

The oscillations of the field and the direction of the travel are confined to one single plane.

66
Q

Define polarising filter.

A

A polarising filter produces a plane-polarised light by selective absorption of one component of the incident oscillations- the filter transmits only one component of the light polarised perpendicular to that direction.

67
Q

When demonstrating polarisation of light using sheets of Polaroid, what is the first sheet called?

A

It is labelled a polariser.

68
Q

When demonstrating polarisation of light using sheets of Polaroid, what is the second sheet called?

A

The analyser

69
Q

What is Maul’s law?

A

States that when a perfect polariser is put into a beams of polarised light, The intensity of the light passes through it is give by I=Imax cos2deta. Also, Imax is the maximum intensity transmitted (at deta=0degrees).

This ;law also shows if the analyser is at a right angle to the polariser, then deta=90 and no light will pass through (crosses Polaroids)

70
Q

What is crossed polaroid’s?

A

The situation where the analyser is at a right angle to the polariser and no light will pass through.

71
Q

What happens to light as it is reflected?

A

It comes partially polarised.

72
Q

Use how waves behave to explain why the sky and sea is blue.

A

Light reflects from water, for example the surface of a lake, and becomes partially polarised. Therefore, blue light is more easily scattered by dust particles and water vapour in the atmosphere than red light. (it is because of this blue light being scattered, sky’s are blue and sunsets are red).

73
Q

How can anglers use polarisation of light to help them catch fish?

A

Anglers cannot usually see the fish use the most of the light being reflected from the surface of the water giving a glare. However, polaroid glasses cut out horizontally polarised light reflected from the waters surface, but allow the vertically polarised light reflected from objects below the surface to pass. Tis means that any fish in the water become visible.

74
Q

What is stain analysis?

A

Strain analysis is used to produce coloured images that change as the plastics are stretched or squashed?

75
Q

How does strain analysis work?

A

Certain plastics, such as those used for making rulers or sellotape, contain long chains of molecules, which become aligned during manufacture. These materials are able to rotate the plane of polarisation so that the transmitted light is polarised. When these plastics are placed between crossed polaroid’s, coloured images are produced that change as the plastics are stretched or squashed.

76
Q

What can strain analysis be used for?

A
  • To analyse stresses in models of structures
  • Detailed analysis of crystal shapes
77
Q

What is this an example of?

A

Strain analysis

78
Q

During youngs slit experiment, what would happen to the fringe spacing if you increase the value of a in increased?

A

a will decrease.

79
Q

During youngs slit experiment, what would happen to the fringe spacing if you increase the value of D?

A

D will increase.

80
Q

During youngs slit experiment, what would happen to the fringe spacing if you double the value of a and D?

A

The fringe spacing will not change.

81
Q

Why is the distance between loud and soft regions different for low frequencies?

A

Lower frequencies would mean larger wavelengths, so the distance between overlapping waves that caused constructive or destructive interference would be greater.

82
Q

Why are the fringes closer together for green light compared to red light?

A

Green light has a shorter wavelength than red light, so the fringe width will be smaller.

83
Q

What is the equation for young’s slit experiment and what do all the letters represent?

A

λ= ax/D

λ= wavelength

a= double slit width

x= distance between fringes

D= distance between the double slits and the screen

84
Q

What is refraction?

A

One of the main phenomenons experienced by electromagnetic radiation.

85
Q

When does refraction occur?

A

When a wave passes from one transparent or translucent medium to another.

86
Q

What will happen to the wave during refraction?

A
  • Wave will change speed
  • Wave will change direction
87
Q

What happens to a wave when it moves from a material of lower refractive index to an area of higher refractive index?

A

Speed of the wave decreases.

88
Q

What happens to a wave when it moves from a material of higher refractive index to an area of lower refractive index?

A

Speed of wave increases.

89
Q

What is the refractive index?

A

Different materials have different refractive indices. The higher the refractive index, the slower electromagnetic radiation travels through compared with its speed in a vacuum.

90
Q

How can you work out the refractive index of a material?

A

Refractive index= speed of light in a vacuum/ speed of light in the material

91
Q

What is the normal?

A

A line drawn as 90° to the boundary between two materials.

92
Q

What does Snell’s law link together?

A

There is a link between the refractive indices of two materials and the directions at which the incident and refracted rays will travel with respect to the normal.

93
Q

What equations explain Snell’s law?

A

n1 x sinθ =n2 x sinθ

or n sinθ = constant

n= refractive index of material

sinθ= angle of incidence

94
Q

What is an angle of incidence?

A

The angle between a ray incident on a surface and the normal.

95
Q

When travelling through a material, why is the emergent ray is parallel to the incident ray?

A

Upon leaving the material of higher refractive index and re-entering the material of lower refractive index, the light ray speeds up to its original speed, hence making the same angle with respect to the normal.

96
Q

Why does the human eye have a range of refractive indices?

A

The lens of the eye changes its thickness, which changes its refractive index. To read or view objects that are close to the reader, the lens needs to be made thicker so that light rays are refracted more. When reading or viewing distant objects, the lens is thinner as light rays need to be bent less to fall on the retina.

97
Q

What is a diffraction grating?

A

A piece of optical equipment made of glass, onto which many thousands of very thin, parallel and equally spaced grooves have been accurately engraved using a diamond.

98
Q

What happens to light shone at a diffracting grating?

A

Light that passes through the diffraction grating will be diffracted at different angles based on the wavelength of the incident light and the separation of the grooves.

99
Q

What factors affect the angles at which flight is diffracted at when it passes through a diffraction grating?

A
  • The wavelength of the light
  • Separation of grooves on the diffraction grating
100
Q

What does the practical using a light source and diffraction grating look like?

A
101
Q

What can diffraction grating be used for?

A

Finding the wavelength of light.

102
Q

Why is using a piece of diffraction grating to find the wavelength of light better than using young’s double slit experiment?

A

It is difficult to find the wavelength of light using Young double-slit experiment because the diffraction fringes are quite blurred which makes measuring fringe width difficult. Using a diffraction grating, increases the number of slits which increases the sharpness of the maxima. The maxima are also further apart, so the angle can be measure with a lower percentage of uncertainty.

103
Q

In terms of the phase difference and path difference, what conditions must there be for two waves to be constructive?

A

Path difference must be 0 and phase difference must be nλ.

104
Q

In terms of the phase difference and path difference, what conditions must there be for two waves to be destructive?

A

Path difference must be 180° and phase difference must be (n+½)λ.

105
Q

What happens to the position and intensity of the maxima when the amplitude of a transmitted wave is halved?

A
  • Position does not change as intensity changes.
  • The intensity decreases by a factor of 4.
106
Q

What are progressive waves?

A

Continuous waves travelling in the same direction and amplitude. These are transverse and longitudinal waves.

107
Q

What are stationary waves?

A

When two harmonic waves of equal frequency and amplitude travelling through a medium (say string) in opposite directions superimpose each other, we get stationary waves. They interfere with the principle of superposition. These are also known as standing waves.

108
Q

Where is a common place to find stationary waves?

A

Stringed instruments use stationary waves to produce a sound.

109
Q

What conditions must there be for a stationary wave to be produced?

A

Waves must:

  • Be Travelling in opposite directions.
  • Have the same frequency.
  • Have approximately the same amplitude.
110
Q

What do you get when you add two waves together?

A

A vector sum.

111
Q

What is a node?

A

Nodes are points in stationary waves at which there is no displacement of the particles at any time.

112
Q

What is an antinode?

A

Antinodes are points on stationary waves when the displacement of the particles in a stationary wave varies by the maximum amount.

113
Q

How far is between a node and an antinode?

A

Quatre of a wavelength.

114
Q

How far is between two adjacent nodes/ antinodes?

A

Half a wavelength.

115
Q

How are stationary waves produced on a string?

A

When progressive waves travelling in opposite directions, are superposed.

116
Q

How are longitudinal and transverse waves similar?

A

They both transfer energy from one place to another without any net movement of matter.

117
Q

How are longitudinal and transverse waves different?

A

Longitudinal waves have vibrations that are parallel to their direction of energy transfer, whereas transverse waves have vibrations that are at right angles to their direction of energy transfer. Longitudinal waves require a medium to travel through, whereas some transverse waves (electromagnetic waves) do not.

118
Q

How is an oscillation different from a wave?

A

An oscillation describes the periodic motion of a particle about its mean position or equilibrium position, whereas a wave refers to the motion of the energy outwards from the initial disturbance.

119
Q

What would happen to the frequency of a wave as if travels from air to glass?

A

It will not chnage.

120
Q

If the area was reduced by 25#5 of its original size, what factor will the intensity change by?

A

It will increase by a factor of 4.

121
Q

What sort of waves can be reflected?

A

All waves.

122
Q

What can we call the reflection of sound waves?

A

An echo.

123
Q

How do echos work?

A

Sound waves spread out in all directions from the source, and those waves that a wall continue to spread as they travel back (after they’re reflected) towards the source. An echo is heard when returning waves reach the original source of the sound.

124
Q

What is a ray on a diagram?

A

A ray is a single line used often to simplify diagrams in which the waves themselves are not shown. Rays are always drawn at right angles to the wavefront. They’re used to indicate the direction of the wave.

125
Q

What is a wavefront?

A

Wavefronts are lines of constant phase, such as crests. They’re drawn for each successive wave, with the distance between wavefronts representing wavelength.

126
Q

How is the wavelength affected after a wave has been reflected?

A

It does not change.

127
Q

When does refraction occur?

A

When one wave travels from one material to another.

128
Q

Why does refraction occur?

A

The two different materials the wave moves through, has different optical densities so the wave will change speed and direction.

129
Q

What can be observed when refection occurs?

A
  • The wave will change speed.
  • There may be a change in direction.
130
Q

How can stationary waves be set up with a microwave transmitter?

A

A microwave transmitter will transmit microwaves towards a metal sheet. The microwaves are reflected back from the sheet along their initial path, resulting in the formation of a stationary wave.

When you move a microwave detector along the stationary wave, it registers the microwaves as signals.

131
Q

What effects the frequency of vibrations of a string on a musical instrument?

A
  • Its mass per unit length.
  • Its tension.
  • The length of the string.
132
Q

How are stationary weaves set up on a violin?

A

While bowing a violin, you create a progressive transverse wave that travels in the direction away from the bow. Where these waves reach a point, They are reflected back along the string. They then interfere with each other producing a stationary wave.

133
Q

What is the equation to find the frequency of a string which relates tension, mass and length?

A

f-½L squareroot T/m

134
Q

What is the fundamental mode?

A

The simplest stationary wave that can be set up. It is half the wavelength.

135
Q

What is the fundamental frequency on a string?

A

It is the lowest frequency and highest wavelength that can be produced on a string.

136
Q

What is a harmonic?

A

Notes of higher frequencies can be produced by higher harmonics. These are stationary waves that are multiples to the fundamental frequency.

137
Q

How do binoculars make use of internal reflection?

A

Binoculars use internal reflection in prisms to redirect light from the object viewed into the eyepiece for viewing by the observer without the loss of intensity.

138
Q

How do optical fibers make use of internal reflection?

A

Optical fibres use total internal reflection to transmit information in the form of electromagnetic radiation.

139
Q

How does the transmission of radio waves in the upper atmosphere make use of total internal reflection?

A

Radio waves are totally internally reflected when they interact with the charged layers in the Earth’s upper atmosphere, enabling information to be sent from one place to another around the world via a series of internal reflections.

140
Q

How does endoscopes make use of total internal reflection in endoscopes?

A

Endoscopes are used for viewing internal structures inside the human body. Light is emitted down cables using internal reflection to send the light around the non-linear pathway of the probe. The light is reflected by the internal organs and sent back through a set of coherent bundles to be viewed by the surgeon. There is minimal loss of light intensity.

141
Q

What conditions are necessary for light to be totally internally reflected?

A

Light must be passing from a material of higher refractive index to one of a lower refractive index.