Section 2 - Waves Flashcards
What do waves transfer?
Energy, NOT matter
What is a wave’s amplitude?
The displacement from the rest position to the crest. (Not from crest to trough)
What is the wavelength?
The distance from one point on a wave to the next corresponding point. (e.g. From crest to crest)
What is a wave’s frequency?
The number of waves passing a point per second OR the number of waves produced by a source per second.
What is the symbol for wavelength?
Lambda
What is frequency measured in?
Hertz (Hz)
What is 1 hertz?
1 wave per second
What is a wave’s time period?
The time it taken for one complete wave to pass a point.
What is time period measured in?
Seconds
What are the top and bottom of a wave called?
Top: Peak
Bottom: Trough
What is the equation for frequency (relative to time period)?
Frequency = 1 / Time Period
F = 1 / T
What are some examples of transverse waves?
All EM waves
What are transverse waves?
Waves which have oscillations perpendicular to the direction of energy transfer.
What are some examples of longitudinal waves?
Sound, ultrasound and shock waves
What are longitudinal waves?
Waves which have oscillations parallel to the direction of energy transfer.
Are mechanical waves longitudinal or transverse?
They can be both.
Give some examples of mechanical waves.
- Water waves
- Shock waves
- Waves in springs
What is the squashing up and stretching out of particles in a material when a longitudinal waves pass through called?
Compressions and rarefactions
What is the formula for wave speed?
Wave speed (m/s) = Frequency (Hz) x Wavelength (m)
v = f x lambda
What is the unit for wavelength?
Metres
What three things can happen to a wave at an obstacle?
- Reflection
- Diffraction
- Refraction
What determines whether you get a reflection off a surface?
How smooth the surface is. If it is even, there is a clear reflection (e.g. Off a mirror). If it is uneven, there is no clear reflection.
Why does a smooth surface allow clear reflection?
The waves all bounce off at the same angle.
What is the law of reflection?
Angle of incidence = Angle of reflection
What is the normal?
An imaginary line that is perpendicular to a mirror at the point of reflection.
Where are the angle of reflection and angle of incidence measured from?
Between the normal and the ray (NOT between the ray and the surface)
What are the features of a reflected image in a plane mirror?
- Same size as object
- Virtual
- Upright
- Laterally inverted
How do you draw a ray diagram for an image in a plane mirror?
- Draw the virtual image (it is as far from the mirror as the object is in front)
- Draw the reflected ray from the image to the top of the eye (dotted line behind mirror and solid line in front)
- Draw the corresponding incident ray from the object to the mirror
- Repeat 2 and 3 with a ray that goes to the bottom of the eye
What is diffraction?
The spreading out of waves as they pass through a gap or pass an object.
What factors increase diffraction?
- Narrower gap / Longer wavelength
* Gap similar size to wavelength
When does maximum diffraction occur?
When the gap is the same size as the wavelength.
What is interference?
When two identical waves disturb each other.
Do all waves cause a disturbance in their medium?
Yes - water waves disturb water particles, EM waves disturb electric and magnetic fields, sound waves disturb air particles, etc.
What are the two types of interference?
Constructive and destructive
What is constructive interference?
When two waves disturb in the same direction and reinforce each other.
What is destructive interference?
When two waves disturb in opposite directions and cancel each other out.
What happens after two waves interfere with each other?
They keep travelling in the direction they were travelling, just as they were before.
What is the total displacement during interference?
The sum of the displacements of the waves at a point (i.e. how high or low the pulse is)
How does high density affect the speed of EM waves?
It slows them down.
How does high density affect sound waves?
They speed up.
What happens when a wave crosses a boundary between mediums?
It changes speed.
What is refraction?
The change in direction of waves when crossing a boundary between mediums.
What happens when light travels from a less dense to more dense medium?
It slows down and bends towards the normal.
What happens when light travels from a more dense to a less dense medium?
It speeds up and bends away from the normal.
What is the angle of refraction?
The angle between the refracted ray and the normal.
What happens when light enters a triangular prism?
It is dispersed.
What is dispersion?
When white light is split into a spectrum of colours after passing through a triangular prism.
Why does dispersion only happen in triangular prisms, not rectangular blocks?
In a triangular prism, the two sides the light passes through are not parallel, so the different light waves don’t emerge parallel, whereas in a rectangular block they do.
Why does dispersion happen?
Different wavelengths (colours) of light refract by different amounts, so the light is split into colours.
Which colour of light is refracted the most?
Violet
Which colour of light is refracted the least?
Red
What is the refractive index of a material?
- It tells you how fast light travels in that material
* It is the ratio of the speed of light in a vacuum to the speed of light in the material
What is the formula for refractive index (in terms of speed of light)?
Refractive Index = Speed of light in vacuum / Speed of light in material
n = c / v
What is the speed of light in a vacuum?
3 x 10^8 m/s
What is the refractive index of glass?
About 1.5
What is the refractive index of water?
About 1.33
What is the refractive index of air?
1 (to 2 d.p.)
What is the formula for refractive index (in terms of angles)?
Refractive Index = Sin i / Sin r
This is when light passes from AIR to the MATERIAL, not vice versa
Is total internal reflection a form of refraction?
Yes, even if the name suggests otherwise.
How is light kept inside optical fibres?
Total internal reflection
What are optical fibres?
Long tubes of glass or plastic which use total internal reflection to transfer light through them.
How do optical fibres work?
They bounce light waves off the sides of the inner core of glass or plastic until they reach the other end of the tube.
Can total internal reflection happen when the waves are travelling from any medium towards any medium?
No, only when waves are travelling in a dense medium towards a less dense medium.
What happens when the angle of incidence is smaller than the critical angle?
- Most of the light passes through the boundary
* Some is internally reflected
What happens when the angle of incidence is equal to the critical angle?
- The emerging light ray comes out along the surface
* There is also quite a bit of internal reflection
What happens when the angle of incidence is greater than the critical angle?
- No light passes through the boundary
* All of it is internally reflected (total internal reflection)
How does a material’s density affect its critical angle?
The more dense a material, the lower the critical angle (i.e. more light is internally reflected).
Why are diamonds so sparkly?
The critical angle is very small, so a large amount of light is internally reflected.
What is the formula for refractive index (in terms of the critical angle)?
Refractive Index = 1 / Sin c
What is an endoscope?
A thin tube containing optical fibres that lets surgeons examine inside the body.
Describe how an endoscope works.
- 2 bundles of optical fibres -> 1 to carry light to the area + 1 to carry an image back for viewing
- Image can be seen through an eyepiece or displayed on a monitor
What is the advantage of using endoscopes?
It allows for keyhole surgery - where the surgeon can now perform many operations by only cutting a small hole.
Do all EM waves have the same properties?
No, it depends on their wavelength.
How many types of EM waves are there?
7
What is the arrangement of EM waves called?
The EM spectrum
Name the EM spectrum by decreasing wavelength and increasing frequency.
- Radio waves
- Microwaves
- Infrared
- Visible light
- Ultraviolet
- X-rays
- Gamma rays
What happens as the wavelength of EM waves increases?
The frequency decreases and energy decreases.
Which EM wave has the longest wavelength?
Radio wave
Which EM wave has the shortest wavelength?
Gamma ray
Which EM wave has the most energy?
Gamma ray
Which EM wave has the least energy?
Radio wave
Which EM wave has the highest frequency?
Gamma ray
Which EM wave has the lowest frequency?
Radio wave
Which other EM wave is red light closest to?
Infrared
Which other EM wave is violet light closest to?
UV
What is the range in wavelengths of the EM spectrum?
10^-15 to 10^4 m
What is the speed of all EM waves in a vacuum?
3 x 10^8 m/s
What is the wavelength of radio waves?
Over 10cm
What is the wavelength of visible light?
10^-7 m
What is a good mnemonic for remembering the EM spectrum?
Rabbits Mate In Very Unusual (and) Expensive Gardens
What are the different types of radio waves and microwaves used for in communications?
- Microwaves - Satellite phone (can travel through atmosphere)
- Less than 10m - TV (can carry a lot of information)
- 10 - 100m - Local radio stations (limited range)
- More than 100m - International radio stations (long range)
What are long-wave radio waves used for and why?
International TV, because the are able to travel a long distance (since they diffract around the earth).
Why do long-wave radio waves travel far?
They are able to diffract around the Earth and around hills.
What are medium-wave radio waves used for and why?
- Local radio, because they have a limited range.
* However, the shorter ones may be able to reflect off the ionosphere and travel very far.
What are short-wave radio waves used for and why?
TV, because they can carry large amounts of information, but cannot travel very far.
For each radio wavelength, explain why they can or cannot travel very far?
- Long - Travel far - Can diffract around the Earth
- Medium - Sometimes travel far - May reflect off ionosphere
- Short - Don’t travel far - Cannot diffract or reflect off ionosphere
What type of wave does Bluetooth use?
Short-wave radio waves
What is the ionosphere?
An electrically charged layer of the Earth’s upper atmosphere.
What types of EM waves are used for communications and how?
- Radio - TV and radio
- Microwaves - Satellite and mobile phones
- Infrared - Remote controls + Optical fibres
- Visible light - Optical fibres
What are microwaves used for in terms of communications and why?
Satellite communications, remote sensing satellites and mobile phones - They can pass through the atmosphere, unlike radio waves.
How do mobile phones use microwaves?
The waves are sent between the phone and the nearest transmitter.
Why do some people think mobile phones may be bad for your health?
- Some wavelengths of microwaves are absorbed by water and heat this up.
- If this body is in your body cells, it might cause damage, although there is no evidence for this.
What are infrared waves used for in communications?
- Remote controllers
* Optical fibres
How do remote controls work?
They emit different patterns of infrared waves to the TV depending on the command.
How does a camera work?
Uses a lens to focus visible light onto a light-sensitive film or electronic sensor.
In a camera, what does aperture control?
The amount of light entering the camera.
In a camera, what does shutter speed control?
How long the film or sensor is exposed to the light.
What two things can a photographer vary to capture the correct amount of light on a photograph?
- Aperture
* Shutter speed
What are some uses of UV radiation?
- Sunbeds
* Security marking
How can UV radiation be used for security marking?
- Banks print special markings in fluorescent ink on their bank notes -> Allows them to be seen under a UV light, whereas fake notes lack this.
- Security pens -> Used to mark property with your name to help police identify it if it is stolen.
How does fluorescent ink work?
UV light is absorbed and visible light is emitted.
What are some uses of X-rays?
- X-Ray pictures of broken bones
- Tumour therapy
- CT scanners
How are the dangers of an X-ray scan minimised?
Radiographers and patients protected by lead aprons and shields.
What are some uses of gamma radiation?
- Sterilising medical instruments
- Sterilising food
- Killing cancer cells
What does ‘ionising’ mean in terms of EM waves?
- When the radiation enters cells, it collides with electrons, knocking electrons off and causing ionisation -> Damages or destroys cells
- Lower doses -> Cell mutation and cancer
- Higher doses -> Kills the cell
What do low doses of ionising radiation cause?
Cell mutation and cancer
What do high doses of ionising mutation cause?
Kills the cells -> Radiation sickness
What determines the negative effect of an EM wave?
The higher the frequency, the more harmful it is.
What are the dangers of microwaves?
Can cause heating of body cells.
What are the dangers of infrared radiation?
Can cause skin burns.
What are the dangers of UV waves?
- Blindness
* Ionising -> Causes skin cancer
What are the dangers of X-rays and gamma rays?
Can ionise cells, which can kill or damage the cell. Lower doses can cause cell mutation and cancer.
How can the effects of microwaves be minimised?
Microwave ovens need to have shielding to prevent microwaves from reaching the user.
How can the effects of infrared be minimised?
Use of insulating materials -> Minimises amount of IR reaching your skin
How can the effects of UV be minimised?
- Sunscreen with UV filter
* Staying out of strong sunlight
How can the effects of gamma rays be minimised?
Keeping radioactive sources in lead-lined boxes.
How can the effects of X-rays be minimised?
Radiographers: • Wear lead aprons • Stand behind lead screen • Leave the room during the scan Patients: • Lead is used to shield areas of patient's body
What are radio waves used for?
Communications -> Radio, TV, etc.
What are microwaves used for?
- Communications -> Satellite communication, mobile phones, etc.
- Heating food
How do X-ray scans work?
• X-rays are directed at the patient’s body
• They pass through soft tissue, but are easily absorbed by bones, etc.
• The parts of the detector screen that X-rays reach turn black, leaving a white negative image
OR
• A CCD (charge-coupled device) is used to form an image
How can an image of an organ be produced using X-rays?
The patient is given a substance called a CONTRAST MEDIUM, which absorb X-rays easily. This can be done by giving a patient a barium meal before the scan.
What is a CCD?
A charge coupled device, which has sensors covered in a substance which converts X-rays to light. This light rays create electronic signals in the sensors, that are sent to computer, which creates an image.
What does CT stand for?
Computer tomography
How does a CT scan work?
A patient is put in a cylindrical scanner, and an X-ray tube fires X-rays onto a detector on the other side. The X-ray tube and detector are rotated around the patient. The multiple scans can be used to make a 3D image.
How are X-rays produced?
Fast moving electrons are made to hit a metal target.
How can X-rays be used to treat cancer?
- X-rays are focused on a tumour using a wide beam
- This kills the cancer cells
- Beam is rotated around the patient
- This minimises the exposure of normal cells to radiation
How is sound passed through a medium?
Mechanical vibrations are passed through as a series of compressions.
What type of wave is sound?
Longitudinal
How does medium density affect the speed of sound?
Sound travels faster in more dense mediums (e.g. solids rather than gases)
Why can’t sound travel in a vacuum?
There are no particles.
What types of surfaces reflect sound?
Hard flat surfaces
Do sound waves refract?
Yes, because they travel faster in dense mediums.
Do sound waves diffract?
Yes, they can diffract around obstacles and through gaps - this is why you can hear sound around a corner or in another room.
What determines the pitch of a sound?
The higher the frequency, the higher the pitch.
What is the frequency of sound?
The number of complete vibrations each second.
What is the human hearing range?
20 to 20,000 Hz
What determines the loudness of a sound?
The amplitude of the waves
What happens when an ultrasound wave hits a boundary?
It is partially reflected.
What property of ultrasound allows it to be used for imaging?
It is partially reflected at boundaries between mediums, so the time taken for a reflection to reach a detector can be used to calculate the distance to that boundary.
What equation can be used to calculate the distance between boundaries when given an oscilloscope trace?
Distance = Speed x Time
s = v x t
(Remember that the distance needs to be halved, because the wave is travelling there and back)
What device is used to display ultrasound traces?
Oscilloscope
What are the uses of ultrasound?
- Removing kidney stones
2. Pre-natal scans
How can ultrasound be used to remove kidney stones?
Ultrasound waves are concentrated at the kidney stone, breaking it up into sand-like particles.
How can ultrasound be used for pre-natal scans?
Ultrasound waves pass through the body, but when they reach a boundary, they are partially reflected back and are detected. The timing of these echoes is processed by a computer to produce an image.
How do lenses produce an image?
They refract light.
What is a converging lens?
A convex lens, which buldges outwards like this:
()
What is a diverging lens?
A concave lens, which caves inwards like this:
)(
What is the axis of a lens?
The horizontal line passing through the middle of the lens.
What is the principal focus of a converging lens?
The point where rays hitting the lens parallel to the axis all meet. (See diagram pg 47)
What is the principal focus of a diverging lens?
The point where rays hitting the lens parallel to the axis appear to all come from - This is behind the lens. (See diagram pg 47)
What is the focal length?
The distance from the centre of the lens to the principal focus.
How many principal foci are there?
There is one on each side of the lens.
What is a real image?
Where the light from an object comes together to form an image on a ‘screen’.
What is a virtual image?
When the rays are diverging, the light appears to be coming from a different point.
What type of image is formed in a mirror and why?
Virtual - the object appears to be behind the mirror.
Give an example of two times when a virtual image is formed.
- Mirror
- Magnifying lens
What things do you need to talk about when describing an image?
- Magnified or Diminished
- Upright or Inverted
- Real or Inverted
When will a magnifying glass work?
When the object is closer to the lens than the focal length.
How does a magnifying glass work?
- Object must be closer to the lens than the focal length
- The light rays coming off the image are refracted by the lens
- To a person looking on the other side of the lens, the light rays appear to be coming coming from an image larger and further back
- This is a VIRTUAL IMAGE since the light rays don’t actually come from that place
(See diagram pg 47 of revision guide)
Can a virtual image be projected onto a screen?
No, it can only be seen through a lens.
What is the equation for magnification?
Magnification = Image height / Object height
What type of lens does a magnifying glass use?
Converging
What are the 3 rules when drawing ray diagrams for a converging lens?
- Incident ray parallel to axis refracts through lens and passes through the principal focus on other side
- Incident ray passing through centre of lens carries on in the same direction
- Incident ray passing through the principle focus before entering the lens refracts and travels parallel to axis
In ray diagrams, when in the lens does the ray change direction?
In the middle.
Describe how the ray diagram for a converging lens can be drawn.
(See page 48)
- Draw line from top of object to the lens, parallel to the axis.
- This line then goes through the principle focus on the other side.
- Draw line from the top of object to the middle of lens.
- This line then carries on straight until it crosses the other ray
- Where the lines meet is the top of the image
(6. Third line going through principle focus then parallel to axis can be drawn, but is not necessary)
Describe the image formed by an object at 2 focal lengths from a converging lens.
- Real (on other side of lens)
- Inverted
- Same size as object
- 2 focal points away on other side of lens
Describe the image formed by an object between 1 and 2 focal lengths from a converging lens.
- Real (on other side of lens)
- Inverted
- Bigger than object
- Over 2 focal points away on other side of lens
Describe the image formed by an object less than 1 focal length from a converging lens.
- Virtual (on same side of lens)
- Right way up
- Bigger than object
- Same side of lens as object
What are the 3 rules when drawing ray diagrams for a diverging lens?
- Incident ray parallel to axis up to lens refracts so it appears to have come from the principle focus on the near side of the lens.
- Incident ray passing through the centre of lens carries on in the same direction.
- Incident ray travelling towards principal focus on far side of lens turns at the lens and travels parallel to axis.
Describe how the ray diagram for a diverging lens can be drawn.
(See page 49)
- Draw line from top of object to the lens, parallel to the axis.
- This line then refracts so it appears to have come from the principle focus on the near side of the lens.
- Dotted line is drawn from the lens to the principle point.
- Draw line from the top of object to the middle of lens.
- This line then carries on straight.
- Where the two lines meet is the top of the image (on near side of lens)
(7. Third line going towards principle focus on far side of lens then parallel to axis can be drawn, but is not necessary)
Remember to revise drawing lens diagrams.
Pgs 48 and 49 of revision guide
Describe the image formed by a diverging lens.
- Always virtual
- Always upright
- Always smaller than object
- Always on the same side of lens as the object
What does a lens’ power refer to?
How strongly it can converge rays of light.
What is the equation for the power of a lens?
Power (D) = 1 / Focal length (m)
What is the unit for lens power?
Dioptres (D) or m^-1
How do the powers of converging and diverging lenses compare?
Converging: Positive
Diverging: Negative
What two factors affect the power of a lens?
- Lens curvature
* Refractive index of material
How can a lens be made more powerful without increasing the lens curvature?
Making it out of a material with a high refractive index.
What type of lens is a convex lens?
Converging
What type of lens is a concave lens?
Diverging
What is the lens equation (in terms of focal length, image distance and object distance)?
1 / Focal Length = 1 / Object Distance + 1 / Image Distance
1/f = 1/u + 1/v
All units are m.
In the lens equation, what do “f”, “u” and “v” represent?
f = Focal length u = Object distance v = Image distance
Which factors can have either a positive or negative value in the lens equation?
- f - Focal length - Positive if converging lens, negative if diverging lens
- v - Image length - Positive if image is real, negative if image is virtual
In the lens equation, when is “f” positive and when is it negative?
- Positive with converging lenses
* Negative with diverging lenses
In the lens equation, when is “v” positive and when is it negative?
- Positive with real images
* Negative with virtual images
Remember to do some practice questions on the lens equation.
Pg 50 notes
Remember to revise the structure of the eye.
Pg 51 of revision guide or labelled diagram off internet
What is the cornea and what does it do?
- Transparent ‘window’ on the outside of eye with convex shape
- It does the most of the eye’s focusing
What is the iris and what does it do?
- Coloured part of the eye -> Made of muscles
* Controls size of pupil + amount of light entering eye
What is the pupil and what does it do?
- Hole in the middle of the iris
* Size of pupil decides amount of light entering eye -> Controlled by iris
What is the lens and what does it do?
- Lens found behind the pupil
* Changes shape to focus light onto retina -> Shape controlled by ciliary muscles
What are the suspensory ligaments and ciliary muscles?
- Suspensory ligaments connect lens to ciliary muscles
* Contractions of ciliary muscles control shape of lens
What is the retina and what does it do?
- At the back of the eye, covered in light-sensitive cells
* Image is formed on the retina and these cells detect light and send signals to the brain to be interpreted
What happens to the lens when the ciliary muscles contract?
Tension is released and the lens takes on a more fat, rounded shape.
What happens to the lens when the ciliary muscles relax?
Tension is created in the suspensory ligaments and the lens takes on a thinner, flatter shape.
What is the far point of the eye?
The furthest distance the eye can focus on comfortably.
What is the near point of the eye?
The closest distance the eye can focus on comfortably.
What is the far point for normal-sighted people?
Infinity
What is the near point for normal-sighted people?
25cm
What happens to the power of the eye as it focuses on closer objects?
Its power increases.
How does a camera work?
- An image is formed on the film (or CCD) by the converging lens
- It is real, inverted and diminished
- The focus is changed by moving the lens closer to or further from the object.
Describe the image formed by a camera.
Real, inverted and diminished.
What is short-sightedness?
When the person is unable to focus on distant objects - their far point is closer than infinity.
What causes short-sightedness?
• Eyeball being too long
OR
• Cornea and lens system being too powerful
Where do light rays converge in the eyeball of a short-sighted person?
In front of the retina
Which type of lens is used to correct short-sightedness and why?
Diverging lens - This diverges light before it enters the eye, so the light rays converge on the retina, instead of in front of it.
What is long-sightedness?
When the person is unable to focus on near objects - their near point is further than normal.
What causes long-sightedness?
• Eyeball being too short
OR
• Cornea and lens system being too weak
Where do light rays converge in the eyeball of a long-sighted person?
Behind the retina
Which type of lens is used to correct long-sightedness and why?
Converging lens - This converges light before it enters the eye, so the light rays converge on the retina, instead of in behind of it.
What is a laser?
Narrow, intense beam of light.
What are lasers used for in surgery?
- Treating skin conditions -> e.g. Acne scars
* Eye surgery
Why are lasers good for surgery?
They cauterise (burn and seal shut) small blood vessels as they cut through the tissue. This reduces blood loss and infection.
How are lasers used in treating acne scars?
They burn off the top layers of scarred skin, revealing the less-scarred lower layers.
How are lasers used in eye surgery?
They are used to vaporise some of the cornea to change its shape - this changes the focusing ability.
How is the size of the universe changing?
It is expanding and the galaxies are moving away from each other.
What is red-shift?
The light observed coming from distant galaxies appears shifted to the red end of the spectrum because they are moving away from us.
What is the Doppler effect?
When something that emits waves moves towards you or away from you, the wavelengths and frequencies of the waves seem different compared to when the object is stationary.
How do the frequency and wavelength of a wave change when its emitter is moving toward you?
Frequency: Higher
Wavelength: Shorter
How do the frequency and wavelength of a wave change when its emitter is moving away from you?
Frequency: Lower
Wavelength: Longer
Does the Doppler effect affect both longitudinal and transverse waves?
Yes
How does the red-shift of near and far galaxies compare?
The further away a galaxy is, the greater the red-shift, because it is moving away faster.
What does red-shift tell us about a galaxy?
How fast it is moving away from us.
How does an object’s speed affect red-shift?
The faster an object moves, the greater the red-shift.
What does red-shift provide evidence for?
The Big Bang theory.
What is the theory of the Big Bang?
The idea that all the matter and energy in the universe must have been compressed into a very small space. Then it exploded from that initial ‘point’ and started expanding.
How can we estimate the age of the universe?
By looking at the rate of the expansion from the Big Bang.
How old is the universe?
About 14 billion years old.
What is an alternative theory to the Big Bang theory and what does it suggest?
The “Steady State” theory - The universe has always existed as it is now and always will. It explains expansion by suggesting that matter is being created in spaces as the universe expands.
What are some pieces of evidence for the Big Bang theory?
- Cosmic Microwave background radiation
* Universe expanding
What is cosmic microwave background radiation (CMBR)?
- Low frequency electromagnetic radiation coming from all parts of the universe.
- Created just after the Big Bang as gamma radiation.
- Due to expanding universe, it now reaches us as longer wavelengths - microwaves
Is the Big Bang a perfect theory?
No, for example it predicts that the expansion of the universe should be slowing down, but in reality it is speeding up.
What are the two main theories for the future of the universe?
- Big Yawn
- Big Crunch
