Download Waves and Radiation

24/05/2017
Space for
Reflection
W Richards
The Weald School
24/05/2017
P5a Satellites, Gravity and Circular Motion
The Earth’s Orbit
Ellipse
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Gravity
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Gravity is an attractive force that affects anything with mass:
Note that this
force goes both
ways – the Earth
is attracted to us.
Centripetal force and The Earth
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Gravity (and the fact that the Earth is moving
at high speeds) keeps the Earth in orbit.
Notice that the orbit path is slightly elliptical
Orbit times
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Mercury = 88 days
Mercury
Venus
Earth
Mars
Mars = 687 days
Pluto =
Jupiter
90,500 days
Saturn
Uranus
Neptune
Pluto
Satellites
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The word “satellite” can be used to describe anything that
_____ something else. The moon is a _______ satellite of
the Earth and we also have many ________ satellites. All of
these satellites are continually ________ towards the Earth
but their “tangential” ________ keeps them moving in a
circular orbit.
Words – velocity, orbits, accelerating, natural, artificial
Comets
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Comets are balls of dust and frozen
gas. They have very elliptical orbits:
What happens to the speed of the comet when it approaches
the sun and why?
More information on gravity
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The amount of gravity attracting an object
decreases the further out the object is…
F
If you double the
distance the gravitational
force divides by 4…
F/4
If you triple the
distance the force
divides by 9…
F/9
Artificial Satellites
Geostationary
orbits:
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Low polar orbits:
Artificial Satellites
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Artificial satellites have been around for 50 years and have 3 main uses:
1) Observation (e.g. Hubble Space Telescope) –
these are in orbit high above the Earth and can
observe the universe without interference by the
____________
2) Communications (e.g. ___, phone, car
“SatNav” systems) – these satellites are
in “geostationary” orbits. This means
that the satellite always stays above
____ ____ point on the Earth and takes
a ______ to complete an orbit
3) Monitoring (e.g.
weather, spy
satellites) – these
satellites have a
“___ _____” orbit
and may scan
around the Earth
several times a day
and travel _____.
Words – the same, atmosphere, low polar, TV, day, faster
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P5b Vectors and Equations of Motion
Speed vs. Velocity
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Speed is simply how fast you are travelling…
This car is travelling at a
speed of 20m/s
Velocity is “speed in a given direction”…
This car is travelling at a
velocity of 20m/s east
Relative Speed
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Consider two cars driving past each other:
20mph
50mph
What is the relative speed of the cars compared to each
other?
Circular Motion
1) Is this car travelling at constant speed?
2) Is this car travelling at constant velocity?
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Speed vs. Velocity
Speed =
Speed =
Velocity =
Velocity =
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Start
-1 metre
1 metre
Speed
Speed
= =
Velocity
Velocity
= =
“Speed” is how fast you go. “Velocity” is how fast in a given
direction.
Vector vs. scalar
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Scalar quantities have size (“magnitude”) only and no direction.
Vector quantities have both size and direction.
Scalar or vector???
Scalar
Vector
8. Power
2. Distance12. Acceleration
1. Mass
6. Energy
7. Time
3. Displacement
4. Speed
11. Force
10. Current
5. Velocity
9. Momentum
Adding Vectors
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Calculate the “resultant vector” for these pairs of vectors:
10N
5N
10km
100ms-1
5ms-1
10km
14.1km
100.1ms-1
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Distance, Speed
and Time revision
Speed = distance (in metres)
time (in seconds)
S
V
T
1) Simon walks 200 metres in 40 seconds. What is his speed?
2) Howard covers 2km in 1,000 seconds. What is his speed?
3) How long would it take Ryan to run 100 metres if he could
run at 12m/s?
4) Ben throws a book at Dan and it travels at 50m/s for 0.2s.
How far away was Dan?
5) Chris is learning to drive. He drives his car at 85mph
(about 40m/s). How long does it take him to drive 20km?
Equations of Motion
u+v
s=
2 t
v = u + at
s = ut + ½at2
v2 = u2 + 2as
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Some hard questions
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1) Ben drops a ball on Dan’s foot. How long does the ball take
to fall 1m? 2m? Why is the second answer not twice the
first?
2) Ryan flies to Belgium. His aeroplane has a maximum
acceleration on the ground of 3.4ms-2. What is the
minimum length of runway needed to reach its take off
speed of 110ms-1 and how long will this take?
3) Luke likes watching kangaroos. A kangaroo jumps to a
vertical height of 2.8m. For how long was it in the air?
4) Tom likes baseball. A baseball pitcher can release a ball at
40ms-1 after accelerating through a distance of 2.5m.
Calculate the average acceleration of the ball.
P5c Projectile Motion
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Vertical Projection
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If I throw this ball upwards with a speed of 40ms-1
how high will it go?
Use v2 = u2 + 2as
0 = 402 + (2 x -9.81 x s)
0 = 1600 – 19.62s
1600 = 19.62s
s = 1600/19.62
s = 81.5m
Practice Questions
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1) How far will a cricket ball go if it is thrown upwards with an
initial velocity of 10ms-1?
2) How far will a table tennis ball go if it is thrown upwards
with an initial velocity of 5ms-1?
3) A human cannonball is projected vertically upwards and she
reaches a vertical height of 20m before coming back down.
How fast was she going when she left the cannon?
4) A test tube falls off the table. If the table is 1m high how
fast was the test tube going when it hit the floor?
Projectile Motion
Aha! If I let go of the branch when
he fires his gun I’ll be safe because
the bullet will go above me…
This curved path is called a “trajectory”
and its shape is “parabolic”.
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Analysing Projectile Motion
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Throughout this motion
the horizontal velocity
stays the same:
The vertical velocity
changes due to the
effect of gravity:
Projectile Motion
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Question – how long did this take
and how fast was the bullet?
1.5m
50m
1) Use x = ut + ½at2 vertically to find the time
2) Then use speed = distance / time horizontally to get the
speed
Example questions
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1) Ben throws a bowling ball at Tom and it lands on his foot.
If the ball started 1.2m above Tom’s foot and the distance
between them was 2m calculate both the time taken and
the initial velocity of the ball.
2) Rob fires a gun and the bullet leaves the barrel at a speed
of 200ms-1. If it landed on the ground 500m away calculate
how long the journey took and how high up Rob was holding
the gun from ground level.
3) Andrew likes knocking test tubes off the table. If he hits
one with an initial velocity of 2ms-1 and the table is 1m high
calculate the time taken for the test tube to hit the floor
and how far away from the table it landed.
Recap questions
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1) Andrew Murray hits a tennis ball and it passes horizontally
over the net and lands just inside the baseline of the court.
The net has a height of 1.07m and is 11.9m from the
baseline. Find the horizontal speed of the ball.
2) Ronaldo takes a free kick and it flies into the top corner
horizontally. If the corner is 2.4m above the ground and
the goal is 18m away calculate the time taken for the ball
to reach the goal.
Projectile Motion in Sport
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When playing golf, football, throwing a
javelin etc the range clearly depends on
the angle. What is the best angle for the
longest range?
P5d Action and Reaction
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Action and reaction
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When body A exerts a force on body B, body
B exerts an equal and opposite force on body
A. My third law of motion!
My third law says
that if I push to
the right I will
move backwards
as well.
Newton 1642-1727
Action and reaction
What will happen if I push
this satellite away from me?
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Action and reaction
Consider a man standing on the Earth:
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Momentum
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Any object that has both mass and
velocity has MOMENTUM. Momentum
(symbol “p”) is simply given by the formula:
P
Momentum = Mass x Velocity
(in kgms-1)
(in kg)
(in ms-1)
M
What is the momentum of the following?
1) A 1kg football travelling at 10ms-1
2) A 1000kg Ford Capri travelling at 30ms-1
3) A 20g pen being thrown across the room at 5ms-1
4) A 70kg bungi-jumper falling at 40ms-1
V
The Conservation of Momentum
24/05/2017
In any collision or explosion, momentum is conserved. Here is
an example:
Before I fired this gun I had no momentum. This
means that after I fired the gun I must also have
no momentum. Therefore, if the bullet goes
forwards, I will have to move backwards to
balance the bullet’s momentum.
Conservation of Momentum
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In any collision or explosion momentum is conserved (provided that there
are no external forces have an effect). Example question:
Two cars are racing around the M25. Car A collides with the back of car B
and the cars stick together. What speed do they move at after the
collision?
Speed = 50ms-1
Mass = 1000kg
Speed = 20ms-1
Mass = 800kg
Mass = 1800kg
Speed = ??ms-1
Momentum before = momentum after…
…so 1000 x 50 + 800 x 20 = 1800 x V…
…V = 36.7ms-1
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Momentum in different directions
What happens if the bodies are moving in opposite directions?
Speed = 50ms-1
Mass = 1000kg
Speed = 20ms-1
Mass = 800kg
Momentum is a VECTOR quantity, so the momentum of the
second car is negative…
Total momentum = 1000 x 50 – 800 x 20 = 34000 kgms-1
Speed after collision = 34000 kgms-1 / 1800 = 18.9ms-1
More questions…
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1) A white snooker ball moving at 5ms-1 strikes a red ball and pots it.
Both balls have a mass of 1kg. If the white ball continued in the same
direction at 2ms-1 what was the velocity of the red ball?
2) A car of mass 1000kg heading up the M1 at 50ms-1 collides with a
stationary truck of mass 8000kg and sticks to it. What velocity does
the wreckage move forward at?
3) A defender running away from a goalkeeper at 5ms-1 is hit in the back
of his head by the goal kick. The ball stops dead and the player’s speed
increases to 5.5ms-1. If the ball had a mass of 500g and the player had
a mass of 70kg how fast was the ball moving?
4) A gun has a recoil speed of 2ms-1 when firing. If the gun has a mass of
2kg and the bullet has a mass of 10g what speed does the bullet come
out at?
Another example
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Consider the nuclear decay of Americium-241:
237
93
Np
241
95
Am
The momentum before the decay was
zero, so the Neptunium atom and alpha
particle must have equal and opposite
momentum.
4
2
α
Particle Motion in Gases
24/05/2017
Gas pressure is caused by particles hitting the side of a
container. Anything we do that increases those collisions will
increase the pressure:
These collisions mean that the particles are changing in
momentum every time they hit the sides of the container.
Therefore the side of the container is exerting a force back
on the particles.
Particle Motion in Gases
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Consider decreasing the volume:
The particles should collide with the sides of the container
_____ often, therefore the pressure is ________.
Particle Motion in Gases
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Now consider increasing the temperature as well:
The particles should collide with the sides of the container
_____ often, therefore the pressure is ________. This
could cause the container to ______.
Another example
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Consider a rocket:
Rockets use the ideas of ______ and Newton’s third law. The
gas is under high _______ which means the particles are
pushed out with a large ______. The particles therefore
exert an equal and opposite reaction on the rocket, pushing it
upwards. To launch a satellite into space, a ______ force is
needed so you’ll need lots of ____ and it should be under high
pressure.
Words – fuel, momentum, large, force, pressure
P5e Satellite Communication
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Diffraction
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Diffraction is an effect seen when a wave travels around a corner or
through a narrow gap:
More diffraction if the size of the gap is similar to the wavelength
More diffraction if wavelength is increased (or frequency decreased)
Artificial Satellites
24/05/2017
Satellites use digital microwaves to
send us communications:
Geostationary satellites use higher
frequency waves
The satellite dish needs to be pointed
exactly at the satellite as the
microwaves are not diffracted much
due to the size of the transmitter on
the satellite being much bigger than
the wavelength of the microwaves.
Low polar satellites use lower
frequency waves
Analogue vs. Digital Signals
24/05/2017
Analogue signals (like talking or
music) continually vary in
amplitude and/or frequency
1
0
+
Digital signals, however, are either
off or on, and the information is sent
in a series of pulses
There are two main advantages of digital:
1) More information can be sent down the same cable
2) Better quality, because a digital signal can be amplified without
amplifying the extra noise:
Radio Waves
24/05/2017
Some radio waves (frequencies between
30Mhz and 30GHz) pass through the Earth’s
atmosphere – therefore microwaves are used
to communicate with satellites.
Some radio waves (above 30GHz) are
absorbed or scattered by the rain and
dust in the atmosphere.
Some radio waves are
reflected by the
atmosphere (they have a
frequency below 30MHz).
Diffraction of Radio Waves
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A high frequency (short wavelength)
wave doesn’t get diffracted much – the
house won’t be able to receive it…
Diffraction depends on frequency…
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A low frequency (long wavelength) wave
will get diffracted more, so the house
can receive it…
P5f Nature of Waves
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Interference
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Interference is seen when two waves of the same type cross:
“Reinforcement”
“Cancellation”
Interference Patterns in Water
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Interference of Sound Waves
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Path Difference
Constructive
interference
Destructive
interference
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1st Max
Min
Max
Min
1st Max
2nd Max
Phase Difference
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Phase difference means when waves have the same frequency
but oscillate differently to each other. For example:
These two waves have
different amplitudes but
the same frequency and hit
their peaks at the same
time – they are “in phase”
These two waves start
opposite to each other –
they are “in antiphase”
Coherence
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Two waves are said to be “coherent” if they have the same
frequency and the same constant phase difference. For
example:
These waves have a
different frequency,
so phase is irrelevant.
Coherence
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These waves have the same frequency,
the same amplitude and they are in
phase so they are “coherent”
How Light Travels
Light travels in transverse waves in straight lines:
Laser
Shadows are evidence of this:
However, light can “bend” when it
goes through a more dense
medium:
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Interference Patterns from 1 slit
Intensity
Distance
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Interference Patterns from 2 slits
Intensity
If white light is used you see this:
Distance
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Interference Patterns from 2 slits
Consider red light (monochromatic, so it’s coherent) being
shone through a “double slit”:
The fact that light is
diffracted in the first
place is evidence that
light travels as waves.
Constructive
interference
(reinforcement)
For the best effect,
the size of the gaps
must be comparable
to the wavelength
Destructive
interference
(cancellation)
Polarisation
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All electromagnetic waves are transverse. Consider one wave:
If you looked at it “end on” it might look like this:
And lots of them
might look like this:
Polarisation
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Polaroid sunglasses use this
effect to “tint” light. Light
reflected from water is also
polarised. What would
happen if you looked at light
reflected from water using
polaroid sunglasses?
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Particle Theory and Wave Theory
Light can be reflected, refracted and
diffracted. These three things are called
“wave behaviour” so light must travel as a
wave. It makes sense!
Isaac Newton,
1643-1727
Ah yes, but light also demonstrates some
“particle behaviour” so many scientists say
that it travels as a set of particles called
photons. However, not everyone agrees with
this!
Max Planck,
1858-1947
P5g Refraction of Waves
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Refraction through a glass block:
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Wave slows down and bends
towards the normal due to
entering a more dense medium
Wave slows down but is
not bent, due to entering
along the normal
Wave speeds up and bends
away from the normal due to
entering a less dense medium
Refraction
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Refraction is when waves ____ __ or slow down due to travelling in a
different _________. A medium is something that waves will travel
through. When a pen is placed in water it looks like this:
In this case the light rays are slowed down by the water and are _____,
causing the pen to look odd. The two mediums in this example are ______
and _______.
The amount of refraction that a medium will do can be measured by its
“refractive index” – the higher the index, the more refractive the medium
is.
Words – speed up, water, air, bent, medium
Calculating the Refractive Index
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The refractive index can be calculated by comparing the speed
of light in the medium to the speed of light in air:
Refractive index =
Speed of light in vacuum
Speed of light in medium
1) If the speed of light is 3x108m/s and a medium slows this
down to 2x108m/s what is the medium’s refractive index?
2) Another ray of light enters a medium with refractive index
1.4. If its speed in a vacuum was 3x108m/s what will its
speed in this medium be?
Dispersion of Light
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Different colours of light have different refractive indices
(and a different speed) when travelling through glass.
Therefore this happens:
RED LIGHT is
refracted THE
LEAST
PURPLE LIGHT is
refracted THE MOST
Finding the Critical Angle…
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1) Ray gets refracted
3) Ray still gets refracted (just!)
2) Ray still gets refracted
4) Ray gets totally
internally reflected
THE CRITICAL
ANGLE
The critical angle is ______ for a medium with high refractive index
Calculating the Critical Angle
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Consider when the light was refracted at 90O:
THE CRITICAL
ANGLE
The critical angle can be
calculated if you know the
refractive index of the two
mediums:
Sin c =
nr
ni
1) The refractive index of water is 1.3 and the refractive
index for air is 1. Calculate the critical angle for a ray of
light emerging from water into air.
2) Determine the critical angle for glass or plastic using the
equipment provided.
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Uses of Total Internal Reflection
Optical fibres:
An optical fibre is a long, thin, _______ rod made of
glass or plastic. Light is _______ reflected from one
end to the other, making it possible to send ____
chunks of information
Optical fibres can be used for _________ by sending
electrical signals through the cable. The main advantage
of this is a reduced ______ loss.
TIR is also used in Cat’s Eyes.
Words – communications, internally, large, transparent, signal
P5h Optics
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Converging and diverging lenses
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CONVERGING (Convex)
Thickest at the centre
A thinner convex lens
Ray diagrams for convex lenses
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A “distant
object”
Focal length
The rays of light are
refracted INWARDS and
meet at the focus, F.
F
The image formed is REAL –
in other words, it can be
seen on a screen
Ray diagrams
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To draw ray diagrams follow these three rules:
1) Draw a ray from the TOP of the object PARALLEL to the axis and
then going through F:
F
F
2) Draw a ray from the TOP of the object going
through the CENTRE of the lens (which will be
undeviated)
3) Draw a ray from the top of the object through F
to the left of the lens and parallel to the axis
This image is REAL,
INVERTED and
DIMINISHED
Ray diagrams 2
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If the object is below the axis follow this step:
4) Draw a ray from the bottom of the object parallel to the axis and
then up through the focal point:
F
F
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F
F
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F
F
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F
F
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F
F
More about lenses
24/05/2017
Compare thin and thick lenses:
Notice that these
glasses have got a large
curvature. How would
you make strong glasses
but also make them
thinner and with less
curvature?
Practical uses of lenses
24/05/2017
Cameras use the lens arrangement where the
object is beyond twice the focal length – this
is why they can’t be used at very short range.
Magnifying glasses use the arrangement where
the object is between the focal point and the
lens – this is why they don’t work when you move
them away from the object.
Magnification
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Basically, magnification means “how much bigger the object
looks”:
Magnification =
Image size
Object size
Example questions:
1) What is the magnification of a magnifying glass that
enlarges a 4mm ant to 20mm?
2) A microscope has a 100x magnification. If it is used to look
at a speck of dust that is 0.01mm big how big will it look
through the microscope?