Transcript The angle of refraction

Waves, Photons and Medical Physics
AS Module 2
2.1
Waves 
2.2
Refraction
2.4
Superposition and Interference
2.5
Diffraction
2.6
Sound
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Waves: Physics AS Level
2.2 Refraction
You need to be able to:
•
Describe an experiment to verify Snell’s law
•
Recall and use the formula sin i / sin r = n
•
Perform and describe an experiment to measure
refractive index
•
Demonstrate knowledge and understanding of total
internal reflection
•
Recall and use the formula sin C = 1/n
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Waves: Physics AS Level
Refraction
Refraction occurs when a wave (e.g. light) travels from one medium
to another (e.g. air to glass). Its direction of travel is changed.
When a wave slows down, the direction of travel moves towards the
normal to the surface:
The angle of
refraction
(angle B) is
smaller than
the incident
angle (angle
A) because
the wave has
slowed down
going into the
prism.
The angle of
the
emergent
ray is bigger
(angle C)
again as the
wave
speeds up
leaving the
prism.
When a wave speeds up, the direction of travel moves away from the
normal to the surface.
NB: The word medium means the substance the wave is travelling through
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Waves: Physics AS Level
Partial Reflections and Energy
When a wave travels from one medium into another not all of the ray
passes into the second material. There will also be a weak reflected
ray, which will obey the laws of reflection. This is called partial
reflection.
Incident
wave
Weak
reflected
wave
i
r
refracted
wave
This means that some of the energy from the incident wave has
been transferred to the reflected wave (~10%), and the rest to the
refracted wave (~90%). The exact amount of energy transferred
depends upon how different the two materials on each side of the
boundary are.
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Waves: Physics AS Level
Snell’s Law
Snell’s Law states: ‘For light travelling from one material to
another, the ratio sin i is a constant.’
sin r
This is normally shown as the equation sin i = n, where n is a constant
sin r
n is called the Refractive index, i is the angle of incidence (angle
between the incident ray and the normal) and r is the angle of
refraction (the angle between the refracted ray and the normal).
n depends upon the materials through which the wave is travelling.
The refractive index of a wave travelling from air to glass is written as:
airnglass
What does a refractive index of
air n water tell
us about the wave?
** Since n is a ratio,
Pageit5 will not have any units**
Waves: Physics AS Level
Snell’s Law: Examples
1. When a light wave travels from air to water the angle of incidence is
measured, i = 27.0o , and the angle of refraction, r = 20.0o. Calculate
the refractive index airnwater.
Airnwater =
sin i = sin (27o) = 0.454 = 1.33
sin r sin (20o) 0.342
2. What is the angle of refraction when light travels from air into
glass with an angle of incidence of 60o. The refractive index airnglass
is 1.5.
Airnglass =
sin i = sin (60o) = 0.454 = 1.5
sin r
sin r
sin r
So sin r = 0.454 = 0.302. Therefore sin-1(0.302) = r
1.5
r = 17.6o
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Waves: Physics AS Level
Snell’s Law Experiment
If you draw a graph of sin i against sin r you should get a straight
line through the origin. This shows that sin i = constant.
sin r
sin i = gradient = n
sin r
sin i
sin r
This will be true for any refractive index.
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Waves: Physics AS Level
Refraction…what’s happening?
When a light ray is shone into a glass block, why does it refract?
The light wave slows down as it enters the glass, which is a more
dense medium. It therefore bends towards the normal.
What will happen to the light ray as it leaves the glass block?
The light wave speeds up as it leaves the glass and bends away
from the normal.
This can be shown on the diagram below:
r
i
Air
Glass
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Air
Waves: Physics AS Level
Refraction…what’s happening?
Since how much a wave refracts depends upon its speed, the
refractive index, n can be written as a ratio of two speeds:
medium 1
n medium 2 = speed of light in medium 1
speed of light in medium 2
Example:
The refractive index for light moving from a vacuum into air is
1.0003, and the speed of light in a vacuum, c=2.9979x108ms-1.
What is the speed of light in air?
2.9979x108
vacuumnair = speed of light in vacuum => 1.0003 =
speed of light in air
Speed of light in air
∴ speed of light in air = 2.9979x108 = 2.9970 x 108ms-1
1.0003
** This answer is very close to the speed of light in a vacuum**
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Waves: Physics AS Level
Air and vacuum
When light travels from a vacuum of space into our atmosphere
there is a very slight refraction. This is normally not noticed,
except when there is a total eclipse of the moon.
During the total eclipse stage, the moon is not visible, but will
appear very slightly. This is because it has been lit up by the
sunlight refracted by the Earth’s atmosphere.
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Waves: Physics AS Level
Refraction in Practice (ii)
Shorter Wavelengths bend the most
All colours of light travel at the same speed in air. But different
colours of light travel at different speeds in glass – so different
colours bend at different amounts in glass. Red light is diffracted
least because it travels fastest in glass (higher wavelength); violet
light is diffracted most as it travels slowest.
Angle of deviation
Wavelengths
Red >700 x 10-6m
Violet 400 x 10-6m
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Waves: Physics AS Level
Ultrasound Scans
An ultrasound scan can be used to take measurements of your eye,
detect cysts or tumours or to monitor a developing foetus. It works in
a similar way to how sonar is used to monitor sea beds etc.
The ultrasound scanner can transmit and detect ultrasound waves.
Ultrasound waves are transmitted into the patient and when they
meet material, some of the wave is reflected back to the scanner to
pick up a picture, while the rest of the energy carries on into the
body.
However, because of the difference between
air and skin, you cannot just point the probe
at the skin and get ultrasound to enter the
body. Something is needed to match the
skin with the air more closely – nowadays
the most common practice is to smear oil on
the patients skin. This will reduce the
amount of wave energy reflected back and
allow the wave to continue into the patient.
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Waves: Physics AS Level
Total Internal Reflection 1
3 rays of light are passing from
water to air as shown. Each ray has
different angles of incidence, so
have different angles of refraction.
As the angle of incidence increases,
the refracted ray gets closer and
closer to the water surface.
2
3
3
2
1
Eventually at ray 3, the light only just escapes from the water.
The incident angle between ray 3 and the normal in water is
called the critical angle. This is the largest angle at which
refraction out of a denser medium is just possible.
When the angle of incidence is greater than the critical angle,
total internal reflection occurs. This means that all of the light
is reflected back into the water.
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Waves: Physics AS Level
Total Internal Reflection
Once the critical angle has been passed, total internal
reflection occurs and there is no refraction: all the light is
reflected back into the glass.
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Waves: Physics AS Level
Total Internal Reflection in
Optical Fibres
As we have seen before, information is transmitted down optical
fibres using light emitted from LEDs.
The optical fibre is made from two materials – an inner glass core
and a more dense material on the outside.
The angle of the light wave emitted from the LED is always much
more than the critical angle. When the ray hits the boundary of the
two materials total internal reflection occurs and the wave continues
down the fibre.
Ray hits boundary and total internal
reflection occurs
Light ray
from LED
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Waves: Physics AS Level
Applications for Optical Fibre
1. Telecommunications:
Advantages
• the glass can be made very pure so there is little energy loss as
the wave travels
• it is very secure as the signal can only be extracted by breaking
the cable
• many more channels can be transmitted down a fibre optic cable
than copper cable.
Problems
• If the optical fibre is scratched the light can escape because a ray
can meet the surface of the scratch with an angle of incidence less
than the critical angle.
• The pulses from the LED need to follow down the fibre one after
the other to give a pure signal:
The red wave will arrive
before the green wave. This
is avoided by making the
glass fibre very thin
Wave 2
Wave 1
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Waves: Physics AS Level
Applications for Optical Fibre (ii)
2. Medical Endoscope
An endoscope consists of bundles of glass fibres made into a glass
pipe which is passed down a patient’s throat to gain information about
internal organs or remove samples, gallstones etc. without the need
for surgery.
Endoscopes work using the
principle of total internal
reflection, like fibre optic cables.
Normally two bundles of glass
fibres are used: one to light up
the region of interest and the
other to pass images back to
the surgeon.
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Waves: Physics AS Level
Total Internal Reflection
Incident ray
Refracted ray
reflected ray
1. The incident ray is refracted
by the glass block. There is a
very weak reflected ray just
visible
2. The refracted ray is now 90o.
It is at this point the angle of
incidence is called the critical
Refracted angle is 90o angle.
Incident ray
c
Reflected
ray is weak
Incident ray
C+
Reflected ray is bright
3. At any point beyond the
critical angle, the refracted ray
disappears and the reflected ray
becomes v bright.
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Waves: Physics AS Level