Midterm Exam
Average: 13.2/20
Paper B
answers in
columns 1-20:
have been
corrected
Marks and statistics
are on the web site
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WileyPLUS Assignment 3 is Available
Chapters 21, 22, 24, 25
Due Thursday, March 11 at 11 pm
Week of March 9-11
Experiment 4: Geometrical Optics
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39
Chapter 26 so far...
Refractive index:
v = c/n = f!
The frequency of the light is unchanged on refraction
Snell’s law:
n1 sinθ1 = n2 sinθ2
Apparent depth:
d = dn1/n2
Total Internal Reflection
sinθc = n2 sin900/n1
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Total internal reflection around the bend
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Optical fibre – total internal reflection at
the walls steers the light around bends
Applications:
• Medicine – flexible optical fibres used to look inside the body.
“Keyhole” surgery – add surgical instrument, laser beam to vaporize tissue.
• Communications – transmit telephone, radio, TV, internet signals on a
laser beam inside a fibre optic cable – no external interference, much
greater amount of information can be transmitted than with copper cable.
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Uses of Optical Fibres
Using an endoscope to collect samples of
tissue and fluid from the lung of a patient
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Arthroscopic surgery
43
The optical fibre shown consists of a core made of flint glass
surrounded by a cladding made of crown glass.
A beam of light enters the fibre from air at an angle θ1 with respect
to the normal. What is θ1 if the light strikes the core-cladding
interface at the critical angle θc?
B
n1 = 1
A
θ2 = 90◦ − θc
n3 = 1.523
n2 = 1.667
θc = 660, θ1 = 42.70
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Total internal reflection in a prism
45◦ > !c
Glass: n ! 1.5
!c � sin−1(1/1.5) = 42◦
Prisms “fold” the light
path to make the
binoculars shorter.
Each arm acts as a
longer telescope.
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Polarization of light by reflection
Light reflected from a surface is in general partially polarized.
The reflected light is 100% polarized parallel to the surface when
reflection occurs at the “Brewster angle” θB, corresponding to a 900
angle between reflected and refracted rays.
θB + θ2 + 90 = 180
◦
◦
!2
!B + !2 = 90◦
90º
!B
From the triangle: sin !2 = cos !B
Snell: n1 sin !B = n2 sin !2 = n2 cos !B
So, tan !B =
n2
n1
Brewster angle
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Polarization of light by reflection
• Sunlight reflected from water – polarized horizontally. θB = 53º
• Polaroid type sun glasses reduce glare from reflected sunlight by
filtering out horizontally polarized light.
• Digital watches – emitted light is polarized vertically (top to
bottom in the display).
• Display turns dark if rotated by 90o when viewed through
Polaroid sun glasses.
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Dispersion by a prism
lower n, less refraction
!Violet is refracted more than red
higher n, greater refraction
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Prob. 26.43/38: A ray of sunlight is passing from diamond into crown
glass; the angle of incidence is 35º.
Indices of refraction for red and blue light:
Blue: ndiamond = 2.444
ncrownglass = 1.531
Red: ndiamond = 2.410
ncrownglass = 1.520
Determine the angle between the refracted red and blue rays in the
crown glass.
θblue - θred = 0.870
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Dispersion by rain drops – rainbows
Dark
region
Secondary
rainbow,
colours
reversed
Primary
rainbow
Light
region
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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Dispersion by a raindrop – primary rainbow
The refractive index for violet is larger
than for red.
! violet is refracted through a larger
angle than red
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Dispersion – formation of a rainbow
The colours of the rainbow come
from raindrops at different
height, red from higher up, violet
from lower down.
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Violet is refracted through a larger angle than red
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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Sun Dogs
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Sun Dogs
Refraction by hexagonal
ice crystals
Violet is refracted through a
larger angle than red
hyperphysics.phy-astr.gsu.edu/hbase/atmos/halo22.html#c3
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Lenses
A positive (converging, convex) lens
Focal point
Focal point
A negative (diverging, concave) lens
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Formation of image by thin lenses
Parallel to axis, passes
through focal point on right
Passes through focal point on
left, emerges parallel to axis
Passes through centre
of lens in a straight line
Parallel to axis, ray traced
back to axis passes
through focal point on left
Heads toward focal point
on right, emerges parallel
to axis
Passes through centre of
lens in a straight line
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Formation of a real image by a converging lens
Light appears
to originate
from image
Object is outside
the focal point
A “real” image – can be
seen on a screen placed at
the position of the image.
Image is inverted.
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Formation of a virtual image by a converging lens
Light appears
to originate
from image
A “virtual” image – cannot be formed on a
screen. Image is upright, and magnified.
Object is inside
the focal point
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Formation of virtual image
by a diverging lens
Light appears
to originate
from image
Image is virtual, upright, diminished
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Thin lens equation
1
3
!
ho
!
!
!
1
3
f
Object distance
tan ! =
So,
ho hi
=
do di
hi
di di − f
= =
ho do
f
That is:
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1 1 1
+ =
do di
f
Image distance
tan ! =
ho
hi
=
f
di − f
Divide by di :
Thin lens equation
1
1 1
= −
do
f di
Applicable to diverging
lenses too with f < 0
63
Linear magnification
!
ho
!
!
!
f
Linear magnification, m = (height of image)/(height of object)
m=
hi
ho
Similar triangles:
hi di
=
ho do
(or from tan !)
Sign convention, image is inverted, so: m = −
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di
do
64
f>0
Converging lens, f > 0
do (> 0)
di (> 0)
Object
Lens
Image
Diverging lens, f < 0
f<0
do (> 0)
di (< 0)
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