physics for scientists and engineers ii, summer semester 2009 1 lecture 23: july 17 th 2009 physics...
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Physics for Scientists and Engineers II , Summer Semester 2009
1
Lecture 23: July 17th 2009
Physics for Scientists and Engineers II
Physics for Scientists and Engineers II , Summer Semester 2009
2
The Wave under Refraction
NormalIncident Ray Reflected Ray
21 '1
2Refracted Ray
Air
Glass
Angle of Refraction
12 vv
1v
Physics for Scientists and Engineers II , Summer Semester 2009
3
The Wave under Refraction
Incident Ray, Reflected Ray, and Refracted ray are all in one plane.
1 mediumin light of Speed
2 mediumin light of Speed
sin
sin
1
2
1
2 v
v
Physics for Scientists and Engineers II , Summer Semester 2009
4
The Wave under Refraction
NormalIncident Ray Reflected Ray
1 '1
12 Refracted Ray
Air
Glass
Angle of Refraction
12 vv
1v
Physics for Scientists and Engineers II , Summer Semester 2009
5
Index of Refraction – not yet covered in class but needed for homwork.
v
c
medium ain light of speed
in vacuumlight of speedn: Refraction ofIndex
1n :mediaother All
1n :For vacuum vacuum
n
n
nnn
n
nc
nc
v
v
fv
fv
fvfvfff
22111
2
2
1
2
1
2
1
2
1
221121
changes.ngth but wavele constant, remainsfrequency
:medium a enterslight When
Wavelength in vacuum
Wavelength in medium
n
Physics for Scientists and Engineers II , Summer Semester 2009
6
Snell’s Law of Refraction – not yet covered in class but needed for homwork.
2211
2
1
1
2
1
2
sinnsinn
n
n
sin
sin
v
v
Snell’s Law of Refraction
Physics for Scientists and Engineers II , Summer Semester 2009
7
Huygens’s Principle (1678)
All points on a given wave front are taken as point sources for the production of spherical secondary waves, called wavelets, that propagate outward through a medium with speeds characteristic of waves in that medium. After some time passed, the new position of the wave front is the surface tangent to the wavelets.
Plane wave
tc
Old wavefront
New wavefront
Old wavefront
New wavefront
Physics for Scientists and Engineers II , Summer Semester 2009
8
Huygens’s Principle : Reflection
1
B
A C
D
'1
'
'11
'11
''
'
9090coscos
BCAD andcos andcos
AC
AD
AC
BC
Physics for Scientists and Engineers II , Summer Semester 2009
9
Huygens’s Principle : Refraction
1
B
A C
D
22111
2
2
1
2
1
2
1
2
1
22
11
sinsinsin
sin
sin andsin
nnn
n
nc
nc
v
v
tv
tv
AC
tv
AC
AD
AC
tv
AC
BC
1
2
2
Physics for Scientists and Engineers II , Summer Semester 2009
10
Dispersion
n is a function of .
n
nm,700400
red
blue
red. than more refracted is blue
Physics for Scientists and Engineers II , Summer Semester 2009
11
The Prism
deviation) of (angle
angle)(apex
Physics for Scientists and Engineers II , Summer Semester 2009
12
The Prism
1
23
4
3421 4321 sinsinsinsin nn
290
390
3232 1809090
34
21
Physics for Scientists and Engineers II , Summer Semester 2009
13
The Prism
421
53.4074.1960
74.19333.arcsin5.1
30sinarcsin
sinarcsinsinsin
23
1221
n
n
390
1
23
4
290
32
Calculate:30 and,60, 1.5n Assume 1
1.779747.arcsin53.40sin5.1arcsinsinarcsinsinsin 3434 nn
8.4653.401.7774.19303421
Physics for Scientists and Engineers II , Summer Semester 2009
14
Refraction and Reflection in a Sphere (e.g., drop of water) – didn’t get to it in lecture, but if you are interested, here it is……
sinRy
incoming direction
outgoing direction
R
2360
Physics for Scientists and Engineers II , Summer Semester 2009
15
Angle of Deflection
242360360
R
yRy arcsinsin
nR
y
n
αβnα arcsin
sinarcsinsinsin :Refraction
R
y
nR
yarcsin2arcsin424
Physics for Scientists and Engineers II , Summer Semester 2009
16
Dispersion of the angle of deflection
0
10
20
30
40
50
0 0.5 1y/R
Red
Blue
Largest angle of returnand also the most intenselight in that angle region.
40 :blueFor
42 :redFor
max
max
Physics for Scientists and Engineers II , Summer Semester 2009
17
How we see the rainbow
Eye For lower drops red misses the eye Lower drops look blue
For higher drops blue misses the eye Higher drops look red
Physics for Scientists and Engineers II , Summer Semester 2009
18
Total Internal Reflection
Incident Ray
21 nn
2n
c
1
2
221
sin
90sinsin
n
n
nnn
c
c
Physics for Scientists and Engineers II , Summer Semester 2009
19
Optical Fibers
Not within the “cone of acceptance”(light falls too steep onto the fiber wall and is notTotally reflected)
Total internal reflection