physics for scientists and engineers ii, summer semester 2009 1 lecture 23: july 17 th 2009 physics...

Physics for Scientists and Engineers II , Summer Semester 2009

1

Lecture 23: July 17th 2009

Physics for Scientists and Engineers II


2

The Wave under Refraction

NormalIncident Ray Reflected Ray

21 '1

2Refracted Ray

Air

Glass

Angle of Refraction

12 vv

1v


3


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


4


NormalIncident Ray Reflected Ray

1 '1

12 Refracted Ray

Air

Glass

Angle of Refraction

12 vv

1v


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


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


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


8

Huygens’s Principle : Reflection

1

B

A C

D

'1

'

'11

'11

''

'

9090coscos

BCAD andcos andcos

AC

AD

AC

BC


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


10

Dispersion

n is a function of .

n

nm,700400

red

blue

red. than more refracted is blue


11

The Prism

deviation) of (angle

angle)(apex


12

The Prism

1

23

4

3421 4321 sinsinsinsin nn

290

390

3232 1809090

34

21


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


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


15

Angle of Deflection

242360360

R

yRy arcsinsin

nR

y

n

αβnα arcsin

sinarcsinsinsin :Refraction

R

y

nR

yarcsin2arcsin424


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


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


18

Total Internal Reflection

Incident Ray

21 nn

2n

c

1

2

221

sin

90sinsin

n

n

nnn

c

c


19

Optical Fibers

Not within the “cone of acceptance”(light falls too steep onto the fiber wall and is notTotally reflected)

Total internal reflection

physics for scientists and engineers ii, summer semester 2009 1 lecture 23: july 17 th 2009 physics...

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