Electromagnetic Waves
r Electromagnetic waves (EM wave): it is characterized by time varying electric field E r and magnetic induction (field) B . In EM waves, these two fields are interdependent to each other.
Maxwells Equations
Maxwells Equations: in fr
Read Hecht, Chapter 2 Bring Hecht textbook with you tomorrow!
Spherical Harmonic Waves
Assume the wave is isotropic: it propagates radially out uniformly in all directions, it does not depend on and For a constant k this is described by: kr =const, or r =
Read Hecht, Chapter 2: 2.1-2.6
Waves: Mathematical preliminaries
The gradient operator: (cartesian coordinates):
r r r = i+ j+ k x y z
When the gradient is applied to a scalar function U(x,y,z) the result is a vector called the gradient of U:
U r U r U r
Read Hecht, from Chapter 5: 5.7 and Chapter 6
Comment: matrix for reflection and the sign for the elements of the ray vector
Refraction:
n2 2 1 n2 n1 n11 R Y = Y1 2 0 1
1 D R= 0 1
D= (n2 n1 ) R
(2)
Reflection:
(n=n1=-n2)
n2 2 1 2n1 n11 R Y = 2 0 1 Y1
1
Read Hecht, from Chapter 5: 5.3 and 5.7 from Chapter 6: 6.1 to 6.3
Matrix method: summary
Translation:
n 2 1 Y = d 2 n
0 n 1 1 Y1
1 = d n
0 1
(1)
Refraction:
n2 2 1 n2 n1 n11 R Y = Y1 2 0 1
1 D R= 0 1
D= (n2 n1 ) R
(2)
Reflection:
(n=n1=-n2)
n2 2 1
Read Hecht, from Chapter 6: 6.1 to 6.3
Matrix method in paraxial optics
When a ray passes through a optical system (no matter how complicated) there are three types of processes: 1) 2) 3) translation (i.e. the ray continues in a straight line); refraction
Read Hecht, from Chapter 5: 5.4 Chapter 6: 6.1 to 6.3
Thin Lenses in Contact
In general, f.f.l. b.f.l., however, if d contact, we have: 0, that is when the lenses are brought in
f . f .l. = b. f .l. =
f1 f 2 f1 + f 2
or
111 =+ f f1 f 2
(37)
If we have N t
Read Hecht, from Chapter 5: 5.1 to 5.5 HW1 due today by 6pm Mailbox: Rm. 257 (Robinson) OR box outside Rm. 209 (STC)
Paraxial ray conditions: cos 1 and sin
Spherical surface:
n1 n2 n2 n1 + = So Si R
Thin lenses:
111 += So Si f
1 1 1 = (nl 1) R R f 2 1
Fo
Read Hecht, from Chapter 5: 5.1 to 5.5
Paraxial ray condition and image formula
However, under the paraxial ray conditions: cos 1 and sin (6)
The spherical surface can be approximated as an ideal optical system. Under these conditions, lo = So, li = Si, E
Refraction from Fermats principle
Q A OB
OB = x AQ = h
QO = d1
Q
AO = p x
Q ' B = h'
Q' O = d 2 = n1 d1 + n2 d 2
Optical path length:
There is only one variable in the problem; why? Fermats principle:
() = 0
d = 0 n1 sin 1 = n2 sin 2 dx
Example I: Atomi
Nature of Light
Light is both a wave and a particle in a non-classical sense. Wave property (1) light can have interference and diffraction (2) it is a part of electromagnetic spectrum, from 400 to 800 nm (this is the visible spectrum for a human eye > ou
Read Hecht, Chapter 3: 3.1-3.3.3 Monday, October 19: Seminar in STC, Rm. 136. This seminar will replace our regular class that Monday!
Maxwells Equations
Maxwells Equations: in free space Integral form
= o
= o and = 0
Differential form
r J =0
r rr B r E