Post on 31-Dec-2015
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Geometrical Optics – Part II
Chapter 24
1
Going Backwards
2
'
0'
1
)2
(1/s 2
2
'
11
ss
R
Rs
Rss
Stuff We continue with mirrors and lenses and even
refractive surfaces. Quiz on Friday For a while, office hours will be in, of all
places, my office. We really don’t need MAP-318 except before exams. And the hours are too confusing.
Next Exam is on Wednesday, December 2nd. I give up on the remaining evil clickers.
Clicker grade=0. Let’s move on.
3
4
When the Center of Curvatureis on the same side of theoutgoing ray, RR is positive.
Otherwise, if the center of curvature is not on the same sideas the outgoing ray, RR is negative.
Concave Mirror/Paraxial Approximation
Consequently
Rss
R
h
s
h
s
h
2
'
11
2
'
MIRROREQUATION
5
Image Formation
6
0'
0
0
s
R
s
‘
‘
y’<0(from the diagram) so image is inverted.
The geometry……
7
s
s'-m
and '
'
s
y
so Triangles,Similar
diagram)in image inverted fromsign (- '
s
y
y
ym
Let’s try an example
8
A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 15 cm from the mirror.
9
10 cm 5 cm
Normal to mirrorand bounces backalong incomingpath.
mmys
sm
s
fRss
4
5.'
5.7'
12
'
11
A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 10 cm from the mirror.
10
10 cm 5 cm
mmys
sm
cms
fRss
8
0.1'
10'
12
'
11
A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror.
11
10 cm 5 cm
eyemmys
sm
cms
fRss
8
0.2'
5'
12
'
11
virtualimage
The Concave Mirror
12
More Convex Mirror
13
Graphical Methods are very useful to check your work.
14
Moving on to refractive surfaces
15
Spherical Refractive Surfaces
16
air glass
A closer look atthe Math ….
17
bbaa
b
a
nn
)(
'
s
h
b
a
b
aab n
n
n
nR
h
s
h
Ignoring
R
nn
s
n
s
nR
hnn
s
hn
s
hn
bnnn
nnnn
n
n
abba
abba
baab
aabb
b
a
)(
'
)('
)(
)(
No for the height of the image
18
sn
sn
y
ym
s
ynn
s
ynn
s
ys
y
s
a
bbbaaa
b
aa
'''
''
'
tan
Check this out – how big is R?
19
From the math:
20
0'
)(
'
s
n
s
nR
nn
s
n
s
n
ba
abba
sn
sn
y
ym
s
a ''
1
1'
''
0'
m
sn
sn
snsns
n
s
ns
n
s
n
a
b
ba
ba
ba
21
The Thin Lens We ignore the
thickness of the lens.
We will use mostly geometrical methods.
Any ray that bends is assumed to bend only once at the center of the lens.
22
From whence it came
23
Surface 1
Surface 2
n=1 n=1.5 n=1
Surface 2n>1
The thin lens - geometry
24
parallel
More Geometry
Lens is thin Actual thickness of the lens is ignored.
Image from first surface provides the object for the second surface.
Paraxial Ray Approximation sin(x)=tan(x)=x cos(x)=1 x is in RADIANS
25
More Geometry
26
Triangle PQO andtriangle P’Q’O aresimilar.
s
s
y
y ''
We will show that fora very thin lens:
F1=F2=f
fss
s
sm
f
fs
y
y
or
fs
y
f
y
1
'
11
'''
'
'
AOP'at Looking
The Thin Lens Equation
27
This, of coursedepends on where the
object is placed with respect to f.
Thin Lens (con’t)
28
Image thatwould form
if material “a”was all on this
side of the lens.
Object for secondsurface.
29
Procedure for equation
•Solve for image position for first surface•Use image as object for the second surface.•Use the refraction equation in both cases.
222
b
111
a
's
n
:surface secondFor
's
n
:#1 SurfaceConsider
R
nn
s
n
R
nn
s
n
bcc
abb
For a lens. na=nc=1So we can call the middle one just n
12 ' : ssNote
Mess with the algebra and you will get:
221
111
1
'
1
s'
n-
1
's
1
R
n
s
R
n
s
n
FINALLY – with some algebra and obvious substitutions, we get:
30
fRRn
ss
111)1(
'
11
21
The Lensmaker’s Equation
Two Ways to do this STUFF Algebraically using the lens equation (with the
1/f if you know it) Using graphical Methods
31
Graphical Methods:
32
Graphical Methods:
33
Most important case: converging lensObject to left of F1
34
Most important case: converging lens
35
Most important case: converging lens
36
Most important case: converging lens
37
Most important case: converging lens
38
Most important case: converging lens
39