Lec. 8: Ch. 3 - Geometrical Optics
We are
here
1.
2.
3.
4.
Virtual images (review)
Spherical mirrors
Spherical lenses
Aberrations of lenses
Homework is due Tuesday next week.
Next week: Concept questions Tues. and Thurs.
We covered about 31
of these viewgraphs.
Next Thursday: Exam review
Tuesday, Sept. 28: Exam 1
Read: Ch. 4.1 and 4.2.
1
Web tutorials with Java Applets
•
•
•
•
•
Useful web links on curved mirrors
http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html
http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html
http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html
http://micro.magnet.fsu.edu/primer/java/mirrors/convex.html
•
•
•
•
•
•
Useful web links on lenses
http://micro.magnet.fsu.edu/primer/lightandcolor/lenseshome.html
http://micro.magnet.fsu.edu/primer/java/lenses/simplethinlens/index.html
http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html
http://micro.magnet.fsu.edu/primer/java/lenses/diverginglenses/index.html
http://micro.magnet.fsu.edu/primer/java/components/perfectlens/index.html
2
1
Review: We now have several distinct
cases for mirror ray tracing
• Convex spherical mirror object outside only
• Concave spherical mirror, object outside center
• Concave spherical mirror, object between center
and focus
• Concave spherical mirror, object between focus
and mirror
For each case, you can now answer: Image
larger? Virtual? Where? What good is it?
AND you can answer these question by ray tracing with three simple rules
3
On to lenses: first, review refraction
air
n=1 (nearly)
v = c (nearly)
glass, e.g.
n=1.5
v = c/n < c
Rays bend toward normal when entering slower medium (larger n),
away from normal when entering faster medium (smaller n).
4
2
A trick to remember which way rays bend
Soldiers in mud analogy (challenge: where does this analogy break down?)
As soldiers slow down, space
between them narrows
“rays” (perpendicular to
fronts)
“fronts”
pavement
(soldiers go
fast)
deep mud (soldiers
march slower
through deep mud)
5
Ray tracing with lenses
Brute force ray tracing:
n=1
Rays entering
“slower” material
bend toward
normal
n>1
Rays entering
“faster” material
bend away from
normal
1. As long as ray stays in same
medium, it goes straight.
2. At each interface to a different
medium, use Snell’s law to
calculate how it will bend. Go
back to 1.
This gets tedious!
6
3
Thin convex (converging) lens
focal length
F
F
foci
7
Thin convex lens: three easy rules for ray tracing
focal length
1) A ray parallel to the axis
is deflected through the
focus on the other side
2) A ray through the center
of the lens continues
undeviated
3) A ray coming from the
focus on one side goes
out parallel to the axis
on the other
1 1
2 2
3
3
F’
F
3
foci
The ray might have to be extended to find the image
8
4
Note light-focusing property of convex
(converging) lens
a good light collector or solar
oven; can also fry ants with
sunlight, but please don’t do that
unless you’re going to eat them
9
Note light-dispersing property of
convex lens
The “backwards” light collector:
create a collimated light beam
10
5
Where will this ray go?
Ray Tracing
foci (focuses?)
11
Ray Tracing
Where will this ray go?
Suppose it’s emitted from this
object
foci (focuses?)
12
6
Ray Tracing
Where will this ray go?
Suppose it’s emitted from this
object
We know where these 3 rays go, using
the simple ray rules
foci (focuses?)
13
Ray Tracing
Amazing property of this lens:
all rays from the tip of the
object will converge to the
same point
We know where
these 3 rays go,
using the simple
ray rules
14
7
Ray Tracing
Where will this ray go?
Suppose it’s emitted from this
object
Amazing property of this lens:
all rays from the object will
converge to the same point
We know where these 3 rays go, using
the simple ray rules
15
Thin concave (diverging) lens
Guess how this ray will be bent:
F
F’
For diverging lens focal length defined to be negative
(of the distance between focus and lens)
16
8
Thin concave (diverging) lens
F’
F
For diverging lens focal length defined to be negative
17
Thin concave (diverging) lens: three easy ray rules
1) A ray parallel to the axis
is deflected as if it came
from the focus
2) A ray through the center
of the lens continues
undeviated
3) A ray aimed at the focus
on the other side comes
out parallel
1
2
3
F’
F
Ray might have to be extended
For diverging lens focal length defined to be negative
18
9
Difference between convex (converging) and
concave (diverging) lenses
1
F
F’
(Rule 3, the backwards
version of rule 1, also differs)
1
F
F’
19
Ray tracing a convex lens: object inside focus
20
10
Ray tracing a convex lens: object inside focus
The image appears larger (and farther away) than the object.
This is a magnifying glass. {Demo}
(Remember: a magnifying glass is a convex lens.)
Aside: near-sighted people need concave/diverging lenses; can a marooned
myopic start a fire with his eye-glasses?
21
Web tutorials with Java Applets
•
•
•
•
•
Useful web links on curved mirrors
http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html
http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html
http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html
http://micro.magnet.fsu.edu/primer/java/mirrors/convex.html
•
•
•
•
•
•
Useful web links on lenses
http://micro.magnet.fsu.edu/primer/lightandcolor/lenseshome.html
http://micro.magnet.fsu.edu/primer/java/lenses/simplethinlens/index.html
http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html
http://micro.magnet.fsu.edu/primer/java/lenses/diverginglenses/index.html
http://micro.magnet.fsu.edu/primer/java/components/perfectlens/index.html
Can demo some of these in lecture if there is time.
22
11
Lec. 8: Ch. 3 - Geometrical Optics
We are
here
1. Virtual images
2. Spherical mirrors, ray tracing
3. Spherical lenses, ray tracing
Thin lens approximation
3 formulas
4. Aberrations of lenses
23
Some definitions
• Radius of curvature (for a curved mirror):
the radius of the sphere the mirror is "cut from," (a distance).
• Center of curvature for a mirror, C:
the center of the sphere mentioned above (a place).
• Focal point, F:
the point or points where rays appear to converge (a place)
• Focal distance or focal length:
the distance from the mirror (or lens) to the focal point (a length),
usually you are told what it is. This is a property of the lens.
• Paraxial ray:
a ray of light coming into the mirror parallel to the axis (a line)
24
12
Thin lens approximation
Light is refracted at the two glass-air surfaces but we
pretend that there is one bend at the midplane of the lens.
Distances XO and XI are measured from the midplane.
25
Object distance, image distance, focal length
Xobject
Ximage
F
26
13
Lec. 8: Ch. 3 - Geometrical Optics
1.
2.
3.
We are
here
Virtual images (review)
Spherical mirrors
Spherical lenses
Thin lens approximation
Formulas
Magnification
Adding lenses
Image distance
4.
Aberrations of lenses
27
Magnification formula
S0 = object height
Si = image height
Note the similar triangles.
Si
S
=− o
Xi
Xo
or
Si
X
= − i = Magnification
So
Xo
Distances below the horizontal axis are defined as negative.
This slide had an error that was fixed
28
Demo: big mama lens and bulb
14
Image distance equation
F = focal length
XO = object distance
XI = image distance
Usually, F is given.
1
1
1
+
=
XO X I F
1
1
1
= −
X I F XO
Distant objects:
Let Xo be very large, say 1,000,000 meters.
Then 1/Xo = 0.000001, which is very small. You can ignore it.
Then
1
1
≅
XI F
For distant objects,
the image is at the focal point
(ask a burnt ant)
29
Demo: find focal length of the big lens
What is lens power (or diopters)?
Lens power: D = 1/F
Units of D are 1/meters, also called diopters
Eyeglass lenses are measured in diopters.
Example: D = 2/m = what focal length?
F = 1/D = 1/(2/m) = (1/2) m = 0.5 m
15
How thin lenses add
Ftot = final focal length
F1 = focal length lens 1
F2 = focal length lens 2
Diverging lenses (concave)
have negative focal lengths
This is the same as adding
powers:
Dtot = D1 + D2
Hint: convert to meters if
given cm or mm.
31
Demo: suppose focal lengths 25 cm and 50 cm?
Compound Lenses
• Can have less aberration.
• A modern lens can have 16 elements and can “zoom”.
“stop”
Reduces aberration
Image
plane
32
16
Fresnel Lens
Used in lighthouses
Lighthouse lens
Fresnel stage light
33
34
http://sandiartfullyyours.com/NewFiles/lighthouse3/images/Ponce%20Fresnell.jpg
17
Concave mirror gadgets
Solar cooker
Auto headlight
35
Web tutorials with Java Applets
•
•
•
•
•
Useful web links on curved mirrors
http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html
http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html
http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html
http://micro.magnet.fsu.edu/primer/java/mirrors/convex.html
•
•
•
•
•
•
Useful web links on lenses
http://micro.magnet.fsu.edu/primer/lightandcolor/lenseshome.html
http://micro.magnet.fsu.edu/primer/java/lenses/simplethinlens/index.html
http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html
http://micro.magnet.fsu.edu/primer/java/lenses/diverginglenses/index.html
http://micro.magnet.fsu.edu/primer/java/components/perfectlens/index.html
36
18
Lec. 8: Ch. 3 - Geometrical Optics
1. Virtual images (review)
2. Spherical mirrors
3. Spherical lenses
3 formulas
We are
here
4. Aberrations of lenses
37
Aberrations
•
•
•
•
•
Field curvature
Off-axis aberration
Spherical aberration
Distortion
Chromatic aberration
38
19
Aberration: field curvature
Image does not
lie in one plane
39
Off axis aberration
Edges of images are less clear.
40
Demo with lens and bulb
20
Spherical
aberration
Rays at the edge focus
closer to the mirror
41
Demo with lens, not mirror
Aberrations: Distortion
42
Demo with overhead and small lenses
21
Chromatic Aberration
43
Demo with lens and bulb
22