Refraction for thin lenses

1
Refraction for thin lenses
PH103
Dr. James van Howe Lecture 3
Starting a fire with an ice lens
http//www.primitiveways.com
March 14, 2008
2
Bonus The reign of terror was

• The mass killings and executions of nobility and
  enemies of the French revolution
• An early Sam Raimi B-horror film
• The name of the Black Sabbaths 1983 world tour
• The self-given name describing a terror campaign
  by ETA

3
A beam of light shines into a transparent medium
with parallel surfaces. Part of the beam is
reflected back into the air as diagrammed below.
(The figure is NOT to scale). The index of
refraction of the medium is 1.5. Which of the
following is true?
air
medium

Problem 73. MCAT, Test 8
4
Solution
air
B.
medium
For reflection angle incident is same as reflected
5
If a ray of light travels slightly at an upward
angle, what is the trajectory for the scenario
below?
Cooler Air, more dense
Warm Air, less dense
Hot pavement
A
B
C
6
Highway Mirage
7
How a lens works Snells law
Toward Normal
Away from Normal
In middle lens is flat, Normal incidence
Greater bending at edges focusing.
Converging lens
8
Diverging lens also bends rays most at edges,
just away from a common point defocusing
Toward Normal
Away from Normal
9
Power of lens focusing strength
In diopters (ophthalmolog /optometry units m-1)
lensmakers equation
R is the radius of curvature of the glass surfaces
How do you make a higher power (more tightly
focusing) lens?
10
A lens transforms a plane wave into a spherical
wave
A Plane wave is light from infinity, it focuses
at the focal point of the lens, f. Likewise, a
point source originating at the focal point is
imaged to infinity. A point source at the focus
becomes a plane wave.
11
A lens transforms a plane wave into a spherical
wave
Same thing is true for a diverging lens except
the original source is virtual. It is as if we
had a point source at the focal spot even though
nothing is there.
12
23.7 Thin Lenses Ray Tracing
13
When the object is farther than focal length
Image is real, inverted
14
Object within focal length
Image is virtual, upright and always magnified
15
23.7 Thin Lenses Ray Tracing
For a diverging lens, we can use the same three
rays the image is upright and virtual.
16
23.8 The Thin Lens Equation Magnification
The thin lens equation is
Solving for di
Magnification
The power of a lens is positive if it is
converging and negative if it is diverging.
17
23.8 The Thin Lens Equation

• The sign conventions are slightly tricky
• The focal length is positive for converging
  lenses and negative for diverging.
• The object distance is positive when the object
  is on the same side as the light entering the
  lens (not an issue except in compound systems)
  otherwise it is negative.
• The image distance is positive if the image is
  on the opposite side from the light entering the
  lens otherwise it is negative.
• The height of the image is positive if the image
  is upright and negative otherwise.

18
23.8 The Thin Lens Equation Magnification

• Problem Solving Thin Lenses
• Draw a ray diagram. The image is located where
  the key rays intersect.
• Solve for unknowns.
• Follow the sign conventions.
• Check that your answers are consistent with the
  ray diagram.

19
23.9 Combinations of Lenses
In lens combinations, the image formed by the
first lens becomes the object for the second lens
(this is where object distances may be negative
in the case of a virtual object).
20
Book Example done a little differently
60 cm
80 cm
Recall
Dob Not just dia, be careful!!
21
Book Example done a little differently
60 cm
80 cm
22
To help with the ray diagrams and intuition, you
may want to use the free online software below
below software.
http//webphysics.davidson.edu/alumni/MiLee/java/F
inal_Optics/optics.htm
23
Name_________________________
Lens Combinations, March 14,
Diverging lens f -10 cm,
Converging lens f10 cm,
Distance between lenses d15 cm,
1. Sketch a ray diagram 2. Find both the location
and magnification of the final image
Note that if an object seems to be illuminated
from the wrong side of the lens (rays seem to
come out of nowhere), it is virtual
24
Homework
Will be posted after section 02