College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
College Physics B - PHY2054C
Types of Lenses
Image
Formation
Converging Lenses
Optics: Lenses & Image Formation
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
10/22/2014
My Office Hours:
Tuesday 10:00 AM - Noon
206 Keen Building
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Outline
1 Reminder: Snell’s Law
Total Internal Reflection
Types of Lenses
Image
Formation
Converging Lenses
2 Lenses
Types of Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
3 Image Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
4 Examples
The Eye
Rainbows
Aberrations
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Snell’s Law
The ratio c/v is called index of refraction and is denoted by n:
• n = c/v
➜
sin θ 1 = n sin θ 2
A more general statement can be applied to any two materials
with indices of refraction n1 and n2 :
n 1 sin θ 1 = n 2 sin θ 2
Snell′ s Law
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Index of Refraction
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Snell’s Law
Snell’s Law applies whether light begins in the material with the
larger or smaller index of refraction. Refraction is reversible:
• Possible angles of refraction are between 0◦ and 90◦ .
• Side with larger index of refraction has smaller angle.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Snell’s Law
Snell’s Law applies whether light begins in the material with the
larger or smaller index of refraction. Refraction is reversible:
• Light is refracted toward the normal when moving into the
substance with the larger index of refraction.
• Light is refracted away from the normal when moving into
the substance with the smaller index of refraction.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Snell’s Law
Snell’s Law applies whether light begins in the material with the
larger or smaller index of refraction. Refraction is reversible:
• Light is refracted toward the normal when moving into the
substance with the larger index of refraction.
• Light is refracted away from the normal when moving into
the substance with the smaller index of refraction.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Total Internal Reflection
When light is incident from the side with a higher index of refraction, it is bent away from the normal according to:
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
n 1 sin θ 1 = n 2 sin θ 2
Snell′ s Law
What happens at θ 2 = 90◦ ?
Examples
The Eye
Rainbows
Aberrations
θ2 > θ2
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Total Internal Reflection
When light is incident from the side with a higher index of refraction, it is bent away from the normal according to:
Lenses
Types of Lenses
Image
Formation
n 1 sin θ 1 = n 2 sin θ 2
Snell′ s Law
Converging Lenses
Diverging Lenses
Thin-Lens Equation
θ 2 = 90◦ ➜ θ 1 = θ crit :
θ crit = sin−1
n2
n1
Examples
The Eye
Rainbows
Aberrations
θ2 > θ2
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Total Internal Reflection
When light is incident from the side with a higher index of refraction, it is bent away from the normal according to:
Lenses
Types of Lenses
Image
Formation
n 1 sin θ 1 = n 2 sin θ 2
Snell′ s Law
Converging Lenses
Diverging Lenses
Thin-Lens Equation
θ 2 = 90◦ ➜ θ 1 = θ crit :
θ crit = sin−1
n2
n1
Examples
The Eye
Rainbows
Aberrations
The angle of incidence for which the angle of refraction is 90◦
is called the critical angle:
• If the angle of incidence is increased beyond the critical
angle, Snell’s Law has no solution for θ 2 .
• This behavior is called total internal reflection.
➜ Physically, there is no refracted ray.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Total Internal Reflection
When light is incident from the side with a higher index of refraction, it is bent away from the normal according to:
Lenses
Types of Lenses
Image
Formation
n 1 sin θ 1 = n 2 sin θ 2
Snell′ s Law
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
θ 2 = 90◦ ➜ θ 1 = θ crit :
θ crit = sin−1
n2
n1
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Total Internal Reflection
When light is incident from the side with a higher index of refraction, it is bent away from the normal according to:
Lenses
Types of Lenses
Image
Formation
n 1 sin θ 1 = n 2 sin θ 2
Snell′ s Law
Converging Lenses
Diverging Lenses
Thin-Lens Equation
θ 2 = 90◦ ➜ θ 1 = θ crit :
θ crit = sin−1
n2
n1
Examples
The Eye
Rainbows
Aberrations
The optical fibers are
composed of specially
made glass:
• These signals are
sent as light waves.
• They are directed
along fiber using
internal reflection.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Outline
1 Reminder: Snell’s Law
Total Internal Reflection
Types of Lenses
Image
Formation
Converging Lenses
2 Lenses
Types of Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
3 Image Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
4 Examples
The Eye
Rainbows
Aberrations
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Lenses
A lens uses refraction to form an image.
➜ Typical lenses are composed of
glass or plastic.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Lenses
A lens uses refraction to form an image.
➜ Typical lenses are composed of
glass or plastic.
A The refraction of the light rays as
they pass from the air into the lens
and then back into the air causes
the rays to be redirected.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Lenses
A lens uses refraction to form an image.
➜ Typical lenses are composed of
glass or plastic.
A The refraction of the light rays as
they pass from the air into the lens
and then back into the air causes
the rays to be redirected.
B For simplicity: The rays are drawn
to the center of the lens, although
refraction occurs at both surfaces.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Lenses
A lens uses refraction to form an image.
➜ Typical lenses are composed of
glass or plastic.
A The refraction of the light rays as
they pass from the air into the lens
and then back into the air causes
the rays to be redirected.
B For simplicity: The rays are drawn
to the center of the lens, although
refraction occurs at both surfaces.
C Parallel rays close to the principal
axis intersect at the focal point:
• This is true for incident rays from
either side of the lens.
• Focal points are at equal distances
on the two sides of the lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Spherical Lenses
The simplest lenses have spherical surfaces:
• The radii of curvature of the lenses are called R1 and R2 .
• The radii are not necessarily equal.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Types of Lenses
Converging Lenses
• All the incoming rays parallel to the principal axis
intersect at the focal point on the opposite side.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Types of Lenses
Converging Lenses
• All the incoming rays parallel to the principal axis
intersect at the focal point on the opposite side.
Diverging Lenses
• All incoming rays parallel to the principal axis intersect at
the focal point on the same side as the incident rays.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Focal Point of a Diverging Lens
1
The parallel incident rays from the left are refracted away
from the axis.
2
The rays on the right appear to emanate from a point F
on the left side of the lens.
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
➜ This point F is one of the focal points of the lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Outline
1 Reminder: Snell’s Law
Total Internal Reflection
Types of Lenses
Image
Formation
Converging Lenses
2 Lenses
Types of Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
3 Image Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
4 Examples
The Eye
Rainbows
Aberrations
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Image from a Converging Lens
College
Physics B
Image from a Converging Lens
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
An infinite number of light
rays emanates from object.
For simplicity, choose three
rays that are easy to draw.
➜ Start at the tip of object.
College
Physics B
Image from a Converging Lens
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
An infinite number of light
rays emanates from object.
For simplicity, choose three
rays that are easy to draw.
➜ Start at the tip of object.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Image from a Converging Lens
Parallel ray is initially parallel
to the principal axis:
• Refracts and passes
through the focal point on
the right (FR ).
Focal ray passes through the
focal point on the left (FL ):
• Refracts and goes
parallel to the principal
axis on the right.
Center ray passes through the
center of the lens (point C). If
the lens is thin, the center ray
is not deflected by the lens.
College
Physics B
Image from a Converging Lens
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
The three rays come together
at the tip of the image on the
right of the lens:
1
The image is inverted.
2
The image is real.
➜ Rays pass through
the image.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Rules for Ray Tracing (Lenses)
Draw three rays that emanate from the tip of the object:
• The parallel ray is initially parallel to the principal axis and
after refraction passes through one of the focal points.
• The focal ray is directed at the other focal point and after
refraction the ray is parallel to the principal axis.
• The central ray passes through the center of the lens and
is not deflected.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Rules for Ray Tracing (Lenses)
The point where the three rays or their extrapolation intersect
is the image point:
• If the rays actually pass through the lens, the image is
real.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Rules for Ray Tracing (Lenses)
The point where the three rays or their extrapolation intersect
is the image point:
• If the rays actually pass through the lens, the image is
real.
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
• If the rays do not pass through the lens, the image is
virtual.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Rules for Ray Tracing (Lenses)
Real Image
When a lens forms a real image, the object and image are on
opposite sides of the lens.
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Virtual Image
When a lens forms a virtual image, the object and image are
on the same side of the lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Question 1
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an upright
virtual image?
Types of Lenses
Image
Formation
Converging Lenses
A F/2
B 2F
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
C Any value greater than 2F
D This cannot be done with a convex lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Question 1
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an upright
virtual image?
Types of Lenses
Image
Formation
Converging Lenses
A F/2
B 2F
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
C Any value greater than 2F
D This cannot be done with a convex lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Question 2
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an inverted
virtual image?
Types of Lenses
Image
Formation
Converging Lenses
A F/2
B 2F
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
C Any value greater than 2F
D This cannot be done with a convex lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Question 2
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an inverted
virtual image?
Types of Lenses
Image
Formation
Converging Lenses
A F/2
B 2F
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
C Any value greater than 2F
D This cannot be done with a convex lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Image from a Diverging Lens
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Image from a Diverging Lens
Follow the rules for ray tracing
for lenses:
• Since the refracted rays
do not intersect on the
right side of the lens,
extrapolate the rays back
to the left side of the lens.
➜ The extrapolations do
intersect.
• The point of intersection
is the image point at the
tip of the image.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Question 3
Which of the following best describes the image for a thin convex
(converging) lens that forms whenever the object is at a distance
less than one focal length from the lens?
A inverted, enlarged and real
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
B upright, enlarged and virtual
C upright, diminished and virtual
Rainbows
Aberrations
D inverted, diminished and real
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Question 3
Which of the following best describes the image for a thin convex
(converging) lens that forms whenever the object is at a distance
less than one focal length from the lens?
A inverted, enlarged and real
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
B upright, enlarged and virtual
C upright, diminished and virtual
Rainbows
Aberrations
D inverted, diminished and real
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Question 4
Which of the following best describes the image for a thin concave
(diverging) lens that forms whenever the magnitude of the object
distance is less than that of the lens’ focal length?
A inverted, enlarged and real
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
B upright, enlarged and virtual
C upright, diminished and virtual
Rainbows
Aberrations
D inverted, diminished and real
?
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Question 4
Which of the following best describes the image for a thin concave
(diverging) lens that forms whenever the magnitude of the object
distance is less than that of the lens’ focal length?
A inverted, enlarged and real
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
B upright, enlarged and virtual
C upright, diminished and virtual
Rainbows
Aberrations
D inverted, diminished and real
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Sign Conventions
Assume light travels through the lens from left to right:
• The object will always be located to the left of the lens.
• The object distance is positive when the object is to the
left of the lens (first convention).
• The image distance is positive when the image is to the
right of the lens and negative if the image is to the left of
the lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Sign Conventions
Assume light travels through the lens from left to right:
• The focal length is positive for a converging lens and
negative for a diverging lens.
• The object height is positive if the object extends above
the axis and is negative if the object extends below.
• The image height is positive if the image extends above
the axis and is negative if the image extends below.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Thin-Lens Equation
Geometry can be used to find a
mathematical relation for locating
image produced by a converging
lens.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Thin-Lens Equation
The shaded triangles are pairs of
similar triangles:
Types of Lenses
Image
Formation
Converging Lenses
h0
−hi
=
s0
si
(1)
−hi
h0
=
f
si − f
(2)
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Thin-Lens Equation
The shaded triangles are pairs of
similar triangles:
Types of Lenses
Image
Formation
Converging Lenses
h0
−hi
=
s0
si
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
−hi
h0
=
f
si − f
Rainbows
Aberrations
Taking the ratio of (1) and (2):
h0 /s0
hi /si
=
h0 /f
hi /(si − f )
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Thin-Lens Equation
The shaded triangles are pairs of
similar triangles:
Types of Lenses
Image
Formation
Converging Lenses
h0
−hi
=
s0
si
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
−hi
h0
=
f
si − f
Rainbows
Aberrations
Taking the ratio of (1) and (2):
h0 /s0
hi /si
=
h0 /f
hi /(si − f )
si − f
f
=
s0
si
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Thin-Lens Equation
The shaded triangles are pairs of
similar triangles:
Types of Lenses
Image
Formation
Converging Lenses
h0
−hi
=
s0
si
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
−hi
h0
=
f
si − f
Rainbows
Aberrations
Taking the ratio of (1) and (2):
h0 /s0
hi /si
=
h0 /f
hi /(si − f )
si − f
f
=
s0
si
si f = s0 (si − f )
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Lens Equation & Magnification
The thin-lens equation is found from
analysis of the similar triangles:
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
1
1
1
+
=
s0
si
f
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Lens Equation & Magnification
The thin-lens equation is found from
analysis of the similar triangles:
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
1
1
1
+
=
s0
si
f
Thin-Lens Equation
Examples
The Eye
Rainbows
The magnification can be found
from the similar triangles shown:
Aberrations
m =
hi
s
= − i
h0
s0
These results are identical to the
results found for mirrors.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Outline
1 Reminder: Snell’s Law
Total Internal Reflection
Types of Lenses
Image
Formation
Converging Lenses
2 Lenses
Types of Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
3 Image Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
4 Examples
The Eye
Rainbows
Aberrations
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
The Eye Compared to a Lens
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Corneal Refraction
The indices of refraction are
different for different parts of
the eye:
• Vary from ∼ 1.33 to 1.40.
• Biggest index change
and the largest refraction
occur when the light first
enters the cornea.
Snell’s Law and geometry can
be used to determine the focal
length of the corneal “lens” in
the eye:
f =
n
R
n−1
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Corneal Refraction
For this simplified model of the
eye, the focal length of the eye
is approximately 3.5 R with an
average index of n ≈ 1.4:
• This is about 1.5 R
behind the retina.
• The eye is not truly
spherical.
Snell’s Law and geometry can
be used to determine the focal
length of the corneal “lens” in
the eye:
f =
n
R
n−1
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
Adding the Lens to the Model
Light passes through the lens after
being refracted by the cornea. For
simplicity, assume the lens is just
outside of the eye:
• The lens is a converging lens.
• For a normal person:
The Eye
Rainbows
Aberrations
f lens ≈ 25 cm
Lens maker’s formula:
1
1
1
= (n − 1)
+
f
|R1 |
|R2 |
This form applies only to double
convex lenses in air.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Rainbows
Incident ray from Sun is refracted when it enters water droplet:
• The refracted angle depends on the color of the light.
• Rays for different colors travel at different angles.
• When light reaches the back surface, a portion is reflected.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Rainbows
Incident ray from Sun is refracted when it enters water droplet:
• Reflected rays refracted again when they leave droplet.
• The outgoing rays emerge over a range of angles.
➜ Different colors of a rainbow appear at different positions
(angles) in the sky.
College
Physics B
Reminder:
Snell’s Law
Total Internal
Reflection
Lenses
Types of Lenses
Image
Formation
Converging Lenses
Diverging Lenses
Thin-Lens Equation
Examples
The Eye
Rainbows
Aberrations
Chromatic Aberration
Different colors are actually diffracted by different amounts:
• The focal length of a lens is different for each color.
• Multiple lenses can be used to minimize the effect.