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Refraction and Lenses
The most common application of refraction
in science and technology is lenses.
The kind of lenses we typically think of are
made of glass or plastic. The basic rules of
refraction still apply but due to the curved
surface of the lenses, they create images.
real image
inverted
image formed on the opposite side of lens as object
formed where light rays actually converge (“cross”)
visible on the screen (“projectable”)
virtual image
upright
image formed on the same side of a lens as object
formed where light rays “appear” to cross
not visible on a screen (not projectable)
REAL IMAGE FORMATION BY LENSES
VIRTUAL IMAGE FORMATION BY LENSES
The two main types of lenses are convex and concave
lenses.
The focal length (f) of a lens depends on its shape and
its index of refraction.
A diverging (concave) lens is thin in the center and thick
at the edges.
A converging (convex) lens is thick in the center and
thin at the edges.
Concave Lenses = Diverging Lenses
spread out light rays.
for nearsightedness (myopia)
forms virtual images only
always upright and reduced
aka reducing lenses
Convex Lenses = Converging Lenses
bring light rays to a focus.
for farsightedness (hyperopia)
form virtual images (upright & enlarged)
aka magnifying Lenses
Forms real images
CONVEX LENSES
Where is the object when the image is the same
size?
Where is the object when there is no image?
The eye contains a convex lens. This
lens focuses images on the back wall of
the eye known as the retina.
VISION PROBLEMS:
 MYOPIA
is when image is formed in front
of retina and is also known as
nearsightedness and is corrected with a
concave lens
VISION PROBLEMS:
 HYPEROPIA
is when image is formed
behind the retina and is also known as
farsightedness and is corrected with a
convex lens
VISION PROBLEMS:
 ASTIGMATISM
is when the eye is shaped
like a football rather than the normal eye
that has a round shape similar to
basketball. It causes certain amounts of
distortion or pitched images because of
the uneven bending of light rays entering
the eye.
Parts of a Lens
All lenses have a focal point (f). In a convex lens,
parallel light rays all come together at a single
point called the focal point. In a concave lens,
parallel light rays are spread apart but if they are
traced backwards, the refracted rays appear to
have come from a single point called the focal
point.
Real
f
f
Virtual
Lens Equation
(1/f) = (1/do) + (1/di)
f = focal length
do = object distance
di = image distance
Lens Magnification Equation
M = -(di / do) = (hi / ho)
M = magnification
di = image distance
do = object distance
hi = image height
ho = object height
Lens Sign Conventions
f
+ for Convex lenses
- for Concave Lenses
di
+ for images on the opposite side of the lens (real)
- for images on the same side (virtual)
do
+ always
hi
+ if upright image
- if inverted image
ho
+ always
M
+ if virtual
- if real image
Magnitude of magnification
<1 if smaller
=1 if same size
>1 if larger
Ex. 7 Camera lenses are described in terms of their focal length. A 50 mm lens
has a focal length of 50 mm. Do cameras use converging or diverging lenses?
What does di represent?
a. Where is the image (from the lens) of the above camera when it is focused on an
object 3.0 meters away?
b. What is the magnification of the image?
c. If the object is 1.5 m tall, what is the height of the image?
d. What is the di if the object is 6 m away? As the do increased, what happened to
the di?
Rules for Locating Refracted Images
1. Start at top of object. Light rays that
travel through the center of the lens (where
the principle axis intersects the midline) are
not refracted and continues along the same
path.
2. Start at top of object. Light rays that travel
parallel to the principle axis, strike the lens,
and are refracted through the focal point (f).
Images formed by Convex
lenses
Locating images in
convex lenses
Convex Lenses with the
Object located beyond
2f
Convex Lens
Object located
beyond C
C
C
f
f
Light rays that travel through the center of
the lens are not refracted and continue along
the same path.
Convex Lens
Object located
beyond 2f
2f
2f
f
f
Light rays that travel parallel to the principle axis,
strike the lens, and are refracted through the focal
point (f).
Convex Lens
Object located
beyond 2f
2f
Image:
Real
Inverted
Smaller
2f
f
f
The image is
located where
the refracted
light rays
intersect
Convex Lenses with the
Object located at 2f
Convex Lens
Object located
at 2f
2f
2f
f
f
Light rays that travel through the center of
the lens are not refracted and continue along
the same path.
Convex Lens
Object located
at 2f
2f
2f
f
f
Light rays that travel parallel to the principle axis,
strike the lens, and are refracted through the focal
point (f).
Convex Lens
Object located
at 2f
2f
Image:
Real
Inverted
Same Size
2f
f
f
The image is
located where
the refracted
light rays
intersect
Convex Lenses with the
Object located between
f and 2f
Convex Lens
Object located
between f and 2f
2f
2f
f
f
Light rays that travel through the center of
the lens are not refracted and continue along
the same path.
Convex Lens
Object located
between f and 2f
2f
2f
f
f
Light rays that travel parallel to the principle axis,
strike the lens, and are refracted through the focal
point (f).
Convex Lens
Object located
between f and 2f
2f
Image:
Real
Inverted
Larger
Beyond 2f
2f
f
f
The image is
located where
the refracted
light rays
intersect
Convex Lenses with the
Object located at f
Convex Lens
Object located at f
2f
2f
f
f
Light rays that travel through the center of
the lens are not refracted and continue along
the same path.
Convex Lens
Object located at f
2f
2f
f
f
Light rays that travel parallel to the principle axis,
strike the lens, and are refracted through the focal
point (f).
Convex Lens
Object located at f
2f
2f
No image is
formed.
All refracted light
rays are parallel
and do not cross
f
f
Convex Lenses with the
Object located between
f and the lens
Convex Lens
Object located
between f and the
lens
2f
2f
f
f
Light rays that travel through the center of
the lens are not refracted and continue along
the same path.
Convex Lens
Object located
between f and the
lens
2f
2f
f
f
Light rays that travel parallel to the principle axis,
strike the lens, and are refracted through the focal
point (f).
Convex Lens
Object located
between f and the
lens
2f
2f
f
f
These to refracted rays do not cross to the
right of the lens so we have to project them
back behind the lens.
Convex Lens
Object located
between f and the
lens
2f
Image:
2f
f
f
Virtual
Upright
Larger
Further away
The image is located at
the point which the
refracted rays APPEAR
to have crossed behind
the lens
Images formed by concave
lenses
Locating images in
concave lenses
Concave Lenses with
the Object located
anywhere
Concave Lens
Object located
anywhere
2f
f
f
2f
Light rays that travel through the center of
the lens are not refracted and continue along
the same path.
Concave Lens
Object located
anywhere
2f
f
f
2f
Light rays that travel parallel to the principle axis,
strike the lens, and are refracted through the focal
point (f).
Concave Lens
Object located
anywhere
Image:
2f
f
f
2f
Virtual
Upright
Smaller
Between f and the lens
The image is located
where the refracted
light rays appear to
have intersected
Someone who is nearsighted can see near objects more
clearly than far objects. The retina is too far from the
lens and the eye muscles are unable to make the lens
thin enough to compensate for this. Diverging glass
lenses are used to extend the effective focal length of
the eye lens.
Someone who is farsighted can see far objects more
clearly than near objects. The retina is now too close
to the lens. The lens would have to be considerable
thickened to make up for this. A converging glass
lens is used to shorten the effective focal length of
the eye lens. Today’s corrective lenses are carefully
ground to help the individual eye but cruder lenses
for many purposes were made for 300 years before
the refractive behavior of light was fully understood.