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Optical Density - a property
of a transparent medium that
is an inverse measure of the
speed of light through the
medium.
(how much a medium slows
the speed of light)
Optical refraction bending of light rays as
they pass obliquely
from one medium to
another of different
optical density.
The angle between the
incident ray and the
normal is the angle of
incidence, i. The angle
between the refracted ray
and the normal is the
angle of refraction, r.
The ratio of the speed of light in
a vacuum to its speed in a
substance is the index of
refraction for that substance.
Index of refraction =
“c” in vacuum / “c” in substance
Snell’s Law
n = sin i / sin r
n1 sinq1 = n2sinq2
A ray of light passes from air
into water, striking at an angle
of 25.0° to the normal. The
index of refraction of water is
1.33. Calculate the angle of
refraction of the ray of light.
The index of refraction
is a constant physical
property of a
substance.
It can be measured
using a refractometer.
Three Laws of Refraction:
1. The incident ray, the
refracted ray, and the
normal at the point of
incidence are all in the
same plane.
2. The index of refraction
for any homogeneous
medium is a constant that
is independent of the
angle of incidence.
3. When a ray of light passes
obliquely from a medium of lower
optical density to one of higher
optical density, it is bent toward the
normal to the surface. A ray of light
passing from a medium of higher
optical density to one of lower
optical density is bent away from
the normal to the surface.
Wavelength effects the
refraction of light. Violet light
is bent more than red light
and the other colors fall in
between. This is why a prism
splits light into its component
colors.
Converging lens - convex
lens, thicker in the middle
than at the edges.
Diverging lens - concave
lens, thicker at the edges
than in the middle.
The principal axis
passes through the
two centers of
curvature of the two
surfaces of the lens.
Rays that are parallel to
the PA converge at the
principal focus of the lens.
If they actually pass
through this point it is a
real focus.
If rays do not pass
through a principal
focus, it is a virtual
focus.
The positions of the foci on
the principal axis depend on
the index of refraction of the
lens.
The focal length of a lens is
the distance between the
optical center of the lens and
the principal focus.
Parallel rays that
are not parallel
to the PA are
focused on the
focal plane.
Lenses vs. mirrors:
1. Secondary axes pass
through the optical center
of a lens and not through
either of its centers
of curvature.
2. The principal focus is usually
near the center of curvature.
3. A real image is formed on the
side of the lens opposite the
object. Virtual images are
formed on the same side as the
object.
4. Convex lenses form
images like concave
mirrors, concave
lenses form images like
convex mirrors.
Images formed by rays
passing through the
edges of lenses are not
focused at the principal
focus.
This blurring of
the image
is called spherical
aberration.
The f-number is the light
gathering power of a lens.
If the speed of the lens is
f/4, the focal length is 4 times
its effective diameter. An f/4
is four times as fast as an f/8,
and 16 times as fast as an
f/16.
Images formed by converging lenses:
Case #2 Object at a finite distance
beyond the twice the focal length
Case #3 Object at a distance equal to
twice the focal length
Case #4 Object between one and
two focal lengths
Case #5 Object at principle focus
Case #6 Object at a distance less
than one focal length away
Diverging lenses
Lens equations:
1/f = 1/do + 1/di
hi / h o = d i / d o
do and di are positive for real
objects and real images
do and di are negative for virtual
objects and virtual images
f is positive for converging
lenses
f is negative for diverging lenses
Ex. 8 - A 1.70-m tall person is
standing 2.50 m in front of a
camera. The camera uses a
converging lens whose focal length
is 0.0500 m.
(a) Find the image distance
and determine whether the image
is real or virtual.
(b) Find the magnification and
height of the image on the film.
Ex. 9 - An object is placed 7.10 cm
to the left of a diverging lens whose
focal length is f = -5.08 cm.
(a) Find the image distance and
determine whether the image is
real or virtual.
(b) Obtain the magnification.