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QUESTIONS? PLEASE ASK!
Concave
Review

Mirrors


Definitions, Types
Magnification
M =

h'
q
=h
p
Convex
Mirror equation
1 1
2
1
+
=
=
p q
R
f



Remember the sign
conventions! (Table 23.1)
Ray tracing
Images formed by
refraction
h'

Magnification M =

Object-Image
n1
p
h
+
=-
n2
q
=
n1q
n2 p
n2 - n1
R
Atmospheric Refraction and Mirages


A mirage can be observed
when the air above the
ground is warmer than the
air at higher elevations
The rays in path B are
directed toward the ground
and then bent by refraction


Related to total internal
reflection – n is smaller
near the ground
The observer sees both an
upright and an inverted
image
Thin Lenses
Converging lenses

Thin lens - consists of a piece of
glass or plastic



converging lenses



refracting surfaces are either
spherical or planar
distance between the surface of the
lens and the center of the lens is
negligible
positive focal lengths
thickest in the middle
diverging lenses


negative focal lengths
thickest at the edges
Diverging lenses
Focal Length of Lenses

focal length, ƒ -image distance that
corresponds to an infinite object distance


same as mirrors
thin lens has two focal points, corresponding to
parallel rays from the left and from the right
Converging lenses
Diverging lenses
Lens Equations

The geometric derivation of the
equations is very similar to that of
mirrors
h'
q
M =
=h
p
1 1 1
+ =
p q f
The equations can be used for both converging and
diverging lenses
 converging lens has a positive focal length
 diverging lens has a negative focal length
Focal Length for a Lens

The focal length of a lens is related to the curvature of its
front and back surfaces and the index of refraction of the
material
æ1
ö
1
1
= (n - 1) çç - ÷÷
f
è R1 R2 ø
the lens maker’s equation
Ray Diagrams for Thin Lenses

Three rays are drawn




The first ray is drawn parallel to the first
principle axis and then passes through (or
appears to come from) one of the focal lengths
The second ray is drawn through the center of
the lens and continues in a straight line
The third ray is drawn from the other focal
point and emerges from the lens parallel to the
principle axis
There are an infinite number of rays, these
are convenient
Ray Diagram for Converging Lens, p > f


The image is real
The image is inverted
Ray Diagram for Converging Lens, p < f


The image is virtual
The image is upright
Ray Diagram for Diverging Lens


The image is virtual
The image is upright
Problem 23.36, p 786

The nickel’s image
in the figure has
twice the diameter
of the nickel when
the lens is 2.84 cm
from the nickel.
Determine the focal
length of the lens.
Problem 23.59, p 788

The figure shows a converging lens with radii R1 = 9 cm and
R2 = 11 cm, in front of a concave spherical mirror of radius 8
cm. (a) If the focal points F1 and F2 are 5 cm from the vertex
of the thin lens, what is the index of refraction of the lens? (b)
If the lens and the mirror are 20 cm apart and an object is
placed 8 cm to the left of the lens, what is the position of the
final image and its magnification as seen by the eye in the
figure? (c) Is the final image real or inverted?
Answer to 23.36
Answer to 23.59
Answer to 23.59 (cont’d)