 # General Physics II Mirrors & Lenses

```General Physics II
Mirrors & Lenses
Nothing New!
For the next several lectures we will be studying geometrical optics. You
already know the fundamentals of what is going on!!!
Light propagates as rays in situations in which the length scales
are >> than the light’s wavelength
Reflection:
incident
ray
θ1 = θr
Refraction:
θ1 θr
θ2
n1 sinθ1 = n2 sinθ2
reflected
ray
n1
n2
refracted
ray
• We will use these laws to understand the properties of
mirrors (perfect reflection) and lenses (perfect refraction).
• We will also discover properties of combinations of lenses
which will allow us to understand such applications as
microscopes, telescopes, and eyeglasses.
Page 1
Images formed by mirrors and lenses
may be classified as real or virtual
virtual..
Real Image
formed by actual rays of converging light
Virtual Image
not formed by actual rays of converging
light, but from where the rays of light
appear to come (diverging light rays)
Reflection at a plane surface
The reflected rays entering eyes look
as though they had come from image P’.
P’
virtual
image
P
Light rays radiate from a point object
at P in all directions.
Page 2
do
di
ho
hi
image is erect
image is virtual
M = hi/ho=1
lateral magnification
di = do
Curved
Mirrors
Terminology
center of curvature - C; the center of the original sphere
radius of curvature - r; distance from center of curvature to the
mirror
vertex - V; the center of the mirror
principal axis - a line through C and V
principal focus - F; the point on the principal axis where light rays
parallel and close to the principal axis converge; or from where they
appear to diverge
focal length - f; distance from V to F
V
V
Convex
Concave
Page 3
Concave Spherical Mirrors
We start by considering the reflections from a concave mirror in the
“paraxial” approximation (i.e., small angles of incidence close to a single
axis):
• Parallel Ray: Draw a ray from
the tip of the arrow parallel to the
axis. It passes through the ‘focal
point’ (F) of the mirror.
• Focal Ray: Draw a ray from the tip
of the arrow through the focal point.
This ray is reflected back parallel to
the axis.
C
F
• Principle Ray: Draw a ray
from the tip of the arrow
through the center of
curvature (C). This ray is
reflected straight back since
the angle of incidence = 0o.
The diagram below shows three light rays reflected off
of a concave mirror. Which ray is NOT correct?
R
A)
C)
B)
Page 4
f
Similarly for a Convex Spherical Mirror
The Mirror Equation
1 1
1
+
=
s s′
f
h
f
h’
s’
s
h
s
h’
Now, we can introduce a sign
convention. We can indicate
that this image is inverted if
we define its magnification M
as the negative number given
f
by:
s’
M =−
Page 5
s′
s
Lenses
A lens is a piece of transparent material shaped such that parallel light
rays are refracted towards a point, a focus:
Convergent Lens (Convex)
» light moving from air into glass
will move toward the normal
» light moving from glass back into
air will move away from the normal
» real focus
Positive f
Negative f
Divergent Lens (Concave)
» light moving from air into glass
will move toward the normal
» light moving from glass back into
air will move away from the normal
» virtual focus
The Convex Converging Lens
Ray Trace:
• Parallel Ray: Draw a ray from the tip of the arrow parallel to the axis. Upon
REFRACTION, it passes through the ‘focal point’ on the opposite side of the lens.
• Focal Ray: Draw a ray from the tip of the arrow through the focal point on the same
side of the lens. Upon REFRACTION, this ray moves parallel to the axis.
• Chief Ray: Draw a ray from the tip of the arrow through the center of the lens. Upon
REFRACTION, this ray continues straight along its original path.
Page 6
Similarly for a Concave Divergent
vergent Lens
The Lens Equation….same as the Mirror
h
s’
s
f
h’
1
1
1
+
=
s s′
f
M =−
Page 7
s′
s
End of
Mirrors & Lenses
Lecture
Page 8
``` # ECE 181 Spring 2013 Homework Assignment 2: Due Tuesday April # Rachel’s Ray of Hope January 2014 Newsletter What’s New # General Physics II Geometrical Optics: Reflection & Refraction of Light 