keratometer measures the magnification of the image. The smaller the magnification, the smaller
the radius
of curvature of the cornea. If the light source is 12.0 cm from the cornea and the image’s
magnification is 0.0320, what is the cornea’s
radius of curvature?

CONCAVE MIRRORS
Object position
image type
magnification
d
0
>R
real, inverted
reduced (m<1)
R<d
0
<f
real, inverted
enlarged (m>1)
d
0
<f
Virtual, upright
enlarged (m>1)
m is the absolute value of the magnification factor.

CONVEX MIRROR
Object
location
image type
magnification
d
0
>R
Virtual, upright
reduced (m<1)
R<d
0
<f
Virtual, upright
reduced (m<1)
d
0
<f
Virtual, upright
reduced (m<1)
m is the absolute value of the magnification factor.

LENSES
Spherical lenses have surfaces defined by two spheres,
and the surfaces are either convex or concave

CONVERGING AND DIVERGING LENSES
Converging
or biconvex
lenses (
with both
surfaces convex
) have a
positive
focal length
Converging lenses are thickest at the middle.
Diverging or biconcave lenses (
with both surfaces
concave
) have a
negative
focal length.
Diverging lenses are thickest at the edges.

CONVERGING LENS
Rays of light entering a converging lens parallel to its axis
converge
at its
focal point F
.
(Ray 2 lies on the axis of the lens.) The distance from the center
of the lens
to the focal point is the lens’s focal length
𝑓
.
An expanded view of the path taken by ray 1 shows the
perpendiculars and the angles of incidence and refraction at both
surfaces.

MAGNIFYING GLASS
Sunlight focused by a converging
magnifying glass
can burn paper
.
Light rays from the sun are nearly
parallel and cross at the focal point
of the lens.
The
more powerful
the lens,
the
closer
to the lens
the rays
will
cross.