Review of Geometric Optics

Review of Geometric Optics
1.The ray approximation; Reflection; Refraction; Snell’s law of
refraction; Dispersion; Total Internal Reflection.
2. Images formed by flat mirrors
3. Images formed by Spherical Mirrors
4. Images formed by Refraction
5. Thin Lenses

• 1.The ray approximation: A wave moving through a medium
travels in a straight line in the direction of its rays, which are
perpendicular to the wave front.
• The law of reflection: The angle of reflection equals the angle of
incidence.
• The Snell’s law of refraction: n 1 *sin q 1 = n 2 * sin q 2
• Dispersion: The index of refraction varies with the wavelength of
the light passing through the material.
• Total Internal Reflection:
sin q c =n 2 /n 1 , q 2 = 90 ( for n 1 >n 2 )

Images are classified as real or virtual.
A real image is formed when
light rays pass through and
diverge from the image
point.
A virtual image is formed
when the light rays do not
pass through the image point
but appear to diverge from
that point.

Images formed by flat mirrors
p- the object distance
q- the image distance
Because the triangles PQR and
P’QR are congruent, and p = q,
h = h’.
Lateral magnification :
M
≡
Im age height
Object height
=
h'
h

Images formed by Spherical Mirrors
• A spherical mirror has the shape of a section of a sphere.
• A concave mirror: light is reflected from the inner surface.

Images formed by Spherical Mirrors
A concave mirror
• Center of curvature;
• Principal axis;
• paraxial rays.

Images formed by Spherical Mirrors
A concave mirror

Images formed by Spherical Mirrors
A concave mirror
tanθ
h q
M = ' = −
h p
tanα
1 1 2
+ =
p q R

Images formed by Spherical Mirrors
A concave mirror

Images formed by Spherical Mirrors
A concave mirror
• F- focal point; f- focal length
1 R ≈ 0 q ≈
p 2
f =
R
2

Images formed by Spherical Mirrors
A concave mirror
• F- focal point; f- focal length
f =
R
2

Images formed by Spherical Mirrors
A convex mirror: light is reflected from the outer, convex surface.
The front
side and the
back side of
the mirror.
A diverging mirror: the image is virtual, upright and smaller.

Images formed by Spherical Mirrors
A convex mirror: light is reflected from the outer, convex surface.
Mirror equation:
1
p
+
1
q
=
1
f

A convex mirror:
The same mirror equation:
1
p
+
1
q
=
1
f
Pay Attention to signs!

Ray Diagrams for Mirrors
Special rays help to find the positions and sizes of images.
Ray 1 is drawn from the top of the object parallel to the
principal axis and is reflected through the focal point F.
Ray 2 is drawn from the top of the object through the
focal point and is reflected parallel to the principal axis.
Ray 3 is drawn from the top of the object through the
center of curvature C and is reflected back on itself.

Ray Diagrams for Concave Mirrors
Ray 1 is drawn from the top of the
object parallel to the
principal axis and is reflected
through the focal point F.
Ray 2 is drawn from the top of the
object through the
focal point and is reflected parallel
to the principal axis.
Ray 3 is drawn from the top of the
object through the
center of curvature C and is
reflected back on itself.
When the object is located so that the center of
curvature lies between the object and a concave
mirror surface, the image is real, inverted, and
reduced in size.

Ray Diagrams for Concave Mirrors
Ray 1 is drawn from the top of the
object parallel to the
principal axis and is reflected
through the focal point F.
Ray 2 is drawn from the top of the
object through the
focal point and is reflected parallel
to the principal axis.
Ray 3 is drawn from the top of the
object through the
center of curvature C and is
reflected back on itself.
When the object is located between the focal
point and a concave mirror surface, the image
is virtual, upright, and enlarged.

Ray Diagrams for Convex Mirrors
Ray 1 is drawn from the top of the
object parallel to the
principal axis and is reflected
through the focal point F.
Ray 2 is drawn from the top of the
object through the
focal point and is reflected parallel
to the principal axis.
Ray 3 is drawn from the top of the
object through the
center of curvature C and is
reflected back on itself.
When the object is in front of a convex mirror,
the image is virtual, upright, and reduced in
size.

Images formed by Refraction
n =
sinθ
n sin
1 1 2
θ
2
n =
θ n θ
1 1 2 2

Images formed by Refraction
n n n − n
1
+
2
=
2 1
p q R

Flat Refracting Surfaces
• The image formed by a flat
refracting surface is virtual
and on the same side of the
surface as the object. All
rays are assumed to be
paraxial.
n n
1
= −
2
p q
q
= −
n
n
2
1
p

Thin Lenses
• The image formed by
one refracting
surface serves as the
object for the second
surface.

Thin Lenses
1
p
1
+
n
q
1
=
n −1
R
1

Thin Lenses
2
2
2
1
1
R
n
q
p
n
−
=
+
2 q 1
p
−
=
2
2
1
1
1
R
n
q
q
n
−
=
+
−
1
1
1
1
1
R
n
q
n
p
−
=
+
)
1
1
1)(
(
1
1
2
1
2
1 R
R
n
q
p
−
−
=
+

Thin Lenses
1
p
+
1
q
=
( n
1 1
−1)(
−
R 1
R 2
)
Lens makers’ equation:
1
f
=
( n
1 1
−1)(
−
R 1
R 2
)
f- focal length

Thin Lens equation:
1
1
1
+
=
p
q
f
Magnification of Images:
M
h
= '
=
−
q
h
p

Ray Diagrams for Thin Converging
• Ray 1 is drawn parallel to the
principal axis. After being
refracted by the lens, this ray
passes through the focal point
on the back side of the lens.
• Ray 2 is drawn through the
center of the lens and continues
in a straight line.
• Ray 3 is drawn through that
focal point on the front side of
the lens (or as if coming from
the focal point if p

Ray Diagrams for Thin Diverging
• Ray 1 is drawn parallel to the
principal axis. After being
refracted by the lens, this ray
emerges such that it appears to
have passed through the focal
point on the front side of the
lens.
• Ray 2 is drawn through the
center of the lens and continues
in a straight line.
• Ray 3 is drawn toward the focal
point on the back side of the
lens and emerges from the lens
parallel to the optic axis.
Lenses

Homework assignment #2
• Chapter 36: 9, 11, 13, 15, 21, 23, 24 (1.5 cm/s),
27, 35, 69

Images formed by Refraction
n =
θ n θ
1 1 2 2
θ
1
= α + β
n1α + n2γ
= ( n2
− n1
) β
d
α ≈ tanα
=
β = θ 2
+ γ
β ≈ tan β = γ ≈
p
d
R
tanγ
=
d
q