Physics 201
Professor P. Q. Hung
311B, Physics Building
Physics 201 – p. 1/3
Geometrical Optics
Optics: Behaviour of Light.
When the wavelength of light is much smaller
than the size of the object that it interacts
with, light travels approximately in a straight
line ⇒ Rays. (There are exceptions!)
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Geometrical Optics
Optics: Behaviour of Light.
When the wavelength of light is much smaller
than the size of the object that it interacts
with, light travels approximately in a straight
line ⇒ Rays. (There are exceptions!)
Geometrical Optics: Study of light under the
ray approximation.
Provide an understanding of mirror and
lenses. The eyes are an example.
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Geometrical Optics
Some properties to be studied:
Reflection: How light gets reflected at the
interface between two media.
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Geometrical Optics
Some properties to be studied:
Reflection: How light gets reflected at the
interface between two media.
Refraction: How transmitted light changes
direction at the interface between two media.
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Wave fronts and Rays
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Wave fronts and Rays
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Reflection
For reflected light, one has a very simple
relation:
θr = θi
Angle of reflection = Angle of incidence
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Reflection
For reflected light, one has a very simple
relation:
θr = θi
Angle of reflection = Angle of incidence
Specular reflection: Reflection on smooth
surface, without distortion. Metallic surfaces,
for example, are good for specular reflection.
(Give reasons for that).
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Reflection
For reflected light, one has a very simple
relation:
θr = θi
Angle of reflection = Angle of incidence
Specular reflection: Reflection on smooth
surface, without distortion. Metallic surfaces,
for example, are good for specular reflection.
(Give reasons for that).
Diffuse reflection: Reflection on rough surface
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Reflection
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Reflection
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Plane Mirrors
What are images?
They are formed at the intersection of light
rays, whether real or virtual.
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Plane Mirrors
What are images?
They are formed at the intersection of light
rays, whether real or virtual.
What’s a real image? It’s the one in which
light passes through the image point.
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Plane Mirrors
What are images?
They are formed at the intersection of light
rays, whether real or virtual.
What’s a real image? It’s the one in which
light passes through the image point.
What’s a virtual image? It’s the one in which
light does not pass through the image point.
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Plane Mirrors
What about Plane Mirrors?
The image is virtual.
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Plane Mirrors
What about Plane Mirrors?
The image is virtual.
The image is upright, i.e. not inverted.
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Plane Mirrors
What about Plane Mirrors?
The image is virtual.
The image is upright, i.e. not inverted.
The image has the same size as the object.
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Plane Mirrors
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Plane Mirrors: Example
You are 1.70 m tall and your eyes are 0.10 m
below the top of your head. You stand in front of
a mirror and you want to see your full height, no
more, no less. What is the minimum height of the
mirror?
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Plane Mirrors: Example
Let the light ray coming from your feet strike
the bottom of the mirror and label that path by
AB. See the figure drawn in class. Let BC be
the reflected ray reaching the eye. The
normal to the mirror from its bottom is
denoted by BD. ABD and DBC are identical
triangles.
AD = DC = 21 AC = 12 (1.70 − 0.10) = 0.80m
Physics 201 – p. 13/3
Plane Mirrors: Example
Let the light ray coming from your feet strike
the bottom of the mirror and label that path by
AB. See the figure drawn in class. Let BC be
the reflected ray reaching the eye. The
normal to the mirror from its bottom is
denoted by BD. ABD and DBC are identical
triangles.
AD = DC = 21 AC = 12 (1.70 − 0.10) = 0.80m
Similarly, let the light ray from the top of the
head reaching the top of the mirror be FE and
the reflected ray reaching the eyes be EC. We
have 12 CF = 0.05m.
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Plane Mirrors: Example
The minimum height of the mirror is
d = F A − AD − 21 CF =
1.70m − 0.80m − 0.05m = 0.85m
Half of your height!
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Spherical Mirrors
Spherical Mirrors: Mirrors whose shape is a
segment of a sphere.
Characterized by a principal axis which
intersects with the “middle” of the mirror. On
that axis, there is a point called center of
curvature C situated at a distance R from the
“middle” of the mirror.
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Spherical Mirrors
Spherical Mirrors: Mirrors whose shape is a
segment of a sphere.
Characterized by a principal axis which
intersects with the “middle” of the mirror. On
that axis, there is a point called center of
curvature C situated at a distance R from the
“middle” of the mirror.
Concave Mirror: Spherical mirrors where
parallel light rays from a distance source
when shined on it are reflected at a single
point: focal point F . The focal point is at
f = R/2.
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Spherical Mirrors
Convex mirror: Spherical mirror whose light
rays which are incident on it diverge. Also
called diverging mirror.
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Spherical Mirrors
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Spherical Mirrors
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Spherical Mirrors
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Spherical Mirrors
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Spherical Mirrors
When light rays from an object are incident on
such mirrors, how can one find the image? Is it
real or virtual?
Ray Diagrams for Mirrors:
Ray 1 (F-ray) is drawn parallel to the principal
axis and is reflected back through the focal
point F .
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Spherical Mirrors
When light rays from an object are incident on
such mirrors, how can one find the image? Is it
real or virtual?
Ray Diagrams for Mirrors:
Ray 1 (F-ray) is drawn parallel to the principal
axis and is reflected back through the focal
point F .
Ray 2 (P-ray) is drawn through the focal point.
It is reflected back parallel to the principal
axis.
Physics 201 – p. 21/3
Spherical Mirrors
When light rays from an object are incident on
such mirrors, how can one find the image? Is it
real or virtual?
Ray Diagrams for Mirrors:
Ray 1 (F-ray) is drawn parallel to the principal
axis and is reflected back through the focal
point F .
Ray 2 (P-ray) is drawn through the focal point.
It is reflected back parallel to the principal
axis.
Ray 3 (C-ray) is drawn through the center of
curvature C and is reflected back on itself.
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Spherical Mirrors: Concave Mirror
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Spherical Mirrors: Convex Mirror
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Spherical Mirrors: Image from Con
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Spherical Mirrors
Important characteristics:
For a convex mirror, the image is always
virtual, upright and reduced in size.
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Spherical Mirrors
Important characteristics:
For a convex mirror, the image is always
virtual, upright and reduced in size.
For a concave mirror, it depends on where
the object is located.
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Spherical Mirrors
Beyond C ⇒ inverted, reduced in size, and
real.
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Spherical Mirrors
Beyond C ⇒ inverted, reduced in size, and
real.
At C ⇒ inverted, same as object, and real.
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Spherical Mirrors
Beyond C ⇒ inverted, reduced in size, and
real.
At C ⇒ inverted, same as object, and real.
Between C and F ⇒ inverted, enlarged, and
real.
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Spherical Mirrors
Beyond C ⇒ inverted, reduced in size, and
real.
At C ⇒ inverted, same as object, and real.
Between C and F ⇒ inverted, enlarged, and
real.
Just beyond F ⇒ inverted, approaching
infinity, and real.
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Spherical Mirrors
Beyond C ⇒ inverted, reduced in size, and
real.
At C ⇒ inverted, same as object, and real.
Between C and F ⇒ inverted, enlarged, and
real.
Just beyond F ⇒ inverted, approaching
infinity, and real.
Just inside F ⇒ upright, approaching infinity,
and virtual.
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Spherical Mirrors
Beyond C ⇒ inverted, reduced in size, and
real.
At C ⇒ inverted, same as object, and real.
Between C and F ⇒ inverted, enlarged, and
real.
Just beyond F ⇒ inverted, approaching
infinity, and real.
Just inside F ⇒ upright, approaching infinity,
and virtual.
Between F and the mirror ⇒ upright,
enlarged, and virtual.
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Spherical Mirrors: Concave Mirror
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Spherical Mirrors: Mirror Equation
Let the distance between the object and the
mirror be p (d0 in the book) and the distance
between the image and the mirror be q (di in the
book).
The magnification (ratio between sizes) is
defined by:
M=
′
h
h
=
q
−p
= − dd0i
Physics 201 – p. 28/3
Spherical Mirrors: Mirror Equation
Let the distance between the object and the
mirror be p (d0 in the book) and the distance
between the image and the mirror be q (di in the
book).
The magnification (ratio between sizes) is
defined by:
M=
′
h
h
=
q
−p
= − dd0i
From geometry:
1
1
1
+
=
p
q
f
where
f = R2 .
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Spherical Mirrors: Concave Mirror
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Spherical Mirrors: Sign Convention
f < 0: Convex; f > 0: Concave
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Spherical Mirrors: Sign Convention
f < 0: Convex; f > 0: Concave
m > 0: Upright image; m < 0: Inverted image
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Spherical Mirrors: Sign Convention
f < 0: Convex; f > 0: Concave
m > 0: Upright image; m < 0: Inverted image
q > 0 (di > 0): Image (real) in front of mirror;
q < 0 (di < 0): Image (virtual) behind mirror
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Spherical Mirrors: Example
A concave spherical mirror has a focal length of
10.0cm. Locate the images for object distances of
(a) 25.0cm, (b) 10.0cm, (c) 5.00cm.
1
+ 1q = 10.0cm
⇒ q = 16.7cm.
16.7cm
M = − pq = − 25.0cm
= −0.667 Smaller and
inverted.
1
25.0cm
Physics 201 – p. 31/3
Spherical Mirrors: Example
A concave spherical mirror has a focal length of
10.0cm. Locate the images for object distances of
(a) 25.0cm, (b) 10.0cm, (c) 5.00cm.
1
+ 1q = 10.0cm
⇒ q = 16.7cm.
16.7cm
M = − pq = − 25.0cm
= −0.667 Smaller and
inverted.
1
25.0cm
1
10.0cm
+
1
q
=
1
10.0cm
⇒ q = infinity.
Physics 201 – p. 31/3
Spherical Mirrors: Example
A concave spherical mirror has a focal length of
10.0cm. Locate the images for object distances of
(a) 25.0cm, (b) 10.0cm, (c) 5.00cm.
1
+ 1q = 10.0cm
⇒ q = 16.7cm.
16.7cm
M = − pq = − 25.0cm
= −0.667 Smaller and
inverted.
1
25.0cm
1
10.0cm
+
1
q
=
1
10.0cm
⇒ q = infinity.
1
+ 1q = 10.0cm
⇒ q = −10.0cm. It is virtual
since it is behind the mirror.
q
M = − p = − −10.0cm
5.0cm = 2 Upright and enlarged.
1
5.0cm
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