physics chapter 25
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Chapter 25 The Reflection of Light: Mirrors
25.1 Wave Fronts and Rays
Wave fronts: Surfaces of constant phases (2
apart) of a wave.
Rays: The lines the wave fronts in the direction of propagation.
Spherical waves: Wave fronts are concentric spheres; rays along r.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Plane waves: Wave fronts are parallel planes with rays along a
straight line.
Example: The plane wave (radiation field) from a center-fed antenna
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
25.2 The Reflection of Light
The law of reflection:
(1) The incident ray, the reflected ray, and the normal direction of the
mirror are all in one planethe incident plane;
(2) The incident angle is equal to the reflected angle: i = r.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
What happens if the surface is not flat?
i
r
Digital movie projectors: Application of digital micromirror devices
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
25.3 The Formation of Images by a Plane Mirror
Look into a mirror to see the image of an object, you see
(1) An upright image of the same size of the object: hi = ho;
(2) A (virtual) image formed behind the mirror at the same distance of
the object from the mirror: di = do;
(3) Objects left side becomes images right side, and vice versa.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Real image: Light passes through the image.
Virtual image: The extension of light (but not the light itself) passes
through the image (marked by a negative image distance).
Conceptual Example 1. Full image and half-sized mirror
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
25.4 Spherical Mirrors
Concave mirrors:
Note that parallel paraxial rays converge to a focal point after
reflection; AF = CF f R/2.
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Convex mirrors:
Parallel paraxial rays diverge (as if come from a focal point) after
reflection.
Focal length:
f = di as do . For a concave spherical mirror, f R/2, and
for a convex spherical mirror f R/2.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Spherical aberration and parabolic mirrors:000000111111000111 000111FC F
Spherical Parabolic
Remarks:
(1) A minus sign in a distance means that the corresponding object
or image is virtual without the light actually passing through it;
(2) Focal point is the image of an object at the infinity. So the sign
convention also applies to the focal length.
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25.5 The Formation of Images by Spherical Mirrors
Concave mirrors:
(1) A parallel ray becomes a ray going through the focal point;
(2) A ray from the focal point turns into a parallel ray;
(3) A ray from the spherical center goes back directly;
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(4) A ray to the vertex reflects back symmetrically.
FC
Remarks:
(1) Spherical aberration is ignored in constructing a ray diagram;
(2) The effect of the curvature of the mirror is ignored in calculating
distances and heights;
(3) Two out of the four rays are needed in constructing a ray diagram;
(4) The object and the image are interchangeable in a ray diagram:
The principle of reversibility.
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(5) Image can be real or virtual, upright or inverted, and enlarged or
reduced.
General features:
(1) Image is real, inverted, and reduced if do > 2f;
(2) Image is real, inverted, and enlarged if 2f > do > f;
(3) Image is virtual, upright, and enlarged if do < f.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
An application: The head-up display in a windshield
Multiple reflections: the image from the first mirror is the object of the
second mirror, so forth.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Convex mirrors:
(1) A parallel ray becomes a ray coming from the focal point;
(2) A ray to the focal point turns into a parallel ray;
(3) A ray to the spherical center goes back directly;
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(4) A ray to the vertex reflects back symmetrically.
F C
General features:
(1) The image is always virtual, upright, and reduced;
(2) The image can be deceiving: Warning: Objects in mirror are
closer than they appear! This is the warning on the mirror on the
passenger side of a vehicle.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
25.6 The Mirror Equation and the Magnification Equation
i
d
ho doh
i
f
i
d
ho doh
i
f
From the two pairs of similar triangles, we have
hohi
= dodi
= do ff
,
which leads to
1do
+ 1di
= 1f
; The mirror equation
m =hiho
= dido
. The magnification
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Remarks:
(1) The equations are for both the concave (f > 0) and convex
(f < 0) mirrors;
(2) All types of images can result, real (di > 0) or virtual (di < 0),
upright (hi > 0) or inverted (hi < 0), and enlarged (|m| > 1) or
reduced (|m| < 1);
(3) Plane mirror is a special case with f = , and thus di = do
and hi = ho;
(4) Apparent distance for the image of a convex mirror: d = do/m.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Example 3. A real image of a concave mirrorIf ho = 2.0 cm, do = 7.10 cm, and R = 10.20 cm, find (a) the
image distance di and (b) the image height hi.
(a) The focal length is f = R/2 = 5.10 cm. Then from the mirrorequation we have
di =dof
do f=
7.10 5.10
7.10 5.10cm = 18 cm.
(b) The image height is given by
hi =
di
do ho =
18
7.10 2.0 cm = 5.0 cm.
Example 5. A virtual image of a convex mirror
If do = 66 cm and f = 46 cm, find (a) di and (b) m.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
(a) From the mirror equation, we have
di =
dof
do f =
66 (46)
66 + 46 cm = 27 cm.
(b) The magnification is then given by
m = hiho
= dido
= 2766
= 0.41.
Example 6. Convex mirror versus plane mirror
If do = 9.00 cm and di = 3.00 cm if the plane mirror is replaced
by a convex mirror, find f of the convex mirror.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
From the mirror equation, we have
f =dodi
do + di=
do(do + di)
do do + di= do
d2o
di
=
9.00
9.002
3.00
cm = 18 cm.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
A Quick recap:
The mirror equation and magnification:
1
do +
1
di =
1
f; f =
R
2 ,
m =hiho
= dido
.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Plane mirror:
f , di = do, and m = 1.
Convex mirror:
di =
dof
do f =
doR
2do + R < 0;
m =hiho
= dido
=R
2do + R.
Note that |di| < do and 0 < m < 1.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Concave mirror:
di =dof
do f;
m =hiho
= dido
.
The nature of the image depends on do > 2f (real, inverted, andreduced), 2f < do > f (real, inverted, and enlarged), or do < f
(virtual, upright, and enlarged).
Combination of mirrors:
The image of the previous mirror is the object of the next mirror.
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Chapter 25 The Reflection of Light: Mirrors T. Pang, Ph.D.
Key Issues of the Chapter:
(i) The law of reflection: i = r;
(ii) The mirror equation and magnification:
1do+ 1di
= 1f; m = hi
ho= d
i
do,
where f = R/2 for a spherical mirror;
(iii) The plane mirror is the limit of R .
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