Physics Chapter 25

8/22/2019 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.

General Physics II Page 1


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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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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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What happens if the surface is not flat?

i

r

Digital movie projectors: Application of digital micromirror devices



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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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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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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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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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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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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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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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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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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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(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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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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A Quick recap:

The mirror equation and magnification:

1

do +

1

di =

1

f; f =

R

2 ,

m =hiho

= dido

.



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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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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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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 .


Physics Chapter 25

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