isbn6416-8_23

7/28/2019 isbn6416-8_23

1/42

Fisica Generale - Alan Giambattista, Betty McCarty Richardson

Copyright 2008 The McGraw-Hill Companies s.r.l. 1

Chapter 23: Reflection and

Refraction of Light

Huygenss Principle

Reflection

Refraction

Total Internal Reflection

Polarization by Reflection

Formation of ImagesPlane Mirrors

Spherical Mirrors

Thin Lenses

7/28/2019 isbn6416-8_23

2/42



23.1 Huygenss Principle

A set of points with equal phase is called a wavefront.

7/28/2019 isbn6416-8_23

3/42



A ray points in the direction of wave propagation and is

perpendicular to the wavefronts. Or a ray is a line in the

direction along which light energy is flowing.

7/28/2019 isbn6416-8_23

4/42



Huygenss principle: At some time t, consider every point

on a wavefront as a source of a new spherical wave. These

wavelets move outward at the same speed as the original

wave. At a later time t+t, each wavelet has a radius vt,where v is the speed of propagation of the wave. The

wavefront at t+t is a surface tangent to the wavelets.

7/28/2019 isbn6416-8_23

5/42



Geometric optics is an approximation to the behavior of

light that applies when interference and diffraction are

negligible. In order for diffraction to be negligible, the sizesof objects must be large compared to the wavelength of

light.

7/28/2019 isbn6416-8_23

6/42


Copyright 2008 The McGraw-Hill Companies s.r.l.

6

23.2 Reflection of Light

When light is reflected from a smooth surface the rays

incident at a given angle are reflected at the same angle.

This is specular reflection.

7/28/2019 isbn6416-8_23

7/42



7

Reflection from a rough surface is called diffuse reflection.

Smooth and rough are determined based on the

wavelength of the incident rays.

7/28/2019 isbn6416-8_23

8/42



8

The angle of incidence equals the angle of reflection. Theincident ray, reflected ray, and normal all lie in the same

plane. The incident ray and reflected ray are on opposite

sides of the normal.

7/28/2019 isbn6416-8_23

9/42



9

23.3 Refraction of Light

When light rays pass from one medium to another they

change direction. This is called refraction.

7/28/2019 isbn6416-8_23

10/42



10

Snells Law

2211 sinsin nn

where the subscripts referto the two different media.

The angles are measured

from the normal.

When going from high n to low n, the ray will bend away

from the normal.

7/28/2019 isbn6416-8_23

11/42



11

The incident ray, transmitted ray, and normal all lie in thesame plane.

The incident and transmitted rays are on opposite sides of

the normal.

7/28/2019 isbn6416-8_23

12/42



12

Example (text problem 23.11): Sunlight strikes the surface of

a lake. A diver sees the Sun at an angle of 42.0 with

respect to the vertical. What angle do the Suns rays in air

make with the vertical?

surfacen1 = 1.00; airn2 = 1.33; water

Normal

42

Transmitted

wave

incident wave

1

1.63

8920.0sin42sin333.1sin00.1

sinsin

1

1

1

2211

nn

7/28/2019 isbn6416-8_23

13/42



13

23.4 Total Internal Reflection

The angle of incidence for when the angle of refraction is

90 is called the critical angle.

1

2

221

2211

sin

90sinsin

sinsin

n

nnnn

nn

c

c

7/28/2019 isbn6416-8_23

14/42



14

If the angle of incidence is greater than or equal to thecritical angle, then no wave is transmitted into the other

medium. The wave is completely reflected from the

boundary.

Total internal reflection can only occur when the incident

medium has a larger index of refraction than the second

medium.

7/28/2019 isbn6416-8_23

15/42



15

Example (text problem 23.22): Calculate the critical angle

for sapphire surrounded by air.

4.34

565.0sin

90sin00.1sin77.1

sinsin

1

2211

c

c

nn

surface

n2 = 1.0; air

n1 = 1.77; sapphire

Normal

Transmitted wave

incident wave

2=90

1

7/28/2019 isbn6416-8_23

16/42



16

23.5 Polarization by Reflection

Brewsters angle is the angle of incidence for which the

reflected light is completely polarized.

Light is totally polarized when the reflected ray and the

transmitted ray are perpendicular.

i

tB

BtBtBi

ttii

n

n

nnn

nn

tan

cos90sinsin

sinsin

7/28/2019 isbn6416-8_23

17/42



17

Example (text problem 23.32): (a) Sunlight reflected from

the still surface of a lake is totally polarized when the

incident light is at what angle with respect to the

horizontal?

1.53

33.1

00.1

33.1tan

air

water

B

B

n

n

The angle is measured from the normal, so 90 - 53.1

= 36.9 is the angle from the horizontal.

7/28/2019 isbn6416-8_23

18/42



18

(b) In what direction is the reflected light polarized?

Example continued:

It is polarizedperpendicular

to the plane of

incidence.

Fi i G l Al Gi b tti t B tt M C t Ri h d

7/28/2019 isbn6416-8_23

19/42



19

Example continued:

(c) Is any light incident at this angle transmitted into the

water? If so, at what angle below the horizontal does the

transmitted light travel?

9.36

6000.0sin

sin333.11.53sin00.1

sinsin

2

2

2

2211

nnFrom Snells Law:

The angle is measured from the normal, so 90 - 36.9

= 53.1 is the angle from the horizontal.

Fi i G l Al Gi b tti t B tt M C t Ri h d

7/28/2019 isbn6416-8_23

20/42



20

23.6 Formation of Images

An image is real if light rays from a point on the object

converge to a corresponding point on the image.

A camera lens

forms a real image.

Fisica Generale Alan Giambattista Bett McCart Richardson

7/28/2019 isbn6416-8_23

21/42



21

Your eye focuses

the diverging raysreflected by the

mirror.

The light rays

appear to come

from behind themirror.

An image is virtual if the light

rays from a point on the object

are directed as if they divergedfrom a point on the image, even

though the rays do not actually

pass through the image point.

Fisica Generale Alan Giambattista Betty McCarty Richardson

7/28/2019 isbn6416-8_23

22/42



22

Example (text problem 23.35): A defect in a diamond

appears to be 2.00 mm below the surface when viewed from

directly above that surface. How far beneath the surface is

the defect.

Surface

Actual location

of defect

Air

n2 =1.00

Diamond

n1 = 2.4191

2

1

2

y

y

Fisica Generale Alan Giambattista Betty McCarty Richardson

7/28/2019 isbn6416-8_23

23/42



23

The angles 1 and 2are related by Snells Law:

2211 sinsin nn

The actual depth of the defect is y and it appears to be at a

depth of y. These quantities are related by:

12 tantan yy

Example continued:

Fisica Generale - Alan Giambattista Betty McCarty Richardson

7/28/2019 isbn6416-8_23

24/42



24

Dividing the previous two expressions gives:

2211 coscos ynyn

As long as you are directly above the defect and its image,

the angles 1 and 2 are nearly 0. Rays from only a narrow

range of angles will enter your eye. The above expression

simplifies to:

1

2

21

n

n

y

y

ynyn

(general result)

Example continued:


7/28/2019 isbn6416-8_23

25/42



25

The actual depth of the defect in the diamond is then

mm.84.4mm00.200.1419.2

2

1

yn

n

y

Example continued:


7/28/2019 isbn6416-8_23

26/42

Fisica Generale Alan Giambattista, Betty McCarty Richardson


26

23.7 Plane Mirrors

A point source and its image are at the same distance from

the mirror, but on opposite sides of the mirror.

Treat an extended

object as a set of

point sources.


7/28/2019 isbn6416-8_23

27/42

Fisica Generale Alan Giambattista, Betty McCarty Richardson


27

Example (text problem 23.41): Entering a darkened room,

Gustav strikes a match in an attempt to see his

surroundings. At once he sees what looks like another

match about 4 m away from him. As it turns out, a mirror

hangs on one of the walls. How far is Gustav from the wall

with the mirror?

The image seems 4 m away, but the mirror is only 2 m

away since the rays will appear to come from a point 2 m

behind the mirror.


7/28/2019 isbn6416-8_23

28/42

s ca Ge e a e a G a batt sta, etty cCa ty c a dso


28

23.8 Spherical Mirrors

A convex (or diverging) mirror curves

away from the observer.

Principal

axis

vertexCenter of

curvature

The focal

point


7/28/2019 isbn6416-8_23

29/42

, y y


29

A ray parallel to

the principle axis

is reflected, and it

appears to have

come from point

F, the focal point

of the mirror.

For a convex mirror, the focal point is on the axis and is

located a distance 0.5R behind the mirror, where R is the

radius of curvature.


7/28/2019 isbn6416-8_23

30/42

y y


30

Drawn in green, red, and blue are the principal rays.

1. A ray parallel to the principal axis is reflected as if it came

from the focal point. (green)

2. A ray along a radius is reflected back upon itself. (red)

3. A ray directed toward the focal point is reflected parallel to

the principal axis. (blue)


7/28/2019 isbn6416-8_23

31/42


31

For the pencil in the previous figure, the image is upright,

virtual, smaller than the object, and closer to the mirror

than the object.


7/28/2019 isbn6416-8_23

32/42


32

Principal

axis

vertexCenter of

curvature

The focal

point

A concave (or converging) mirror

curves toward the observer.


7/28/2019 isbn6416-8_23

33/42


33

1. A ray parallel to the principal axis is reflected through the

focal point. (green)

2. A ray along a radius is reflected back upon itself. (red)

3. A ray along the direction from the focal point to the mirror is

reflected parallel to the principal axis. (blue)

Drawn in green, red, and blue are the principal rays.


7/28/2019 isbn6416-8_23

34/42


34

The magnification is defined as .sizeobject

sizeimage

h

hm

An inverted image has m0.

The expression for magnification can also be written as

p

qm where p is the object distance and

q is the image distance.


7/28/2019 isbn6416-8_23

35/42


35

The mirror equation:

fqp

111

where f is the focal length of the mirror.f

7/28/2019 isbn6416-8_23

36/42


36

Example (text problem 23.46): An object 2.00 cm high is

placed 12.0 cm in front of a convex mirror with a radius of

curvature of 8.00 cm. Where is the image formed?

fqp

111

where p = 12.0 cm, f = -0.5R = -4.00 cm, and q is the

unknown image distance. Solving gives q = -3.00 cm. Theimage is behind the mirror.


7/28/2019 isbn6416-8_23

37/42


37

23.9 Thin Lenses

A diverging lens will bend light away from the principle axis.

A converging lens will bend light toward the principal axis.


7/28/2019 isbn6416-8_23

38/42


38


7/28/2019 isbn6416-8_23

39/42


39

Magnification:

The thin lens equation:

p

q

h

hm

fqp

111


7/28/2019 isbn6416-8_23

40/42


40

Example (text problem 23.64): A diverging lens has a

focal length -8.00 cm.

(a) What are the image distances for objects placed atvarious distances from the lens? Is the image real or

virtual? Upright or inverted? Enlarged or diminished?

Objectdistance

Imagedistance

Real /virtual?

Upright /inverted?

Enlarged/diminished

5 cm -3.08 cm Virtual upright Diminished






7/28/2019 isbn6416-8_23

41/42


41

(b) If the object is 4.00 cm high, what is the height of the

image?

Object

distance

Image

distance

Magnification Image height

5 cm -3.08 cm 0.616 2.46 cm

8 cm -4.00 cm 0.500 2.00 cm

14 cm -5.09 cm 0.364 1.45 cm

16 cm -5.33 cm 0.333 1.33 cm

20 cm -5.71 cm 0.285 1.14 cm

Example continued:


7/28/2019 isbn6416-8_23

42/42


Summary

The Laws of Reflection

The Laws of Refraction

Condition for Total Internal Reflection

Condition for Total Polarization of Reflected Light

Real/virtual Images

Mirrors (plane & spherical)

Thin Lenses

Documents

isbn6416-8_23