Geometric Optics

Conceptual Quiz 23

Topics

The Ray Model of Light Reflection Formation of Images by Spherical Mirrors Index of Refraction Refraction Total Internal Reflection Thin Lenses

The Ray Model of Light Reflection Formation of Images by Spherical Mirrors Index of Refraction Refraction Total Internal Reflection Thin Lenses

Conceptual Quiz 23

Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics.

The Ray Model of Light

Conceptual Quiz 23

Law of Reflection

The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection r

equals the angle of

incidence i

i = r

mirror

Incidentray

reflectedray

normal

iθrθ

Reflection

Conceptual Quiz 23

Image in a Plane Mirror

Mirror

Object

Image

Reflection

Conceptual Quiz 23

Image in a Plane Mirror

Mirror

Object

do

di

Image

h

d

h

d oi

The image is as far behind the mirror as the object is in front of the mirror.

h

oi dd

Reflection

Conceptual Quiz 23

Image in a Plane MirrorMirror

Object

ho

doSimilar Triangles

hi

di

Image

Image is the same size as the object.

o

o

i

id

h

d

h oi hh

Reflection

Conceptual Quiz 23

Concave Mirror

Principle Focal Point

Formation of Images by Spherical Mirrors

2R

f

Conceptual Quiz 23

Concave Mirror

Light Source at the Focal Point

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Produces Parallel Rays of Light

Concave Mirror

Real Image

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Concave Mirror

do

di

f

ho

hi

f

fd

h

h i

o

i

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Concave Mirror

ho

hi

do

di

f

o

i

o

id

d

h

h

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

f

fd

h

h i

o

i

o

i

o

id

d

h

h

io d1

d1

f1

io

iodd

ddf

Mirror Equation

o

iid

d

f

fd

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Concave Mirror

Virtual Image

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Concave Mirror

f

df

h

h i

o

i

do

f

ho

hi

di

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Concave Mirror

f

ho

hi

do di

o

i

o

id

d

h

h

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

io d1

d1

f1

f

df

h

h i

o

i

o

i

o

id

d

h

h

o

iid

d

f

df

io d1

d1

f1

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Formation of Images by Spherical Mirrors

Problem 23-10

A mirror at an amusement park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvature?

m 4.13Mdd oi

io d1

d1

f1

io

iodd

ddf or

m 2.4m 4.1

m 2.4m 4.1f

m 1.2

m 2.4 m 1.22f2r

o

i

o

id

d

h

hM

Conceptual Quiz 23

m 2.4di

Convex Mirror

Formation of Images by Spherical Mirrors

Conceptual Quiz 23

Concave Mirror

Formation of Images by Spherical Mirrors

f

do di

Conceptual Quiz 23

Concave Mirror

Formation of Images by Spherical Mirrors

do di

f

hohi

f

df

h

h i

o

i

Conceptual Quiz 23

Concave Mirror

Formation of Images by Spherical Mirrors

do di

hohi

o

i

o

id

d

h

h

Conceptual Quiz 23

f

df

h

h i

o

i

o

i

o

id

d

h

h

oi d1

f1

d1 io d

1d1

f1

Formation of Images by Spherical Mirrors

o

iid

d

f

df

Conceptual Quiz 23

Formation of Images by Spherical Mirrors

Problem 23-15

The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 18 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?

io d1

d1

f1 cm 18f

cm 36 cm 812f2r

cm 1811

Conceptual Quiz 23

In general, light slows somewhat when traveling through a medium. The index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium:

Index of Refraction

vc

n

Conceptual Quiz 23

Problem 23-24

The speed of light in ice is 2.29 x 108 m/s.What is the index of refraction of ice?

Index of Refraction

vc

n m/s 10x 29.2

m/s 10x 00.38

8 31.1

Conceptual Quiz 23

Light changes direction when crossing a boundary from one medium to another. This is called refraction, and the angle the outgoing ray makes with the normal is called the angle of refraction.

Refraction

Conceptual Quiz 23

The angle of refraction depends on the indices of refraction, and is given by Snell’s law:

Refraction

1n

2n

1θ

2θ

2211 θsinnθsinn

air

water

Conceptual Quiz 23

Refraction

1n

2n

1θ

2θ

air

water

Conceptual Quiz 23

1v

2v

1λ

2λ

1f

2f

1

2n

n

2

1θsin

θsin

2

1v

v

2

1λ

λ 21 ff

2211 θsinnθsinn

Problem 23-32

Light is incident on an equilateral glass prism at a 45.0o angle to one face. Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.

Index of Refraction

α

β γo45

2θ3θ

4θ

n

air221air θsinnθsinn

2o θsin 58.145sin 00.1 o

2 6.26θ

o180γβα o

3oooo 180θ906.269060 o

3 6.33θ

4air3 θsinnθsinn

4o θsin 00.16.33sin 58.1 o

4 5.60θ

Apparent DepthRefraction

Conceptual Quiz 23

Apparent Depth

h

nw

na

w

ax

h’aw

a

w

w

an

n

θsin

θsin

wwaa θsinnθsinn Snell’s Law

From the diagram

hx

θtan

'hx

θtan

w

a

a

w

w

an

n

'hh

θtan

θtan

n

n h'h

w

a

Refraction

Conceptual Quiz 23

If light passes into a medium with a smaller index of refraction, the angle of refraction is larger. There is an angle of incidence for which the angle of refraction will be 90°; this is called the critical angle:

Total Internal Reflection

1n2n o90

cθ

o2c1 90sinnθsinn

Snell’s Law

1

o2

c n

90sinnθsin

1

2c n

nθsin

Conceptual Quiz 23

Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging (a) or diverging (b).

Thin Lenses

Conceptual Quiz 23

Double Convex Lens

Focal Point

Thin Lenses

Conceptual Quiz 23

Real Image

Double Convex Lens

Thin Lenses

Conceptual Quiz 23

ho

Similar Triangles

Double Convex Lens

f f

do di

hi

f

fd

h

h i

o

i

Thin Lenses

Conceptual Quiz 23

Convex Lens

ho

hif f

do

Similar Triangles

di

o

i

o

id

d

h

h

Thin Lenses

Conceptual Quiz 23

Lens Equation

Double Convex Lens

f

fd

h

h i

o

i

o

i

o

id

d

h

h

io d1

d1

f1

Thin Lenses

o

iid

d

f

fd

Conceptual Quiz 23

Convex Lens

f f

di

ho

Similar Triangles

do

hi

f

fd

h

h i

o

i

Thin Lenses

Conceptual Quiz 23

Convex Lens

f f

hohi

Similar Triangles

di

do

o

i

o

id

d

h

h

Thin Lenses

Conceptual Quiz 23

Convex Lens

Lens Equation

f

fd

h

h i

o

i

o

i

o

id

d

h

h

io d1

d1

f1

Thin Lenses

o

iid

d

f

fd

Conceptual Quiz 23

Formation of Images by Spherical Mirrors

Magnification:

o

i

o

id

d

h

hM

Power:The unit for lens power is the diopter (D).

f1

P

A 30 cm focal length lens has a power

D 33.3m 30.0

1f1

P

Conceptual Quiz 23

Problem 23-44

Sunlight is observed to focus at a point 18.5 cm behind a lens.What kind of lens is it?

Index of Refraction

Pf1

d1

d1

io

What is its power in diopters?

Converging Lens

D 41.5 m 185.0

11P

Conceptual Quiz 23

Virtual Focal Point

Concave Lens

Thin Lenses

Conceptual Quiz 23

Concave Lens

Virtual Image

Thin Lenses

Conceptual Quiz 23

Concave Lens

ho

Similar Triangles

ho

hi

do

f

di

f

df

h

h i

o

i

Thin Lenses

Conceptual Quiz 23

Concave Lens

Similar Triangles

ho

hi

do

f

di

o

i

o

id

d

h

h

Thin Lenses

Conceptual Quiz 23

Concave Lens

Lens Equation

f

df

h

h i

o

i

o

i

o

id

d

h

h

io d1

d1

f1

Thin Lenses

o

iid

d

f

df

Conceptual Quiz 23