SPH3UW: OPTICS I Introduction to Mirrors Light incident on an object Absorption Everything true for wavelengths

SPH3UW: OPTICS I

Introduction to Mirrors

Light incident on an object

Absorption

Everything true for wavelengths << object size

Reflection (bounces)** See it Mirrors

Refraction (bends) Lenses

Often some of each

Reflection

i

r

Angle of incidence = Angle of reflection

ii = = rr

(Angles between light beam and normal)

Object LocationLight rays from sun bounce off object and go in all directions Some of the rays hit your eyesSome of the rays hit your eyes

We know object’s location by the direction the light rays come from.

Color: some light is absorbed by object before bouncing off.

Reflection from a Plane Mirror

The angle of incidence equals the angle of reflection. This assumes the surface is perfectly smooth.

Diffuse Reflection

When the surface is rough, the surface at any point makes some angle with respect to the horizontal. The angle of incidence still equals the angle of reflection.

Plane Mirrors

In the left hand picture with a rough surface, you can place your eye anywhere and you will see some reflected rays. On the right hand side, you eye has to be in the correct position to see the reflected light. This is called specular reflection.

Plane Mirrors

A plane mirror provides the opportunity to fool you by making your eye and brain perceive an image.

Plane Mirrors

The image appears to be the same distance behind the mirror as the object is in front of the mirror.

Plane Mirrors

The image is called a virtual image because if you placed a piece of paper at the image location, you wouldn’t see any light.

Plane Mirror All you see is what reaches your eyes

You think object’s location is where rays appears to come from..

r

i

Object Image

All rays originating from peak will appear to come from same point behind mirror!

How to Draw the Image in a Plane Mirror

(3) Where the extended lines appear to intersect (a distance d behind mirror) is the image location.

d d

(1) Draw first ray perpendicular to mirror i =00= r

(2) Draw second or third ray at angle. i = r

Light rays don’t really converge there, so it’s a “Virtual Image”

r

i

Virtual: No light actually gets here.

r

i

How Big a Mirror?

0.80 m

Why do ambulances have “AMBULANCE” written backwards?

Question

Solution

So you can read it in your rear-view mirror!

Question

Can you see Fido’s tail in mirror?

mirror

(You) (Fido)

Solution

Can you see Fido’s tail in mirror?

mirror

No!

(You) (Fido)

You need light rays from the tail to bounce off mirror and reach your eye!

ACT: Plane MirrorsYou are standing in front of a short flat mirror which

is placed too high, so you can see above your head, but only down to your knees. To see your shoes, you must move:

(1) closer to the mirror.(2) further from the mirror.(3) to another mirror.

Changing distance doesn’t change what you see of yourself

ACT: Plane MirrorsYou are standing in front of a short flat mirror

which is placed too high, so you can see above your head, but only down to your knees. To see your shoes, you must move:

(1) closer to the mirror.(2) further from the mirror.(3) to another mirror.

Two Mirrors

How many images of money will you see (not How many images of money will you see (not including the actual money)? including the actual money)?

1

Two MirrorsHow many images of money will you see (not

including the actual money)?

2

3

R

Curved mirrorsA Spherical Mirror: section of a sphere.

C = Center of Curvature

In front of concave mirror

Behind convex mirror.

principal axis

light ray

•

Concave

mirror

RC

Convex mirror

principal axis

light ray R

C•

Understanding

An organic chemistry student accidentally drops a glass marble into a silver nitrate mirroring solution, making the outside of the marble reflective.

What kind of mirror is this?

(1) concave

(2) convex

(3) flat

Concave Mirror

Principal Axis Focus

Rays parallel to principal axis and near the principal axis (“paraxial rays”) all reflect so they pass through the “Focus” (F).

R

f=R/2

The distance from F to the center of the mirror is called the “Focal Length” (f).

Rays are bent towards the principal axis.

2

Rf

What kind of spherical mirror can be used to start a fire?

concave

convex

How far from the paper to be ignited should the mirror be held?

farther than the focal length

closer than the focal length

at the focal length

Understanding

Concave Mirror

Principal Axis FF

Rays traveling through focus before hitting mirror are reflected parallel to Principal Axis.

Rays traveling parallel to Principal Axis before hitting mirror are reflected through focus

Convex Mirror

Principal Axis Focus

Rays parallel to principal axis and near the principal axis (“paraxial rays”) all reflect so they appear to originate from the “Focus” (F).

R

f=-R/2

The distance from F to the center of the mirror is called the “Focal Length” (f).

Rays are bent away from the principal axis.

2

Rf

Concave Mirror –Drawing image

f

c

1) Parallel to principal axis reflects through f.

#13) Through center.

#3

Image is (in this case):

Real or Imaginary

Inverted or Upright

Reduced or Enlarged

**Every other ray from object tip which hits mirror will reflect through image tip. You need at least two of the above techniques to draw image

2) Through f, reflects parallel to principal axis.

#24) At the vertex

V

#4

When object is on the outside of the centre of curvature

Technique

The image is realThe image is invertedThe image is smaller than the object

Concave Mirror –Drawing imageWhen object is on the outside of the centre of curvature

Concave Mirror-Drawing images

fc


#1


Real or Imaginary

Inverted or Upright

Reduced or Enlarged or Same Size

**Every other ray from object tip which hits mirror will reflect through image tip


#23) At the vertex

When object is at the centre of curvature

Technique

#3

V

Concave Mirror-Drawing images

f

c


#1


Real or Imaginary

Inverted or Upright

Reduced or Enlarged



#2

When object is between the centre of curvature and the focus

Technique

3) At the vertex

#3

V

Concave Mirror Principal Rays

f

c


#1


Real or Imaginary

Inverted or Upright

Reduced or Enlarged



#2

When object is between the focus and the Vertex

Technique

#3

V

3) At the vertex

Concave Mirror Principal RaysWhen object is between the focus and the Vertex

The image is virtualThe image is uprightThe image is larger than the object

R f1)

2)3)

p.a.

Understanding

Which ray is NOT correct?

Ray through centre should reflect back on self.

A concave mirror has a positive focal length f > 0

A convex mirror has a negative focal length f < 0

What is the focal length of a flat mirror?

(1) f =0 (2) f = ∞

Mirror Focal Lengths

The flatter the mirror, the larger the radius of curvature, (e.g. the earth is round, but looks flat)

Concave Mirror Image LocationConcave Mirror Image Location

Yep, no image

O

I

Mirror Equation

c

do

di

• do = distance object is from mirror:

Positive: object is _______ of mirror

Negative: object is _______ mirror

• di = distance image is from mirror:

• Positive: _______ image is __________ of mirror

• Negative: _______ image is__________ mirror

• f = focal length mirror:

• Positive: _________ mirror

• Negative: _________ mirror

f0

1 1 1

id d f

In Front

Behind

In front

behind

Inverted

upright

inverted In front

upright behind

Concave

Convex

concave

convex

UnderstandingThe image produced by a concave mirror of a real object is:

1) Always Real

2) Always Virtual

3) Sometimes Real, Sometimes Virtual

In a concave mirror the focal length, f, is >0

Real Object means in front of mirror: do > 00

1 1 1

id d f

0

1 1 1

id f d Therefore di can be positive or negative

Mirror Equation

Practice: Concave MirrorWhere in front of a concave mirror should you place an object so that the image is virtual?

Mirror Equation:1) Close to mirror

2) Far from mirror

3) Either close or far

4) Not Possible

• When do < f then di <0 : virtual image.

• Virtual image means behind mirror: di < 0

• Object in front of mirror: do > 0

0

1 1 1

id d f

0

1 1 1

id f d

• In a concave mirror the focal length, f, is > 0

O

I

Magnification Equationdo

do

ho

Angle of incidence

di

hiAngle of reflection

o

i

o

i

dd

hh

m

o

o

dh)tan(

i

i

dh

di

• ho = height of object:

• Positive:_______________

• hi = height of image:

• Positive: ______________

• Negative: _____________

• m = magnification:

• Positive / Negative: same as for hi

• < 1: image is _______________

• > 1: image is ________________

Always

upright

inverted

reduced

enlarged

Practice Solving EquationsA candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location.

(in front of mirror)

Real Image!

C f

p.a.

Compared to the candle, the image will be:

• Larger

• Smaller

• Same Size

0

1 1 1

id d f

1 1 1

6 2icm d cm

1 1 1

2 6id cm cm

2 2

1 6 2

12 12i

cm cm

d cm cm

1 1

3id cm

3id cm

Note: image is 3 cm in front of mirror, therefore 1 cm to the left of the focus

What is the size of the image?

1) 2 inches

2) 4 inches

3) 8 inches

What direction will the image arrow point?

1) Up 2) Down

o

i

hh

m

(-) sign tells us it’s inverted from object

Magnitude gives us size.

4 inches

Practice: MagnificationA 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of –2.

0ih mh 2 4"

8"

O

Convex Mirror Rays

c



#3I

2) Through center.

#2

Image is: Virtual (light rays don’t really cross) Upright (same direction as object) Reduced (smaller than object)(always true for convex mirrors!):

f

#1

Technique

Convex Mirror Rays

The image is virtualThe image is uprightThe image is smaller than the object

Convex Mirror Images Unlike Concave Mirrors, convex mirrors always produce images which share these characteristics. The location of the object does not affect the characteristics of the image. As such, the characteristics of the images formed by convex mirrors are easily predictable

The diagrams below shows that in each case: the image islocated behind the convex mirrora virtual imagean upright imagereduced in size (i.e., smaller than the object)

OverviewReflection:

Refraction:

Absorption

Flat Mirror: image equidistant behind

Spherical Mirrors:Concave or Convex

Flat Lens:Window

Spherical Lenses:Concave or Convex

Tod

ayLa

st T

ime

Nex

t tim

e

i r

1

2

n2

n1

i = r

n1 sin(1)= n2 sin(2)

Solving ProblemsA candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm.

Determine the image location.

Determine the magnification of the candle.

If the candle is 9 cm tall, how tall does the image candle appear to be?

Image is Upright!

di = - 2 cm (behind mirror)

Virtual Image!0

1 1 1

id d f 1 1 1

6 3icm d cm

0

idmd

2 1

6 3

cmm

cm

0

ihmh

0

19

3

3

ih mh

cm

cm

ProblemWhere should you place an object in front of a convex mirror to produce a real image?

Mirror Equation:

1do

1di

1f

1) Object close to mirror

2) Object far from mirror

3) Either close or far

4) You can’t

0

111dfdi

di is negative!

f is negativedo is positive

• Real image means di > 0

• Convex mirror: f < 0

• Object in front of mirror: do > 0

ProblemA concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror.

a)At What distance from the mirror will the image be formed?b)What is the height of the image?

C f

40.0

cm

24.0

cm 2.5cm



C f

40.0

cm

24.0

cm 2.5cm

0

1 1 1

if d d

2

Rf 24.0

2

cm

1 1 1

12.0 40.0 icm cm d

1 1 1

12.0 40.0 icm cm d

7 1

120 icm d

17.14id cm

12.0cm

The image is 17 cm in front of the mirror



C f

40.0

cm

24.0

cm 2.5 cm

0 0

i ih dm

h d

17.14

2.5 40.0ih cm

cm cm

17.142.5

40.0

1.07

i

cmh cm

cm

cm

The height of the inverted image is 1.1 cm

Problem

Cf4.5

m

80.0

cm 1.7m

A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror.


Problem

Cf4.5

m

80.0

cm 1.7m



0

1 1 1

if d d

2

Rf

0.8

20.4

m

m

1 1 1

0.4 4.5

1 1 1

0.4 4.5

1 4.9

1.8

0.37

i

i

i

i

m m d

d m m

m

d m

d m

Therefore the image is 0.37 m behind the mirror

0.4

m

0.37

m

Problem

Cf4.5

m

80.0

cm 1.7m



0.4

m

0.37

m

0 0

i ih dm

h d

0 0

00

0.371.7

4.50.14

i i

ii

h d

h d

dh h

d

mm

mm

Mirror SummaryAngle of incidence = Angle of ReflectionPrincipal Rays

Parallel to P.A.: Reflects through focusThrough focus: Reflects parallel to P.A.Through center: Reflects back on self

|f| = R/2

1do

1di

1f

o

i

o

i

dd

hh

m

SPH3UW: OPTICS I Introduction to Mirrors Light incident on an object Absorption Everything true for wavelengths

Documents

mirror virtual image

mirror real image

mirror negative

image slide

concave mirror image

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convex mirror images

focal length mirror