Curved Mirrors

Take a look at a curved mirror

• Where can one find a mirror of this type in real life?

• The image you are looking at seems to be behind the mirror.

• The image is (select one) larger / smaller than the object?

sol.sci.uop.edu

Handle a Flexible Mirror• What kitchen utensil is this like?

• Concave or Convex?– TV mirror– Inside of spoon– Outside of spoon

• Can you demonstrate both of the cases that are on the next slide?

Drawing by Paul Hewitt

Types of Images• We say that an image is “Virtual” if no light is actually

coming from the image location. Virtual images are never on a screen.

• We say that an image is “Real” if the light is really coming from the image location. Real images are always on a screen.

• Real or Virtual?– Image from Plane Mirror?– Image from Overhead Projector?– Image due to concave side of spoon?– Image due to convex side of spoon?

Demo: A BIG concave mirror can focus light from the Overhead

Projector onto the ceiling.

• Similar Demo: A small curved mirror can focus light from the room lights onto a piece of paper.

• Demo: A curved mirror can make an image of the window on the wall.

Focus !• A curved mirror has a focal point.

• A curved mirror has a focal length.

• To measure the focal length:– Use light from an object that is far away.

(windows, sun, light from across the room …)– Focus the light onto a screen. – Measure the focal length ( = the length from

the mirror to the screen).

• Now do the Activity: “Focal Length”

• Then do the Lab: “Curved Mirrors.”

Tracing Light Raysfor Curved Mirrors

The Solar Cooker

SUN

Drawing found athttp://library.thinkquest.org/03oct/02144/glossary/concave_mirror.html

The Solar Cooker

• Where (in the picture) do you put the food?

• What shape is the mirror?

• If it is a paraboloid, it works better than a spherical mirror, but it costs more.

Where would you put a screento make the smallest bright dot?

Mirror

Screen

Notice:This point is notthe focal point

The cheapest curved mirrors are made of a section of a sphere.

• These are called “_ _ _ _ _ _ _ _ _” mirrors even though they are merely part of the sphere.

The cheapest curved mirrors are made of a section of a sphere.

• These are called “spherical” mirrors even though they are merely part of the sphere.

The cheapest curved mirrors are made of a section of a sphere.

• These are called “spherical” mirrors even though they are merely part of the sphere.

• The distance from the mirror to the center of the sphere is called the _ _ _ _ _ _ (of course).

The cheapest curved mirrors are made of a section of a sphere.

• These are called “spherical” mirrors even though they are merely part of the sphere.

• The distance from the mirror to the center of the sphere is called the radius (of course).

The cheapest curved mirrors are made of a section of a sphere.

• These are called “spherical” mirrors even though they are merely part of the sphere.

• The distance from the mirror to the center of the sphere is called the radius (of course).

• The distance from the mirror to the focal point (the “focal length”) is half of the radius. f = ______ ÷ 2 (see next slide).

The cheapest curved mirrors are made of a section of a sphere.

• These are called “spherical” mirrors even though they are merely part of the sphere.

• The distance from the mirror to the center of the sphere is called the radius (of course).

• The distance from the mirror to the focal point (the “focal length”) is half of the radius. f = Radius÷2 (see next slide).

C

f

R

Why do concave mirrors bring sunlight to a focus?

[Note: Sunlight comes from so far away, that the rays arrive here

essentially parallel to each other.]

Ray of Sunlight

Plane Mirror

In which way will the ray reflect?

Ray of Sunlight

Plane Mirror

Why does it go that way?

The reason:The angle of ‘incidence’

equalsthe angle of ‘reflection.’

I

R

Ray of Sunlight

Plane Mirrors

In which way do they bounce?

Ray of Sunlight

Ray of Sunlight

Ray of Sunlight

Ray of Sunlight

Replace the plane mirrors witha curved mirror.

This is how a TV Satellite Dish works.

(The electromagnetic rays are collected at the receiver.)

What would happen if the light originated from the focal point?

Light emanates in all directions.

What happens to the light that hits the mirror?

This is how a light bulb is used as a car headlight or in a flashlight.

Why are images created?

(This is a different idea than the hot-dog cooker and the flashlight.)

Most of the light from the pencil point does not hit the mirror.

The light from the pencil point bounces off the mirror following the pattern: I = R.

What would you see if you put your eye at point P, and looked at the mirror?What would you see on a screen placed at point P? The ‘image’ of the point is at P.

P•P is not thefocal point

Most of the light that leaves the eraser, does not hit the mirror.

P•

Following the pattern: I = R, the light bounces off of the mirror, forming an image of just the eraser at point E. What would you see if you put your eye at point E?

P••E

Put a screen at points E and P (and all points in between) and you will see an image of the pencil (smaller, and inverted).

P E

Is the image real or virtual?

• We say that an image is “Virtual” if no light is actually coming from the image location.

• We say that an image is “Real” if the light is really coming from the image location.

About the image• Why do you need a screen to see this

image?

• If you cover part of the pencil how would that change the image? Explain.

• If you cover part of the mirror how would that change the image? Explain.

Where is the image?

What size is the image?

Object

Principal AxisFocal Point

Mirror

Case One. Use the full-sized page in your booklet

In which direction will this ray bounce?

Hint: This is a ‘Solar Cooker’ ray.

Principal Ray #1Starts parallel to the Principal Axis, and reflects through the focal point.

1

1

1

1

Somewhere along this ray is the image,but where?

In which direction will this ray bounce?

Hint: this is a ‘Flashlight’ ray.

Principal Ray #2From the focal point, it reflects parallel to the Principal Axis.

2

2

These two principal rays help us find the location and size of the image:

2

2

1

1

Real or Virtual?

2

2

1

1

Object

Image

ALL RAYS FROM THE TOP OF THE OBJECT (that hit the mirror) WILL PASS THROUGH THE “TOP” OF THE IMAGE

2

2

1

1

The image is Real, Inverted, and Smaller than the object.

Object

Image

In which direction does this 3rd ray bounce?

2

2

1

1

In which direction does this 3rd ray bounce?

2

2

1

1

Case Two:The object is close to the mirror

Principal Axis

Object

Focal Point

Mirror

In which way does the ray bounce?

1

Ray 1 [What is the next ray we should draw?]

1

1This ray should line

up with the focal point

In which way does the ray bounce?

2

Ray 2

2

2

Let’s look at all of the rays we know about, at one time.

What does this mean?

Real or Virtual?

Did you see an image like this in Lab? Describe the image.

In which direction does this 3rd ray bounce?

In which direction does this 3rd ray bounce?

What kind of mirror is this? [How do you know?]

Case Three:The mirror is convex.

In which direction does the light bounce?

Ray 1[What is the next ray we should draw?]

1

1

In which direction does the ray reflect?

Ray 2

2

2

All the rays at once:Where is the image?

1

1

2 2

Describe the image.

http:// PhysicsClassroom.html

Which case is this (1, 2, or 3) ?

An Equation that gives the location of the image:

€

1

f=

1

DO

+1

DI

An equation that gives thesize of the image:

€

M =HI

HO

= −DI

DO

Use the drawings we made to see if we understand how to use the

equations.

Case 1

Measured w Ruler

Calculated

f mm

DO mm

DI mm mm

HO mm

HI - mm mm

f

Case 1

Measured w Ruler

Calculated

f 56 mm

DO mm

DI mm mm

HO mm

HI - mm mm

DO

Case 1

Measured w Ruler

Calculated

f 56 mm

DO 183 mm

DI mm mm

HO mm

HI - mm mm

DI

Case 1

Measured w Ruler

Calculated

f 56 mm

DO 183 mm

DI 76 mm mm

HO mm

HI - mm

- mm

HO

Case 1

Measured w Ruler

Calculated

f 56 mm

DO 183 mm

DI 76 mm mm

HO 25 mm

HI - mm - mm

HI

Case 1

Measured w Ruler

Calculated

f 56 mm

DO 183 mm

DI 76 mm ? mm

HO 25 mm

HI - 10 mm - mm

What numbers do you put in?

€

1

f=

1

DO

+1

DI

Put in the numbers…

€

1

56mm=

1

183mm+

1

DI

What number do you get?

Sign Conventions (Page 1)

DI > 0 Image is Real and Inverted

DI < 0 ?

[Think of an example you have seen.]

Case 1

Measured w Ruler

Calculated

f 56 mm

DO 183 mm

DI 76 mm 81 mm

HO 25 mm

HI - 10 mm - ? mm

What numbers do you put in?

€

M =HI

HO

= −DI

DO

€

HI

25mm= −

76mm

183mm

What number do you get?

Case 1

Measured w Ruler

Calculated

f 56 mm

DO 183 mm

DI 76 mm 81 mm

HO 25 mm

HI - 10 mm - 11 mm

What is the magnification?M = HI ÷ HO

M = HI ÷ HO

M = (-11)÷(25)M = -0.44

Sign Conventions (Page 2)

M > 0 Image is Virtual and Upright

M < 0 ?

[Think of an example you have seen.]

Case 2

Case 2

Measured w Ruler

Calculated

f 143 mm

DO 52 mm

DI -68 mm

HO 26 mm

HI 38 mm

Case 2

Measured w Ruler

Calculated

f 143 mm

DO 52 mm

DI -68 mm - 81.7 mm

HO 26 mm

HI 38 mm

Case 2

Measured w Ruler

Calculated

f 143 mm

DO 52 mm

DI -68 mm - 81.7 mm

HO 26 mm

HI 38 mm 34 mm

Case 3

Case 3

Measured w Ruler

Calculated

f -54 mm

DO 84 mm

DI -33 mm

HO 26 mm

HI 10 mm

Why is this negative?

Case 3

Measured w Ruler

Calculated

f -54 mm

DO 84 mm

DI -33 mm -32.9 mm

HO 26 mm

HI 10 mm

Case 3

Measured w Ruler

Calculated

f -54 mm

DO 84 mm

DI -33 mm -32.9 mm

HO 26 mm

HI 10 mm 10.2 mm

SummaryCase 1

Case 3

Case 2

Recall from the lab, how are Object Distance, and Image

Distance Related?

Do far objects make images near the mirror, or far from the mirror?

Image Distance vs. Object Distance[Where is the focal length on the x axis?]

-300

-200

-100

0

100

200

300

0 20 40 60

http://www.physicsclassroom.com/Class/refln/U13L3a.html

Would you like to run through the whole analysis again, but from a different source?Consider:

http://www.sasked.gov.sk.ca/docs/physics/u3b32phy.html

Would you like a source that does a detailed job of summarizing the crucial ideas? Try:

http://library.thinkquest.org/10796/ch10/mirror.htm

Would you like a resource that just deals with the big ideas? Try: