With CurvedMirrors

Created by Derek J. Wells. Under the expressed written consent of Derek J. Wells in accordance with the rules and by-laws of Derek J. Wells. All events depicted here are fictional. Any similarity to real life situations are merely coincidental.

Types of Mirrors The everyday flat type of mirror is called a “plane mirror”. All light travelling straight towards this mirror reflects right back at you. As such, you always get an image that is an exact duplicate of you. Remember, MIRRORS REFLECT LIGHT, so it bounces off them. This may seem silly in that we already know that, but as we talk of more optical instruments its something you should keep in mind.Curved mirrors are not flat and therefore light reflects differently off them making different types of images. There are two types of curved mirrors

A concave mirror. And A convex mirror

This mirror has a concave shape when looking at it from the left side.

This mirror has a convex shape when looking at it from the left side

This mirror looks like a “cave” if you were walking into it from the left side.

The concave mirror is also called a converging mirror because it causes horizontal light rays to converge (come together) when they reflect off the mirror

The convex mirror is also called a diverging mirror because it causes horizontal light rays to diverge (move apart) when they reflect off the mirror

TerminologyCurved mirrors are approximated

to have a circular shape.

We can make a curved mirror by cutting part of mirrored circle out.

The mirror was cut from a circle.

Terminology

The center of the circle that the mirror is part of is point C.

CThe radius of the circle that the mirror is part of is distance R

R

Point C is called:

C= Center of Curvature

Distance R is called:

R= Radius of Curvature

Terminology

Principle Axis = The horizontal line drawn through the center

f = Focal point (of a concave mirror) = the point through which all horizontal rays hitting the mirror pass through when they reflect

f = Focal point (of convex mirror) = the point at which all horizontal rays hitting the mirror appear to come from when they reflectIMPORTANTThese focal points are negative (-)In the convex mirror

The focal point(f) is 1/2 of the distance to the center of curvature point (C)

f = R / 2

f f CC

Terminology

f fC C

An object placed near a mirror The image of

the object that is produced by the mirror

Front Side of Mirror(the real side)

Back Side of Mirror (the virtual side)

When images are formed on the back side of the mirror they are virtual images. When you look at a mirror and see an object back inside it that looks different than usual you see a virtual image (looking at a spoon, or car side mirror - “objects may appear closer than seem”)

When images are formed on the front side of the mirror they are real images. Real images can be projected onto a screen.

Also

ho = object height

hi = image heightd0

Distance object is placed from the mirror

di

Distance image is formed from the mirror

iddf

111

0

o

i

d

dM

Determining the Image

di = (+) real imagedi = (-) vitual imageM = (+) uprightM = (-) inverted (upside down) | M | = 1 same size| M | < 1 smaller| M | > 1 larger

note | M | = (absolute value of M)

Mirror EquationsMirror Equations - You can find out where and what an image should look like by using the mirror equations

To find the distance of the image from the mirror

To find the Magnification and Orientation of the Image

Important - when using a convex mirror the focal point (f) must be made negative (-)

o

i

h

hM

Concave mirrors can form any types of these images - real or virtual - smaller, same size, or larger - inverted or upside down

Convex mirrors can only form one type of image ALWAYS

- smaller, upright, virtual

id

1

8

1

4

1

id

1125.025.0

id

1375.0

8

) 67.2( cmM

Example: A convex mirror with (f = 4 cm, d0 = 8 cm)

iddf

111

0

o

i

d

dM

cmdi 67.2

Note that the f is (-) since it’s a convex mirror

33.0M

di = (-) so its virtual

M = (+) so its (upright)

| M | < 1 so its smaller

C f

Ray Diagrams (for concave mirrors)We use ray diagrams to draw a picture of what the image would look like

3 Light rays are drawn all originating from the tip of the OBJECT. The point where these rays intersect gives the location where the tip of the IMAGE will be

Lets try an example with f = 5 cm, do = 12 cmThe first light ray we draw goes through the center of curvature of the mirror

This light reflects back upon itself as if unaffected

C f

Ray Diagrams (for concave mirrors)

The second light ray we draw goes horizontally straight towards the mirror

This light ray reflects back and passes through the focal point

C f

Ray Diagrams (for concave mirrors)

The third light ray we draw goes through the focal point before it hits the mirror

This light ray emerges horizontal when it reflects from the mirror

Describe the image:

Real

Inverted

Smaller

A concave mirror (converging) with (f = 2 cm, d0=5 cm)

iddf

111

0

id

1

5

1

2

1

id

12.05.0

Check the math

id

13.0 cmdi 33.3

o

i

d

dM

67.0 5

33.3

M

di = (+) so its real

M = (-) so its inverted

| M | < 1 so its smaller

Putting it all together.Draw all three rays, and the point where they intersect represents the point where the tip of the image will be formed

C f

Image

Special Examples1- When the object is located exactly on (f) the rays will not intersect anywhere and there will be no image

2- When the object is placed right on C, you can only draw two rays. The first ray that is supposed to be drawn through point C, cant be drawn because you are located right on top of it.

C f

Image

Describe the image:Virtual

Upright

Larger

Special Examples3 - When the object is placed in front of C or in front of F. Special rules apply.

The problem with this case is that the object is in front of the points “f” and “c” so it is impossible to draw the rays through those points.

C f

So instead, the rays that are supposed to go through those points, are drawn as if the started there. The first ray is drawn as if it started at C. The second ray is drawn straight and reflects through f. The third ray is drawn as if it started at f.

Image

Notice that these rays do not intersect anywhere over here

We extend the reflected rays back behind the mirror to see where they appear to come from. This is the image point.

Ray Diagrams (for convex mirrors)The nice thing about Convex mirrors is that the ray diagrams are ALWAYS, ALWAYS the same. They are slightly different then the concave mirrors however and you should be careful to notice the differences. In this type of mirror, you always have to extend the reflected rays back behind to find the image

Lets try an example with f = 5 cm, do = 12 cm

The first light ray we draw goes towards the center of curvature on the other side

This light ray reflects back on itself as if unaffected.

Cf

Ray Diagrams (for convex mirrors)

The second light ray we draw goes horizontally towards the mirror.

This light ray reflects back AS IF it came from point “f”

Cf

Ray Diagrams (for convex mirrors)

The third ray goes towards the f on the back side of the mirror

This light ray reflects back horizontally

Cf

Ray Diagrams (for convex mirrors)Put them all together and extend the reflected rays behind the mirror to find the object

Describe the image:Virtual

Upright

Smaller

CfImage

Notice that these rays do not intersect anywhere over here

We extend the reflected rays back behind the mirror to see where they appear to come from. This is the image point.

Mirror Defects

The geometry of a spherical mirror is such that distorted blurred images can be produced by the mirror

Normally, rays that approach the mirror horizontally reflect through the focal point

If light rays are far from the principle axis up towards the top of the mirror, they don’t reflect as much and actually can reflect slightly off from the principle axis

C f

This produces a blurred image.This phenomenon is known as SPHERICAL ABBERATION

Mirror Defects

Correcting Spherical Abberation - The use of a Parabolic mirror eliminates the problem of Spherical Abberation. A Parabolic mirror has a parabolic rather than spherical shape.

The parabolic shape assures that all horizontal rays approaching it will pass through the focal point when reflected

C f

Fini

That’s the end of the mirrors presentation. If you enjoyed this film, look for other great

presentations such as”101 Easy Ways to Fail Physics”

©2001, well not really