10.3+10.410.3+10.4 CURVED MIRRORS-CURVED MIRRORS-

Concave and Convex Concave and Convex

Ever seen Ever seen yourself in a yourself in a funhouse mirror?funhouse mirror?

Funhouse mirrors are curved Funhouse mirrors are curved mirrorsmirrors

The funny images you see created in funhouse mirrors are caused by the special way that light rays reflect off of curved surfaces

While the reflected light ray still follows the Law of Reflection, the reflection is not as straight forward as a flat surface!

This creates unique images as seen in funhouse mirrors

Concave mirrorsConcave mirrors

Mirrors that curve inwards are known as CONCAVE mirrors – if you look into the front of a spoon, you are looking at a concave mirror

There are two types of curved There are two types of curved mirrorsmirrors

Curved mirrors can come in two typesBasically, they can either curve inwards or

outwards, and are best represented by the opposite sides of a spoon

Concave mirrorsConcave mirrors

In a concave mirror, the mirror curves inwards

This is what you see if you look into the bowl of a spoon

It is like looking into the mouth of a cave, hence the word CONCAVE

Concave mirrors are converging Concave mirrors are converging mirrorsmirrors

Concave mirrors cause light rays to converge or focus on one point in front of the mirror

Therefore, they are also known as CONVERGING mirrors

Convex mirrorsConvex mirrors

In a convex mirror, the mirror curves outwards

This is what you would see if you looked into the back of a spoon

Convex mirrors are also diverging Convex mirrors are also diverging mirrorsmirrors

Convex mirrors also cause light rays to diverge or to spread out

Therefore, they are also known as diverging mirrors

Concave and convex mirrors in a Concave and convex mirrors in a spoonspoon

Curved mirror imagesCurved mirror images

We have looked at how plane or flat mirrors create images

But what would happen if we were to warp or curve the surface of a mirror?

On curved surfaces, the law of reflection still applies

Because the surface of the mirror changes, we have to zoom in on the very small piece of the mirror that the incident light ray hits

Another way to look at a curveAnother way to look at a curve

What do you notice about these shapes?

Curved surfaces are made up of Curved surfaces are made up of small flat surfacessmall flat surfaces

Any curve can be broken up into smaller and smaller straight lines

As you can see from the progression of polygons in the previous slides, the more sides there are to a polygon, the closer and closer it gets to becoming a circle

That means a curved surface can be seen as being made up of many, many small flat surfaces

Law of Reflection still rulesLaw of Reflection still rules

That means that when we try to analyze how a curved mirror converges or diverges light rays, we have to understand how a small flat surface applies to a large curved one

Ray diagramsRay diagrams

Ray diagrams are designed to help us predict the type of image formed by a curved mirror

These diagrams are designed to simplify how we see light rays

We track the light rays coming from only ONE POINT of an object

And we only track a maximum of 3 light rays

PRINCIPLE AXIS

VERTEXREAL FOCAL POINT

REAL CENTER OF CURVATURE

C F F’ C’

VIRTUAL FOCAL POINT

VIRTUAL CENTRE OF CURVATURE

Note: f = C/2 :distance of F from the mirror is always half the distance of C from the mirror

OBJECT

Parts of a ray diagramParts of a ray diagram

Focal point: where the light rays converge if they were to

Vertex: the center of the curved mirror that is a perfectly flat surface

Center of curvature: since a curved mirror is really a part of a big sphere, the center of curvature is the radius of that imaginary sphere that the mirror is cut out from

Focal length (f): the distance from the focal point to the vertex of the mirror

Radius of curvature (C): the distance from the center of the mirror to vertex

Tracking an imageTracking an image

Ray diagrams are designed to trace out where the light rays from one part of an image

Wherever these light rays converge back to is where the image of that one point will be created

We use the principle axis as the “ground” where the object sits on relative to the mirror

There are 4 types of rays that we can keep track of for a curved mirror

RAY DIAGRAM CONVENTIONSRAY DIAGRAM CONVENTIONS

FC F’ C’

Ray #1: Any ray that is parallel to the PA is reflected through F

Ray #2: Any ray that passes through F is reflected parallel to PA

Ray #3: Any ray that passes through C is reflected along the same path

IMAGE IS ALWAYS DRAWN FROM PA TO THE POINT OF INTERSECTING LINES

Ray #4: Any ray that hits the vertex is reflected at the same angle

Do I have to use them all?Do I have to use them all?

Note: you only need any 2 of the 4 possible rays that you can draw to locate an image!

Use the ones that you are most comfortable with – but remember that you have to adhere to the rules with using each one very carefully to locate images!

CONVERGING MIRRORSCONVERGING MIRRORS

The location of the object determines the outcome of the image

There are only 6 types of images that can be formed, and they are dependent on where the object is placed

1. Object at great distance: real, inverted, smaller than object, at F

2. Object beyond C: real, smaller, inverted, between C and F

3. Object at C: real, inverted, same size, at C4. Object between F and C: real, inverted, larger,

beyond C5. Object at F: no image formed6. Object between F and V: virtual, erect, larger

C F F’ C’

RAY DIAGRAM CONVENTIONSRAY DIAGRAM CONVENTIONS

FC

1. Object at great distance: real, inverted, smaller than object, at F

RAY DIAGRAM CONVENTIONSRAY DIAGRAM CONVENTIONS

FC F’ C’

2. Object beyond C: real, smaller, inverted, between C and F

RAY DIAGRAM CONVENTIONSRAY DIAGRAM CONVENTIONS

FC F’ C’

3. Object at C: real, inverted, same size, at C

RAY DIAGRAM CONVENTIONSRAY DIAGRAM CONVENTIONS

FC F’ C’

4. Object between F and C: real, inverted, larger, beyond C

RAY DIAGRAM CONVENTIONSRAY DIAGRAM CONVENTIONS

FC F’ C’

5. Object at F: no image formedNote: light rays remain parallel so no image formed

RAY DIAGRAM CONVENTIONSRAY DIAGRAM CONVENTIONS

FC F’ C’

6. Object between F and V: virtual, erect, larger

RAY DIAGRAMS FOR DIVERGING RAY DIAGRAMS FOR DIVERGING MIRRORSMIRRORS

Follow the same rules, but use the VIRTUAL focal point and centre of curvature

You are trying to pinpoint where the reflected light rays APPEAR to be coming from

It is impossible for a real image to be formed in a diverging mirror since all reflected light rays spread out from each other on the real side, therefore, they will never intersect to form an image

DIVERGING MIRRORS ALWAYS PRODUCE IMAGES THAT ARE VIRTUAL, ERECT, AND SMALLER

FCF’ C’

Ray #1: Any ray that is parallel to the PA is reflected as if it has passed through F

Ray #2: Any ray that appears to have passed through F is reflected parallel to PA

Ray #3: Any ray that appears to have passed through C is reflected along the same path

Ray #4: Any ray that hits the vertex appears to have been reflected at the same angle

Equations for curved mirrorsEquations for curved mirrors

Along with ray diagrams, images created by curved mirrors can be determined by using equations

These equations are based on the similar triangles that can be traced out in a ray diagram

F

ho

C

hi

do

di

Similar triangles, therefore:

ho = do-f

hi f

Since:

ho = do

hi di

Rearranging:

do = do-f

di f

1 + 1 = 1

do di f

Magnification Equation

Refer to page 425 in text

m= hi = -di

ho do

m=magnification hi=image height ho= object height

di=image distance to mirror do= object distance to mirror

The image height, hi, is negative if the image is inverted relative to the object

CONVENTIONS FOR CURVED MIRROR CONVENTIONS FOR CURVED MIRROR EQUATIONEQUATION

If the image is VIRTUAL its di/do is a NEGATIVE number

If the image is REAL its di/do is a POSITIVE number

If the object/image is ERECT its hi/ho is a POSITIVE number

If the object/image is INVERTED its hi/ho is a NEGATIVE number

For all divering mirrors, f or focal length, is always a negative number

MAGNIFICATION EQUATION FOR MAGNIFICATION EQUATION FOR CURVED MIRRORSCURVED MIRRORS

Therefore: since the image formed by a converging mirror is inverted, the magnification equation must change since the f, and distances are all positive

M = hi = - di ho doTherefore, this equation can also tell you if

the image is real, virtual, inverted or erect