Post on 15-Dec-2015
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
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
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
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