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**10.3+10.4 CURVED MIRRORS-Concave and Convex**

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

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**Funhouse mirrors are curved mirrors**

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 Funhouse mirrors are curved mirrors

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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 Concave mirrors

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**There are two types of curved mirrors**

Curved mirrors can come in two types Basically, they can either curve inwards or outwards, and are best represented by the opposite sides of a spoon There are two types of curved mirrors

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**Concave 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

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**Concave mirrors are converging mirrors**

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 Concave mirrors are converging mirrors

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**Convex 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

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**Convex mirrors are also diverging mirrors**

Convex mirrors also cause light rays to diverge or to spread out Therefore, they are also known as diverging mirrors Convex mirrors are also diverging mirrors

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**Concave and convex mirrors in a spoon**

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**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 mirror images

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**Another way to look at a curve**

What do you notice about these shapes? Another way to look at a curve

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

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**Law 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 Law of Reflection still rules

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**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 Ray diagrams

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REAL FOCAL POINT VIRTUAL FOCAL POINT VERTEX VIRTUAL CENTRE OF CURVATURE OBJECT C F F’ C’ PRINCIPLE AXIS REAL CENTER OF CURVATURE Note: f = C/2 :distance of F from the mirror is always half the distance of C from the mirror

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**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 Parts of a ray diagram

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**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 Tracking an image

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**RAY DIAGRAM CONVENTIONS**

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 Ray #4: Any ray that hits the vertex is reflected at the same angle C F’ C’ IMAGE IS ALWAYS DRAWN FROM PA TO THE POINT OF INTERSECTING LINES F

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**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! Do I have to use them all?

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**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 Object at great distance: real, inverted, smaller than object, at F Object beyond C: real, smaller, inverted, between C and F Object at C: real, inverted, same size, at C Object between F and C: real, inverted, larger, beyond C Object at F: no image formed Object between F and V: virtual, erect, larger CONVERGING MIRRORS

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C F F’ C’

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**RAY DIAGRAM CONVENTIONS**

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

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**RAY DIAGRAM CONVENTIONS**

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

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**RAY DIAGRAM CONVENTIONS**

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

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**RAY DIAGRAM CONVENTIONS**

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

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**RAY DIAGRAM CONVENTIONS**

5. Object at F: no image formed Note: light rays remain parallel so no image formed C F’ C’ F

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**RAY DIAGRAM CONVENTIONS**

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

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**RAY DIAGRAMS FOR DIVERGING MIRRORS**

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 RAY DIAGRAMS FOR DIVERGING MIRRORS

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**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 F’ C’ C F

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**Equations 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 Equations for curved mirrors

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**Similar triangles, therefore:**

ho = do-f hi f Since: ho = do hi di Rearranging: do = do-f di f = 1 do di f do ho C F hi di

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**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

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**CONVENTIONS FOR CURVED MIRROR EQUATION**

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 CONVENTIONS FOR CURVED MIRROR EQUATION

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**MAGNIFICATION EQUATION FOR CURVED 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 do Therefore, this equation can also tell you if the image is real, virtual, inverted or erect MAGNIFICATION EQUATION FOR CURVED MIRRORS

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