2. With Curved Mirrors 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.

3. 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.

4. 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

5. Terminology Curved 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.

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

7. 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 reflect IMPORTANT These 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 C C

8. Terminology f f C 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 h o = object height h i = image height d0d0 Distance object is placed from the mirror didi Distance image is formed from the mirror

9. Determining the Image d i = (+) real image d i = (-) vitual image M = (+) upright M = (-) inverted (upside down) | M | = 1same size | M | 1larger note | M | = (absolute value of M) Mirror Equations Mirror 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 (-) 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

10. Example: A convex mirror with (f = 4 cm, d 0 = 8 cm) Note that the f is (-) since it’s a convex mirror d i = (-) so its virtual M = (+) so its (upright) | M | < 1so its smaller

11. 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 cm The first light ray we draw goes through the center of curvature of the mirror This light reflects back upon itself as if unaffected

12. 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

13. 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

14. Describe the image: Real Inverted Smaller A concave mirror (converging) with (f = 2 cm, d 0 =5 cm) Check the math d i = (+) so its real M = (-) so its inverted | M | < 1so 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

15. Special Examples 1- 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

16. Describe the image: Virtual Upright Larger Special Examples 3 - 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.

17. 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. C f

18. 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” C f

19. 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 C f

20. 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 C 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.

21. 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

22. 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

23. 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