1. PROOF OF d i = d o ii rr 11 22 

2. DESCRIPTION OF d i = d o  Ray of light leaves base & strikes mirror at  i (reflected at same  )  Angles  1 and  2   +  1 = 90 o   +  2 = 90 o  But  is equal to  r  Opposite angles formed by intersecting lines  Therefore  1 =  2

3. MIRRORS AT RIGHT ANGLES IMAGE 1 IMAGE 3 IMAGE 2

4. RIGHT ANGLES CONTINUED  What would be the equation for the number of images formed when the angle between two mirrors is   (360 o /  ) - 1  (360 o /90 o ) - 1 = 3  images formed  (360 o /60 o ) - 1 = 5  images formed

5. FOCAL LENGTH OF CONCAVE MIRROR  Incident ray strikes at A  Line CA is radius of mirror (normal to surface)  Reflected ray is reflected at angle equal to incident  Angle ACF is also  – CA is transversal of two parallel lines   ACF is isosceles – CF & FA are equal  When incident ray is close to PA, q is small  Therefore CF = FA = FB  Focal length is ½ of radius

6. RAY DIAGRAMS FOR CURVED MIRRORS

7. CONCAVE MIRRORS  Inside surface is polished  Law of reflection applies for curved mirrors as well (  i =  r )  Converging Mirror – Light is concentrated at one point

8. CONCAVE MIRRORS  Center of curvature – center of curved mirror (similar to center of circle)  Principle axis – Straight line drawn through C & the center of mirror.  Focal point – Point where all light will focus (half the distance of C)

9. DRAWING RAYS  Need to draw 3 rays  All rays start from the top (head) of the object  1 st ray – Incoming ray is parallel to the principle axis & is reflected through the focal point.  2 nd ray – Incoming ray goes through the focal point & is reflected parallel to the principle axis  3 rd ray – Serves as a check  Incoming ray goes through the center of curvature & is reflected back along the same line.

10. IMAGE FORMATION  The image is formed where the three reflected rays cross.  Drawn from the principle axis to the point of intersection  If the three rays cross on the same side of the mirror as the object, the image is considered a real image  If the three rays cross on the opposite side of the mirror, the image is consider virtual

15. SIGN CONVENTION FOR SPHERICAL MIRRORS FOCAL LENGTHOBJECT DISTANCE IMAGE DISTANCE MAGNIFICATIO N f + for concave mirror d o is + if object in front of mirror d i is + if image is in front of mirror m is + when image is upright f is – for convex mirror d o is – if object behind mirror d i is – if image is behind mirrror m is – when image is inverted *IF IMAGE IS IN FRONT OF MIRROR (SAME SIDE AS OBJECT), IT IS CONSIDERED A REAL OBJECT **IF IMAGE IS BEHIND MIRROR (OPPOSITE SIDE AS OBJECT), IT IS CONSIDERED A VIRTUAL OBJECT

16. CONVEX MIRROR  Outside surface is polished  Law of reflection applies as well  Diverging mirror – reflected rays will never cross in front of mirror (same side as object)

17. CONVEX MIRROR  Center of curvature is still the same but is considered a negative value since it is on the back side of the mirror  Focal point is also considered a negative value for the same reason (half the distance of C)

18. IMAGES FORMED FROM CONVEX MIRROR  Still draw the same 3 rays to locate the image  Since the reflected rays will never cross on the same side as the object, these rays must be drawn (as dotted lines) behind the mirror  Where they cross is where image is located  Image is considered a virtual image  Virtual image – Light rays do not pass through the image

23. HOMEWORK  Draw the following diagrams:  Object beyond C  Object @ C  Object between C and f  Object at f  Object between f and surface of mirror  1 st four diagrams: C = 10 cm, h o = 2 cm concave mirror  5 th diagram C = 6 cm h o = 1 cm convex mirror

24. CONCAVE MIRROR

25. MIRROR AND MAGNIFICATION EQ. f = focal length of mirror do = object distance di = image distance m = magnification of the mirror – ratio of height of image to height of object