2 Curved MirrorsWhat are some examples of curved mirrors?
3 Concave Spherical Mirrors A spherical mirror has the shape of part of a sphere’s surface.Concave Spherical Mirror (Converging Mirror): A spherical mirror with light reflecting from its silvered, concave surfaceConcave mirrors are used whenever a magnified image of an object is needed
4 Terms you need to know Term Definition Symbol(s) Center of Curvature The center of the spherical shell of which the mirror is a small partCRadius of CurvatureThe distance from the mirror’s surface to the center of curvatureRHeight of objectThe height of the objecth; hoHeight of imageThe height of the imageh’, hiObject distanceThe distance between the object and the mirrorp; doImage distanceThe distance between the image and the mirrorq; diFocal LengthFocal length is equal to half the radius of curvaturef
5 Concave Spherical Mirrors (p.531) ObjectPrincipal AxisCfA spherical mirror is represented as a shell of a sphere
7 The Mirror EquationTo use the mirror equation, you must use the correct signs.Object and image distances are positive if they form on the front side of the mirrorObject and image distances are negative if they form on the back side of the mirror
8 Sample Problem (p.536 #2)A concave shaving mirror has a focal length of 33 cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm.
11 Sample Problem (p.536 #2)A concave shaving mirror has a focal length of 33 cm. Calculate the magnification of the image. Is the image real or virtual? Is the image inverted or upright?
12 Sign Conventions for Magnification Orientation of image with respect to objectSign of MType of imageUpright+VirtualInverted-Real
13 Find the magnification The magnification is negative, therefore the image is real and inverted.
14 Ray DiagramsA ray diagram is a drawing that uses geometry to locate an image formed by a mirror.There are different rules for drawing ray diagrams depending on the type of mirror you have.
15 How to draw a ray diagram (p. 533-534) For spherical mirrors, there are three different reference rays.The intersection of any two rays locates the image
16 Rules for drawing reference rays (p. 534) Line drawn from object to mirrorLine drawn from mirror to image after reflection1Parallel to principal axisThrough focal point F23Through center of curvature (C)Back along itself through C
17 How to draw a ray diagram fCRay 1Ray 3Ray 2The intersectionOf any 2 rays gives the image location
19 Sample Problem (p.536 #2)A concave shaving mirror has a focal length of 33 cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm. Draw a ray diagram to confirm your results.
20 Draw the diagramfCThe image is inverted and about half the height of the object.
21 Convex MirrorsConvex mirrors take objects in a large field of view and produce a small imageSide-view mirrors on cars are convex mirrors. That’s why they say “objects are closer than they appear”
22 Convex Spherical Mirrors (p. 537) A convex spherical mirror (diverging mirror) is silvered so that light is reflected from the sphere’s outer, convex surfaceThe image distance is always negative!The image is always a virtual image!The focal length is negative !
23 Ray diagrams for convex mirrors The focal point and center of curvature are behind the mirror’s surfaceA virtual, upright image is formed behind the mirrorThe magnification is always less than 1fC
24 Drawing the reference rays Ray 1 is drawn parallel to the principal axis beginning at the top of the object. It reflects from the mirror along a line that intersects the focal pointfC
25 Ray 2Ray 2 starts from the top of the object and goes as though its going to intersect the focal point but it reflects parallel to the principal axisRay 1Ray 2fC
26 Ray 3Ray 3 starts at the top of the object and goes as though its going to intersect the center of curvatureRay 1Ray 3Ray 2fC
27 Convex Spherical Image Formation The image forms at the intersection of any two of the three rays behind the mirror.Ray 1Ray 3Ray 2fCThe rays do not intersect in front of the mirror!!
29 Sample Problem (p. 540 #6)A candle is 49 cm in front of a convex spherical mirror that has a focal length of 35 cm. What are the image distance and magnification? Is the image virtual or real? Is the image inverted or upright? Draw a ray diagram to confirm your results.
30 Solving the problemRemember that for convex mirrors, the focal length and image distance are always negative.
31 The Magnification of the Image Since the magnification is positive, the image is upright and virtual
32 Ray diagram for the Image CfRemember that you only need to draw two of the three rays to find the image.