Chapter 23 Mirrors and Lenses 23 1 Flat Mirrors You think object s location is where rays appear to come from i r Smooth Mirror All rays originating from peak will appear to come from same point behind mirror Object Magnification M image height h object height h Positive h upright negative h inverted Image appears Upright m 0 Same size M 1 Facing opposite direction Left Right inverted Why ambulances have AMBULANCE written backwards Virtual Image Light rays don t actually come from image location Image Example How big is the mirror so that the person can see his hat and shoes at the same time Front surface less reflecting than the mirror surface on the back side Larger pupils more sensitive to light at night requires less reflection Pupil size adjusts to light conditions not very fast though on the scale of a minute or two 1 Concave Mirror 23 2 Spherical mirrors A Spherical Mirror section of a sphere Concave mirror light ray R Principal Axis principal axis C Focus f R 2 Rays are bent towards the principal axis Convex mirror light ray C principal axis Rays parallel to principal axis and near the principal axis paraxial rays all reflect so they pass through the Focus F The distance from F to the center of the mirror is called the Focal Length f C Center of curvature In front of concave mirror behind convex mirror f R 2 Ray Diagram Concave Mirror Concave Mirror Principal Rays 1 Parallel to principal axis reflects through f 2 Through f reflects parallel to principal axis F 3 Through center comes to the center O Principal Axis F 1 2 3 Image is in this case Real light rays actually cross Inverted Arrow points opposite direction Reduced smaller than object f c I Rays traveling through focus before hitting mirror are reflected parallel to Principal Axis Rays traveling parallel to Principal Axis before hitting mirror are reflected through focus 2 1 1 1 p q f p distance object is from mirror Positive object in front of mirror Negative object behind mirror q distance image is from mirror Positive real image in front of mirror Negative virtual image behind mirror Positive sign follows the light ray otherwise negative Positive h and M upright otherwise inverted Useful for MCAT f focal length mirror Positive concave mirror Negative convex mirror coming soon Concave mirror f 0 Real Object means in front of mirror p 0 When a concave mirror focuses a beam of light 1 2 3 4 Snell s law is wrong in this case Reflection angle incidence angle Reflection angle incidence angle None above Mirror Equation 1 1 1 p q f 1 1 1 q f p q can be negative or positive depending on the values of f and p In other words the image can be either inverted and real or upright and virtual 3 Magnification Equation p A candle is placed 6 cm in front of a concave mirror with focal length f 2 cm Determine the image location h height of object Positive always h height of image Positive image is upright Negative image is inverted Example O h q M h p q I Angle of incidence h M magnification Positive Negative same as for h 1 image is reduced 1 image is enlarged h q 3 cm in front of mirror p Real Image q Angle of reflection For concave mirror M h h p a R f q p 23 3 Convex Mirror the image is therefore Principal Axis 1 upright 2 behind the mirror 3 either in front or behind the mirror 4 larger Rays are bent towards the principal axis Focus f R 2 Rays parallel to principal axis and near the principal axis paraxial rays all reflect so they appear to originate from the Focus F The distance from F to the center of the mirror is called the Focal Length f f R 2 4 Convex Mirror Rays Example 1 Through f reflects parallel to principal axis A candle is placed 6 cm in front of a convex mirror with focal length f 3 cm Determine the image location 2 Through center O 1 1 1 1 6 cm q 3 cm I 2 f Image is Virtual light rays don t really cross Upright same direction as object Reduced smaller than object broader view Mirrors on the passenger side and in convenience stores c 1 1 1 p q f q 2 cm behind mirror Virtual Image Determine the magnification of the candle M q 2 cm p 6 cm M 1 3 If the candle is 9 cm tall how tall does the image candle appear to be 1 3 h 9 cm h 3 cm Image is Upright 23 4 Images formed by refraction n1 is where the object is n2 is where the object is NOT the other medium n1 n2 n2 n1 p q R M h nq 1 h n2 p Positive sign follows the light ray otherwise negative Positive h and M upright otherwise inverted Same as mirrors and lenses later For q R and f if they are on the side where light ends up they are positive otherwise negative 5 Example The fish is 5 0 m below the surface Find the apparent depth and the magnification h nq n1 n2 n2 n1 M 1 h n p q R 2p 23 6 Thin Lenses Flat Lens Window Incident ray is displaced but its direction is not changed n2 n1 1 1 If 1 is not large and if t is small the displacement d will be quite small d t Converging Lens All rays parallel to principal axis pass through focal point F Double Convex The image produced by a concave mirror is behind the mirror Is the image 1 Real 2 Inverted F P A A beacon in a lighthouse produces a parallel beam of light The beacon consists of a bulb and a converging lens nlens noutside 3 Virtual F P A 6 Diverging Lenses F Object P A Image F F 1 Rays parallel to principal axis pass through focal point 2 Rays through center of lens are not refracted 3 Rays through F emerge parallel to principal axis h q M h p Positive sign follows the light ray otherwise negative Positive h and M upright otherwise inverted Same as mirrors and refracting surfaces F Object F F P A Image 1 Rays parallel to principal axis pass through focal point 2 Rays through center of lens are not refracted 3 Rays toward F emerge parallel to principal axis Image is virtual upright and reduced Image is real inverted and enlarged in this case 1 1 1 p q f Object P A When a converging lens the focal length is 1 2 3 4 negative positive dependent of the object location None above Image 7 Example A 4 inch arrow pointing down is placed 10 inch in front of a lens that creates an image with a magnification of 2 Find q and h Example A real image and an object are 9 …