Millions of light rays reflect from objects and enter our eyes – that ’ s how we see them! When we study the formation of images, we will isolate just a few useful rays: or

Reflection  i = incident angle  r = reflected angle measured from the normal A line  to the surface at the point of incidence  i =  r Law of reflection

Plane (flat) mirrors To locate the image: 1) Draw 2 different rays leaving the same point. 2) Draw their reflections. 3) Extend the reflections behind the mirror. 4) The point where they meet locates the image. image objectmirror

There are two different types of images: Real image Light rays actually meet at that point Virtual image Light rays only appear to emanate from that point Which type do you get from a plane mirror ? For all plane mirrors:  Image is upright  Image is same size as object  object ’ s distance from mirror (d o ) = image ’ s distance from mirror (d i )  Right and left are reversed

dodo didi

How tall a mirror do you need to be able to see your entire body? Does it matter how far away from the mirror you stand?

When mirror surfaces are curved instead of flat, strange things happen……

Spherical Mirrors concave side convex side

Concave Spherical Mirrors principle axis (axis of symmetry) C R C = Center of Curvature R = Radius of Curvature Parallel Rays (distant object): C F f F = focal point f = focal length f = ½ R Concave mirror

Convex Spherical Mirrors C R Parallel Rays (distant object): f = -½ R Convex mirror Since it ’ s behind the mirror f F C

Locating Images: Ray Tracing The use of 3 specific rays drawn from the top of the object to find location, size, and orientation of the image For a Concave Mirror: Ray #1: Parallel to the axis Relects through F Ray #2: Through F Reflects parallel to axis Ray #3: Through C Reflects back on itself

Results: Ray Tracing for concave mirrors Object is behind C: Image is always real, smaller, and inverted CF Object between C and F: Image is always real, larger, and inverted CF Object between F and mirror: Image is always virtual, larger and upright C F Ex: Makeup mirror

For a Convex Mirror: Ray #1: Parallel to the axis / Relects as if it came from F Ray #2: Heads toward F / Reflects parallel to axis Ray #3: Heads toward C / Reflects back on itself

Results: Ray Tracing for convex mirrors (draw in the 3 rays for practice) Wherever the object is: Image is always virtual, smaller and upright CF Car side mirrors  “ Objects in mirror are closer than they appear ”  What type of mirror?  Why would these be used in cars?

Mirror Applications Concave mirrors: Magnification

Mirror Applications Concave Mirrors: Telescopes

Mirror Applications Concave Mirrors: Flashlights (light at focal point)

Mirror Applications Convex Mirrors: Widen range of sight

The Mirror Equation works for both concave and convex mirrors: OR CF f dodo CF f dodo f = mirror ’ s focal length (+ for concave, - for convex ) d o = distance between object and mirror d i = distance between image and mirror The Mirror Equation + for in front of mirror (real) - for behind mirror (virtual)

What about the size of the image ?? h o = height of object h i = height of image m = magnification = h i /h o m>1 if the image is larger than object m<1 if the image is smaller than object The Magnification Equation m is - if the image is inverted m is + if the image is upright

80 cm Ex: The mirror ’ s radius of curvature is 60 cm. Find the location, size and orientation of the image of the cat. 15 cm

80 cm 15 cm Ex: The mirror ’ s radius of curvature is 60 cm. Find the location, size and orientation of the image of the dog.