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

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

Plane (flat) mirrors object mirror image 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.

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 (do) = image’s distance from mirror (di) Right and left are reversed

do di

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

Spherical Mirrors concave side convex side

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

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

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

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

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 C F Object between C and F: Image is always real, larger, and inverted C F Object between F and mirror: Image is always virtual, larger and upright C F Ex: Makeup mirror

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: do C F f do OR f = mirror’s focal length (+ for concave, - for convex ) do = distance between object and mirror di = distance between image and mirror + for in front of mirror (real) - for behind mirror (virtual) The Mirror Equation

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

Ex: 15 cm 80 cm The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the cat. Di = 48 cm M = -.6 Real, upside down, smaller

Ex: 15 cm 80 cm The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the dog. F = -30!! Di = -21 cm M = Smaller, right side up, virtual