Reflection

Wavefront vs. Ray To analyze the behavior of light, we use the ray model Ray is perpendicular to the wavefront By the time you get far away from the source, the wavefronts are basically parallel- thus the rays are parallel

Wavefronts & Rays We Use A Ray To Indicate The Direction Of Motion Of A Wave Front The Rays Of A Circular Wavefront Are Radial Lines The Rays of a Plane Wavefront Are Parallel Lines 3

Wavefronts & Rays We Use Rays To More Easily Track The Direction Of Waves Consider A Wave Striking A Surface At An Angle, A Process We Know As “Reflection” It Is Much More Convenient To Refer To The Rays Associated With The Wavefronts 4

Reflection Waves can reflect off a barrier Ex- echo, mirror

(Angles Measured From Normal) Law of Reflection Angle Of Incidence (i) = Angle Of Reflection (r) i = r (Angles Measured From Normal) 6

Types of Reflection The Law of Reflection Is Always Obeyed, Regardless of the Surface Orientation 7

Types of Reflection Specular Reflection Diffuse Reflection Smooth Surfaces Usually Produces and Image of The Source Mirrors Diffuse Reflection Rough Surfaces Scattered Light Each Individual Ray Follows The Rule of Reflection 8

Specular vs. Diffuse 9

Plane Mirror Images Your brain assumes light travels in straight lines You will perceive a virtual image behind the mirror Image is: Upright Same size as object Located as far behind mirror as object is in front

Virtual Image The image you see appears to be behind the mirror but none of the light rays emanate from the image Thus it is a virtual image We use dotted lines to show rays coming from virtual images

Plane Mirror Images Image will appear to have reverse orientation

Reverse Orientation To see the image, I, you “dot back” from your eye through the mirror to the virtual image Due to the law of reflection, the image appears upright but reversed left to right

Example- minimum length Note how only a 1/2 length mirror is required to see your whole body Now draw a proof to show that how far away you stand from the mirror doesn’t matter

Multiple Reflections When you set 2 mirrors parallel to each other, you can see infinite images Note that you alternately see the front and back of the coke can depending on which mirror the image initiated in

Right Angle Mirrors

Right Angle Mirrors

Spherical Mirrors Concave or Convex C=center of curvature R=Radius of curvature F= focus f=Focal length= 1/2 R f=R/2 Vertex= where axis intersects mirror

Concave Mirrors Parallel incident rays reflected through the focus Incident ray that passes through the focus is reflected parallel to axis Incident ray that strikes the vertex is reflected at equal angle to the axis

Images in concave mirrors Can be virtual or real Real images have light passing through them If we hold a paper there we will see the image

locate image in concave mirror You can locate an image by where these 3 rays intersect 1: runs parallel to axis until the mirror then reflects through the focus

locate image in concave mirror 2: runs straight through the center (C) of mirror and reflects back, never bending 3: passes through focal point (F) on way to mirror and reflects parallel to the axis

What can image look like? Image can shrink and turn upside down

What can image look like? Image can be magnified

What can image look like? Image can be virtual- note that real rays never converge so trace them back to find virtual image

Concave Images Object>1 focal length in front of mirror produces: real image Object =1 focal length produces: no image b/c all reflected rays are parallel so never converge Object < 1 focal length produces: a virtual, enlarged image CONCAVE mirrors considered positive since the mirrored surface curves towards center

Diverging (convex) mirrors F and C are located behind the mirror Use the same 3 rays to locate the image Now rays need to be “dotted back” to locate the image Since the real rays diverge, all images are virtual, upright, reduced, located in front of F

Check: The 3 types of mirrors we have discussed can be classified by the virtual images they form Describe the virtual images formed by each of the following: Plane Concave Convex

Mirror Equation If you need to calculate the location of the image or focus of a spherical mirror: 1/so + 1/si = 1/f Sign conventions: + is in front of mirror So always + Si is + for real image in front and - for virtual image behind f is + for concave (F is in front of mirror) - is behind the mirror Si is virtual and behind f is - for convex mirror (F is behind)

Magnification Equation M = hi/ho = si/so Often, instead of using this as a straight calculation, it is used to compare relative sizes of object and image For example: if a problem states that the virtual image is twice as large as the object, di=-2do Note the relationship and the sign