Geometric Optics – MirrorsFoundations

Near to the source, the waves are circular (or spherical)

Far from the source, the waves are linear (or planar)Waves are represented by rays.

Far from the source, the rays are parallel.

Reflection Wave bounces off a surface.

Angle of incidence = Angle of reflection

θi = θr

θiθr

Mirrors: FlatFlat Creates a virtual

image that is “seen” somewhere behind the mirror.

The image appears as far behind the mirror as the object is in front of the mirror.

do di

virtual image

real object

Spherical Mirrors:

Convex & Concave

C: center of curvature of the mirror

(center of the imaginary circle)

(It is the radius of the circle.)

f: focal point of the mirror

f is ½ of the radius (or C)

fC

Concave Convex

FC

F C

Simple “rules”1. 1st Ray: parallel to the axis,

reflects through the focal point2. 2nd Ray: through the focal point,

reflects parallel to the axis3. 3rd Ray: go through the center of curvature (C)

reflects perpendicular back to the viewer.

Real or Virtual its real if all the reflected rays hit the image.

Upright or Inverted upright on the top of the axis

Larger or Smaller

C F

Ray 1: parallel to axis thru focusRay 2: thru focus parallel to axis

Ray 3: thru center back thru center

ObjectImage

Real or Virtual

Upright or Inverted

Smaller or Larger

Ray 1: parallel to axis thru focusRay 2: thru focus parallel to axis

Ray 3: thru center back thru center

Object

Image CF

Real or Virtual

Upright or Inverted

Smaller or Larger

Sign convention:ho & hi

+ if upright, - if inverteddi & do, f + if on the object side of the mirror

- if on the other side of the mirror

i i

o o

h dm

h d= = −

Magnification Equation height of image divided by height of the object

ho = object height hi = image heightdo = object distancedi = image distance

1 1 1

o id d f+ =

Mirror Equation

Sign convention:ho & hi

+ if upright, - if inverteddi & do, f + if on the object side of the mirror

- if on the other side of the mirror

i i

o o

h dm

h d= = −

Magnification Equation height of image divided by height of the object

ho = object height hi = image heightdo = object distancedi = image distance

1 1 1

o id d f+ =

Mirror Equation