Chapter 23: Light, Mirrors

light usually travels in

a straight line (straight line light rays)

we see an object because

a bundle of light rays has bounced off of it and entered our eye

we can analyze mirrors and lenses by studying the

geometry of light rays (geometric optics)

when a light ray strikes a flat surface at some incident angle, the reflected light will leave the surface at

the same angle

the angle of incidence and the angle of reflection are defined relative to 

the normal to the surface 

the law of reflection still holds for 

each part of the surface 

diffuse reflection

if the surface is rough, light will be reflected in many directions

specular reflection

if the surface is smooth, light will be reflected in one direction

when you look into a mirror, you see an image of yourself and your surroundings

• you appear to be behind the mirror

• this is the location of your image

light rays leave part of you and some of them

reflect off of the mirror and into your eyes 

plane mirrors - the image forms at the location that

the light rays appear to be coming from

a plane mirror is a

flat, mirror, like a bathroom mirror

using the law of reflection, we can work out how image distance and height are related to 

object distance and height 

an image is a representation of a 

physical that is created by manipulating light 

the image may or may not be distorted

• many have a different shape than the object

• might have a different size than the object 

images come in two types

real image and virtual images

a real image is formed when

light rays emitted/reflected from the object converge through a point

• formed on your retina by the lens of your eye 

a virtual image is formed when

light rays emitted/reflected from the object do not actually converge through a point, but rather appear to come from a common point

the distance between the object and the mirror/lens is known as the

object distance (d0)

for a single mirror/lens, we can take the 

object distance to be a positive number 

the distance between the image and the mirror/lens is known as

image distance (di)

the image distance for a real image is

positive

the image distance for a virtual image is

negative

the lateral size of the object is known as the

object height (h0)

the lateral size of the image is known as 

image height (hi)

if the image has the same orientation as the object we call it an

upright image and the image height is positive

if the image has the opposite orientation as the object, we call it an

inverted image and image height is negative

manificationif the ratio of

the image height to the object height (hi/h0)

plane mirrors - the geometry of the diagram allows us to relate the

different distances/sizes

plane mirrors - the image is found to be the same

distance behind the mirror that the object is in front of the mirror

we will label virtual images with a

negative image distance

plane mirror - the height of the image is equal to

the height of the object

a spherical mirror is formed from a section

of a spherical shell

spherical mirror - if the inner surface is mirror, we call it 

a concave mirror 

spherical mirror - if the outer surface is mirrored, we call it 

a convex mirror 

size, location, and orientation of an image depend on

how far the object is located from the mirror

spherical mirror - the amount of curvature of the mirror is parametrized any the

radius of curvature, r

the radius of curvature is the distance between the mirror and the center of the sphere, known as 

the center of curvature, C 

a mirror with a large radius of curvature is 

nearly flat

a mirror with a small radius of curvature is

really curved

the principle axis runs through the

center of curvature and the center of the mirror

spherical mirror - for an object infinitely far away (the Sun and stars approach this), the rays would be 

precisely parallel near the mirrow 

spherical mirror - angle of reflection is equal to

the angle of incidence

for a spherical mirror, the normal direction is the direction

to the center of curvature

spherical mirror - concave

normal point inward, so parallel rays converge inward

spherical mirror - convex:

normal point outward, so parallel rays diverge outward 

focal point - concave mirror

postive

focal point - convex mirror

negative

a ray of light that approaches the mirror parallel to the Principe axis will reflect 

towards the focal point of a concave mirror 

a ray of light that approaches the mirror parallel to the Principe axis will reflect 

away from the local point of a convex mirror 

the distance between the focal point and the mirror/lens is the 

focal length

for a spherical mirror, the focal length is

one-half the radius the curvature

the image of an object located at infinity forms at

the focal point of a mirror 

since all the light rays coming from infinity are parallel to the principle axis near the mirror,

the reflected rays converge to the focal point

if the object is not at infinity, where does the image form? two methods:

geometric ray tracing and mirror equation

construction of an image: ray diagram 1 - concave mirror

the ray that approaches through the center of curvature reflects and passes back through the center of curvature

construction of an image: ray diagram 1 - convex mirror

a ray that approaches toward the center of curvature reflects and passes back away from the center of curvature

construction of an image: ray diagram 2 - concave mirror 

a ray approaches parallel to the principle axis reflects and passes through the focal point 

construction of an image: ray diagram 2 - convex mirror 

a ray that approaches parallel to the principle axis reflects and travels away from the focal point

construction of an image: ray diagram 3 - concave mirror

a ray that approaches through the focal point reflects and travels parallel to the principle axis 

construction of an image: ray diagram 3 - convex mirror 

a ray approaches toward the focal point reflects and travels parallel to the principle axis 

A plane mirrow can only form one type of image:

it is always upright, the same distance as object form mirror, and the same size object 

a concave mirror can

form two types of images

if the object distance is greater than the focal length, the image is

real and inverted

if the object distance is less than focal length, the image is

virtual and upright

a convex mirror can only form one type of mirror:

it is always upright, virtual, and smaller than object 

as an object gets closer to a convex mirrow, the virtual image become

larger but will remain smaller than the actual object

• the image will also appear to be closer to the mirror