Chapter 23: Mirrors

Lecture 13

light usually travels in

a 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 rays strikes at some some incident angle, the reflected light will leave 

the surface at the same angle 

the angle of incidence and the angel of reflection are defines relative to

the normal to surface

if the surface is rough, light will be reflected

in many directions

• this is called diffuse reflection 

if the surface is smooth, light will be reflected in

one direction

• this is called specular reflection

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 each part of you and some them

reflect off of the mirror and into your eyes

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

consider the two rays of light that are reflected from the bottom of the object at point A, reflect off the mirror near point B, and eventually enter your eye

• these rays are diverging, extrapolating them to a common point we see that two rays leaving point C would from the same angle

• repeating this for other points on the object, we get a collection of points behind the mirror where light appears to originate from 

  • this is the location of the image 

An image is a representation of

a physical object that is created by manipulating light

the image may or may not be distorted

• might have a different shape than the object

• might have a different size than the object

images comes in two types

real or virtual

A real image is formed when

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

the image formed on your retina by the lens of your eye is a 

real image

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 mirror/lens is known as

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

the 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 the

image height, hi

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

upright image and 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 

magnification is the ratio of

the image height to the object height

plane mirrors - the image is found be the same distance

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

a spherical mirror is formed from

a section of a spherical shell

in the inner surface is mirrored, we call it a

concave mirror 

if the outer surface is mirrored, we call it a 

convex mirror

size, location, and orientation of an image depends on

how far the object is located from the mirror

the amount of curvature of the mirror is parametrized by 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

a principal axis runs through

the center of curvature and the center of the mirror

for an object infinitely far away (the Sun and stars approach this),

the rays would be precisely parallel near the 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

reflection of spherical mirrors - concave

normal point inward, so parallel ways converge inward

reflection of spherical mirrors - convex

normal point outward, so parallel rays diverge outward

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

the focal point of a concave mirror 

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

from the local point of a convex mirror 

the distance between the focal point, F, and the

mirror/lens is the focal length, f

the image of an object located at infinity forms at the

focal point of amiirow

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

the reflected rays converge to the focal point 

concave mirror 

all three characteristic rays cross at a point after reflecting from the mirror

• this is where the image forms 

• this is a real and inverted image 

convex mirror - the image is

always virtual and upright

convex mirror - moreover, the image is always smaller and

close to the mirror, between the mirror and focal points

• and as the object gets really close to the mirror, the mirror acts more and more like a flat mirror 

A plane mirror can form one type of image:

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

a concave mirror - if the object distance is greater than the focal length, the image is 

real and inverted 

concave mirror - if the object distance is less than the focal length, the image

is virtual, upright, and smaller than object

as an object gets closer to a convex mirror, the virtual image becomes

larger but remain smaller than the actual object

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