Chapter 36

Image Formation 1:

1. Flat mirror

2. Spherical mirrors

Find the image, method 2, the mirror/lens equation

When a spherical mirror is given, we know its radius R.Under paraxial condition, the angle is small, and from the law of reflection and focal point definition, we have

That is the focal length is

2

Rf

for a converging mirror.

N

VNCF

1

2CF FN CN

From the ray diagram to mirror equation

O

Ih

V

Oh

IhO

hI

p OV q IV

Objective: Find the equation that connects object distance, image distance and the focal length.

f FV

Triangle and are similar:hII F VAF

B

A

Triangle and are similar:hOO F VBF

O

I

h f

h q f

O

I

h p f

h f

f p f

q f f

So:

1 1 1

p q f

From the ray diagram to mirror equation

O

Ih

V

Oh

IhO

hIB

AO

I

h f

h q f

And :1 1 1

p q f

From

1

1 11

I

O

h q f

h f

q

f

qp q

q

p

One has :

Converging spherical mirror formulas

1 1 1

p q f

I

O

h qM

h p

Object distance, image distance and focal length:

Focal length and sphere radius:

2

Rf

Object distance, image distance and magnification:

From converging mirror to diverging mirror: change signs

These sign conventions apply to both concave and convex mirrors

The focal length has a different sign convention:

The equations used for the concave mirror then applies to the convex mirror.

2

Rf

2

Rf

Converging

Diverging

Sign Conventions, Summary Table

1M 1M 1M Image smaller Image same size Image larger

Convex mirror, only one case: virtual image, not inverted, smaller

1 1 1

p q f I

O

h qM

h p

2

Rf Formulas to be used:

0f pfp

qp f p f

0fq f

Mp p f p f

1ff

Mp f p f

One has the following:

virtual image

Image not inverted

Image smaller than object

Concave mirror, object 5 locations

1 1 1

p q f I

O

h qM

h p

2

Rf Formulas to be used:

2p R f Case 1:

0fp

qp f

0q f

Mp p f

12

f fM

p f f f

One has the following:

Real image

Image inverted

Image smaller than object

(Case 2 to 5 will be left as homework)

More examples

You use a concave mirror to make a fire with the sun light. The focal length of the mirror is 20 cm. You hold it towards the sun and try to light a small wood stick at its tip. Where you want to place this tip?

More examples

When you look into a flat mirror, the image distance is the same as the object distance. The rear review mirror on the side of your car is a convex mirror with a focal length of -0.60 m. If a truck is 10.0 m from this mirror, what is the size of the truck image compare with the actual truck?