Concave and Convex mirrors:

a quick introduction

Dave Coulson, 2008/2014

This is a concave mirror

(it looks a bit like a cave)

If an object is placed in front of the mirror, where will its image appear?

?? ?

How big will the image be?

?? ?

Will it be inverted or upright??? ?

First, some definitions:

The pole is a line at the average position of the mirror surface.It’s treated as the mirror surface. Pretend all light reflects from the pole.

First, some definitions:

Most mirrors are only very slightly curved so the pole is very close to the mirror surface. In most cases it is okay to treat the pole and the mirror surface as one and the same.

Radius of curvature

(This is usually much further from the mirror than is shown in this picture)

The radius of curvature is the centre of the circle defining the mirror surface.

Radius of curvature

A line that passes through the radius of curvature will reflect back on its path.

The radius of curvature is the centre of the circle defining the mirror surface.

The focal point is halfway between the radius of curvature and the pole

Focal p

oint

A line that strikes the mirror parallel to its axis will pass through the focal point

Focal p

oint

The focal point is halfway between the radius of curvature and the pole

A line that strikes the mirror at its centre will reflect at the same angle

These three lines locate the position of the image

di

f

do

d0 = distance to the object

di = distance to the image

f = distance to the focal point

Object

Image

The position can also be found by calculation:

3f

di

f

Object

Image

Say, for example, that the object is three times as far from the mirror as the focal point.

3f

f

3/2 fObject

Image

The image will be halfway between the radius of curvature and the focal point.

3/2 f

ho

hi

f

Object

Image

The size of the image can also be calculated:

3f

3f

f

3/2 f hi

ho

hiObject

Image

The size of the image can also be calculated:

3/2 f

3f

f

ho

hiObject

Image

The negative sign means the image is upside down

3/2 f

If the object is moved to a point between the radius of curvature and the focal point, where does the image go?

3/2 f

3/2 f

3f

Now shift the object between the mirror surface and the focal point. Where is the image now?

Now shift the object between the mirror surface and the focal point. Where is the image now?

...and how big will it be?

We can verify this geometrically

An image ‘inside’ the mirror is called a virtual image.

Convex mirrors

Focal p

oint

Radius o

f curvatu

re

Convex mirrors

Focal p

oint

Radius o

f curvatu

re

Convex mirrors

Note that the focal point is ‘inside’ the mirror.

Focal p

oint

Radius o

f curvatu

re

Its distance is treated as a negative number.

di is the same sign as f, which means that the image is ‘inside’ the mirror.

Say do = - 2.5f

M is a positive number, which means that the image is upright.

Size calculation:

Say do = - ½ f

Size calculation:

For a convex mirror, no matter where you put the object,the image will always be upright and ‘inside’ the mirror (i.e., ‘virtual’)

That’s all

dtcoulson@gmail.com