Do Now

1. A ray of light is incident towards a plane mirror at an angle of 30-degrees with the mirror surface. What will be the angle of reflection?

2. If Suzie stands 3 feet in front of a plane mirror, how far from the person will her image be located?

23.3 Formation of Images by Spherical

Mirrors

Spherical mirrors are shaped like sections of

a sphere, and may be reflective on either the

inside (concave) or outside (convex).

23.3 Formation of Images by Spherical

Mirrors

Rays coming from a faraway object are

effectively parallel.

23.3 Formation of Images by Spherical

Mirrors

Parallel rays striking

a spherical mirror do

not all converge at

exactly the same

place if the curvature

of the mirror is large;

this is called

spherical aberration.

23.3 Formation of Images by Spherical

Mirrors

If the curvature is small, the focus is much more

precise; the focal point is where the rays

converge.

Terms

• The point in the center of

the sphere from which

the mirror was sliced is

known as the center of

curvature and is

denoted by the letter C

• The point on the mirror's

surface where the

principal axis meets the

mirror is known as the

vertex and is denoted by

the letter A

Terms • The vertex is the geometric

center of the mirror. Midway

between the vertex and the

center of curvature is a point

known as the focal point; the

focal point is denoted by the

letter F.

• The distance from the vertex

to the center of curvature is

known as the radius of

curvature (represented by R).

The radius of curvature is the

radius of the sphere from

which the mirror was cut.

Terms

• the distance from the

mirror to the focal point is

known as the focal

length (represented by f).

• Since the focal point is

the midpoint of the line

segment adjoining the

vertex and the center of

curvature, the focal length

would be one-half the

radius of curvature.

23.3 Formation of Images by Spherical

Mirrors

Using geometry, we find that the focal length is

half the radius of curvature:

(23-1)

Spherical aberration can be avoided by

using a parabolic reflector; these are more

difficult and expensive to make, and so are

used only when necessary, such as in

research telescopes.

1.Check Your Understanding:

• The surface of a concave mirror is pointed

towards the sun. Light from the sun hits the

mirror and converges to a point. How far is this

converging point from the mirror's surface if the

radius of curvature (R) of the mirror is 150 cm?

• Answer: 75 cm

• If the radius of curvature is 150 cm. then the

focal length is 75 cm. The light will converge

at the focal point, which is a distance of 75

cm from the mirror surface.

2. Check Your Understanding:

• It's the early stages of a concave mirror lab.

Your teacher hands your lab group a concave

mirror and asks you to find the focal point. What

procedure would you use to do this?

• You will need to measure the distance from the

vertex to the focal point. But first you must find

the focal point. The trick involves focusing light

from a distant source (the sun is ideal) upon a

sheet of paper. Once you find the focal point,

make your focal length measurement.

Formation of Image

• Upon reflecting, the

light will converge at a

point. At the point

where the light from

the object converges,

a replica, likeness or

reproduction of the

actual object is

created. This replica

is known as the

image.

23.3 Formation of Images by Spherical

Mirrors

We use ray diagrams to determine where an

image will be. For mirrors, we use three key

rays, all of which begin on the object:

1. A ray parallel to the axis; after reflection it

passes through the focal point

2. A ray through the focal point; after reflection

it is parallel to the axis

3. A ray perpendicular to the mirror; it reflects

back on itself

23.3 Formation of Images by Spherical

Mirrors

23.3 Formation of Images by Spherical

Mirrors

The intersection of these three rays gives the

position of the image of that point on the

object. To get a full image, we can do the

same with other points (two points suffice for

many purposes).

Object Located Beyond Center

of Curvature

Object Located at the center of

Curvature

Object is Located Between Center of Curvature and

Focal Point

Object is Located in Front of

Focal Point

Do Now

If a concave mirror produces a real image, is

the image necessary inverted? Explain.

23.3 Formation of Images by Spherical

Mirrors

If an object is outside the center of curvature of a

concave mirror, its image will be inverted,

smaller, and real.

23.3 Formation of Images by Spherical

Mirrors

If an object is inside the focal point, its image

will be upright, larger, and virtual.

Image Characteristics for

Concave Mirrors L – location

O – orientation

S – relative size

T - type

1) Between C and F, inverted,

reduced, real

2) At C, inverted, same

size, real

3) Beyond C, inverted,

magnified, real

4) No image

5) Beyond mirror,

upright, magnified,

virtual

Convex Mirror

A convex mirror is sometimes referred to as

a diverging mirror due to the fact that

incident light originating from the same point

and will reflect off the mirror surface and

diverge.

23.3 Formation of Images by Spherical

Mirrors

For a convex mirror,

the image is always

virtual, upright, and

smaller.

Image Characteristics for

Convex Mirrors • Convex mirrors always produce virtual upright reduced in

size images. The location of the object does not affect

the characteristics of the image.

23.3 Formation of Images by Spherical

Mirrors

Geometrically, we can derive an

equation that relates the object

distance, image distance, and

focal length of the mirror: (23-2)

23.3 Formation of Images by Spherical

Mirrors

We can also find the magnification (ratio of

image height to object height).

(23-3)

The negative sign indicates that the image is

inverted. This object is between the center of

curvature and the focal point, and its image is

larger, inverted, and real.

The +/- Sign Conventions

The sign conventions for the given quantities in the mirror

equation and magnification equations are as follows:

• f is + if the mirror is a concave mirror

• f is - if the mirror is a convex mirror

• di is + if the image is a real image and located on the

object's side of the mirror.

• di is - if the image is a virtual image and located behind

the mirror.

• hi is + if the image is an upright image (and therefore,

also virtual)

• hi is - if the image an inverted image (and therefore, also

real)

23.3 Formation of Images by Spherical

Mirrors

Problem Solving: Spherical Mirrors

1. Draw a ray diagram; the image is where the rays

intersect.

2. Apply the mirror and magnification equations.

3. Sign conventions: if the object, image, or focal point is

on the reflective side of the mirror, its distance is

positive, and negative otherwise. Magnification is

positive if image is upright, negative otherwise.

4. Check that your solution agrees with the ray diagram.