image formation with concave spherical mirrors...sign conventions for spherical mirrors •if the...

© 2017 Pearson Education, Inc. Slide 34-1

The figure shows a

concave mirror, a

mirror in which the

edges curve toward

the light source.

Rays parallel to the

optical axis reflect and

pass through the focal

point of the mirror.

Image Formation with Concave Spherical Mirrors

© 2017 Pearson Education, Inc. Slide 34-2

A Real Image Formed by a Concave Mirror

Sign conventions for spherical mirrors

• If the object point P is on the

same side as the incident

light, then s is positive.

• If the image point is on the

same side as the reflected

light, then is positive.

• If the center of curvature C is

on the same side as the

reflected light, then R is

positive.

Spherical mirror with a point object

• A spherical mirror

with radius of

curvature R forms a

real image of the

point object P.

Focal point and focal length

• When the object is very far

from the spherical mirror,

the incoming rays are

parallel.

• The beam of incident

parallel rays converges, after

reflection from the mirror, to

a focal point, point F.

• The distance from the vertex

to the focal point, denoted

by f, is called the focal

length.

Focal point and focal length

• With the object at the focal

point, the reflected rays are

parallel to the optic axis.

• The reflected rays meet only

at a point infinitely far from

the mirror, so the image is

at infinity.

© 2017 Pearson Education, Inc. Slide 34-7

For a spherical mirror with negligible thickness, the

object and image distances are related by:

where the focal

length f is related

to the mirror’s

radius of

curvature by:

The Mirror Equation

Image of an extended object: Spherical mirror

• Shown is how to determine the position, orientation, and

height of an image formed by a concave spherical mirror.

© 2017 Pearson Education, Inc. Slide 34-9

You see an upright, magnified image of your face

when you look into magnifying “cosmetic mirror.”

The image is located

QuickCheck 34.15

A. In front of the mirror’s surface.

B. On the mirror’s surface.

C. Behind the mirror’s surface.

D. Only in your mind because it’s a virtual image.

Example 1 - A concave mirror forms an image, on a wall 3.00 m in front

of the mirror, of a headlamp filament 10.0 cm in front of the mirror. What

are the radius of curvature and focal length of the mirror? What is the

lateral magnification? What is the image height if the object height is

5.00 mm?

Graphical method of locating images

© 2017 Pearson Education, Inc. Slide 34-12

Example 2

A 3.0-cm-high object is located 20 cm from a concave

mirror. The mirror’s radius of curvature is 80 cm. Determine

the position, orientation, and height of the image.

Example 3 - A concave mirror has a radius of curvature with absolute

value 20 cm. Show graphically the image of an object in the form of an

arrow perpendicular to the axis of the mirror at object distances of 30

cm, 20 cm, 10 cm, and 5 cm.

Example 3 - A concave mirror has a radius of curvature with absolute

value 20 cm. Show graphically the image of an object in the form of an

arrow perpendicular to the axis of the mirror at object distances of 30

cm, 20 cm, 10 cm, and 5 cm.

Example 4 – A object 0.600 cm tall is placed 16.5 cm to the left

of the vertex of a concave spherical mirror having a radius of

curvature of 22.0 cm. Draw a principal-ray diagram, showing the

formation of the image. Determine the position, size, orientation,

and nature of the image.

In-class Activity #1 – A spherical, concave shaving mirror has

a radius of curvature of 32.0 cm. A 3.0 cm tall object with its

base on the optic axis is 12.0 cm to the left of the vertex of

the mirror? Determine the position, size, orientation, and

nature of the image.

© 2017 Pearson Education, Inc. Slide 34-17

The figure shows parallel

light rays approaching a

mirror in which the edges

curve away from the light

source.

This is called a convex

mirror.

The reflected rays appear

to come from a point

behind the mirror.

Image Formation with Convex Spherical Mirrors

© 2017 Pearson Education, Inc. Slide 34-18

A Real Image Formed by a Convex Mirror

Image formation by a convex mirror

• If the mirror is convex, so that R is negative, the resulting

image is virtual (that is, the image point is on the opposite

side of the mirror from the object), erect, and smaller than the

object.

Focal point and focal length of a convex mirror

• When incoming rays that are

parallel to the optic axis are

reflected from a convex

mirror, they diverge as

though they had come from

the virtual focal point F at a

distance f behind the mirror.

• The corresponding image

distance s is negative.

Example 5 – A person looks at their reflection in a convex

mirror 0.750 m away. The radius of curvature is 7.20 cm.

The height of the person is 1.6 meters. Where and how tall

is the image of the person? Is it inverted?

Graphical method of locating images

Example 6 – A object 0.600 cm tall is placed 16.5 cm to the left

of the vertex of a convex spherical mirror having a radius of

curvature of 22.0 cm. Draw a principal-ray diagram, showing the

formation of the image. Determine the position, size, orientation,

and nature of the image.