Image of a point

do di

A’A

Due to the similarity of the triangles on the diagram, all the reflected rays extend backward to one point.

No matter where the observer is, the image is always:

•Behind the mirror

•On the perpendicular line drawn from the object, A.

•At the same distance from the mirror as object.

Image Formation in Plane Mirrorsby a Point Source of Light

dodi

A 1 A’

To construct the image of a point, -sketch a line perpendicular to the mirror through A- measure do (from A to the mirror surface)

- construct image A' on the other side such as do= di

Because all the reflected light rays intersect at one point anyway, there is no need to construct many of them, but only one: the perpendicular to the surface of the mirror.

Image Formation in Plane Mirrors

To construct the image of an object, there is no need to construct an image of each single point of it.

Construct an image of the extreme points (e.g. top and the bottom), then connect these edge points

Properties of Images Formed by Plane Mirrors

S

A

L

T

ttitude

ize

ocation

ype

The image has the same size as the object (no magnification)

The image is up-right but Laterally Inverted (Left / Right)

Image is at the same distance from mirror as the object

(see the next slide first)

Type of the images formed by plane mirrors

Our eye catches diverging rays reflected from mirror.

Observer has a sensation that image is at the intersection of the light rays extended behind the mirror. There is nothing behind the mirror.

Light only appears to us to come from this point.This image is imaginary, or virtual image because there is no real light rays going to or coming from behind the mirror.

Properties of Images Formed by Plane Mirrors

S

A

L

T

ttitude

ize

ocation

ype

The image has the same size as the object (no magnification)

The image is up-right but Laterally Inverted (Left / Right)

Image is at the same distance from mirror as the object

Plane mirrors form virtual images

7

Spherical Mirrors

A spherical mirror has the shape of a section of a sphere.

8

Concave

Concave MirrorsConcave Mirrors

•have the reflecting surface inside of the curve

•AKA Converging mirrors as parallel to the axis rays are reflected inward

9

Concave Mirror Terminology

Principal axis: line connecting the centre of curvature with the mirror’s vertex

Is the centre of the sphere the mirror is cut from. The length of C is the radius of the sphere

Focal Point (focus) : where all parallel to the axis incident rays meet after reflection in the mirror.

Vertex: centre of the mirror, located on axis

Concave Mirror: a mirror with reflecting surface curved inward Focal

distance from F to V

10

Four Principal rays of Concave Mirrors

11

Image Formation using Ray Diagrams for a Concave Mirror: Principal Rays Summary

Incident Ray Reflected Ray

Parallel to principal Axis Through the focal point

Through the focal point Parallel to principal Axis

Through C Through C

On the vertex of the mirror Such as angle with axis is same for incident and reflected ray

Images formed by Concave Mirrors

Watch video showing image formed by a curved mirror

12

How do we see the image

A point object emit (or reflect) light in all directions

13

All the rays reflected by mirror meet at one point

Eye detects light coming out of that point

Brain identifies this point as the image

Ray Diagrams for a Non-Point Source

14

For non-point objects, construct images of few extreme point.

O

O’

For perpendicular to the axis objects, locate the image of the top,

Connect with axis at right angle to locate the bottom of the image

Any point on axis will form image on axis.

Practice

Practice constructing ray diagrams for 5 different locations of the object

Note that the properties of these images will be quite different.

15

16

Object is Located beyond the Centre of Curvature

S: smaller A: inverted L: between F and C T: real

17

Object is located at the Centre of Curvature

Think of mirror as almost flat close to axis to avoid spherical aberration

Image Properties: S: same as obect A: Inverted L: at C T: real

This image is very convenient in determining the mirror’s focal length

18

Object Located between F and C

S: bigger A: inverted L: beyond C T: real

19

Object is located at Focal Point

S: N/AA: N/AL: N/AT: N/A

Light rays are parallel, they never meet.No image formed: no properties

20

Object in between Focal point and Mirror

Size: Enlarged Attitude: Up-right Location: Behind the mirror Type: Virtual

F C

This time, converging mirror actually converges the light rays.

Demo reminder: large mirror

21

Concave Mirror Image Properties Summary

Object location

Size Attitude Location Type

do > c smaller inverted f < di< c Real

do= c same inverted di= c Real

f < do< c bigger inverted di > c Real

do= f N/A N/A N/A N/A

do< f bigger up-right Anywhere behind the mirror

Virtual

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Sample Problem – Scale Ray Diagram

A pencil 15 cm high is located 60 cm in front of a concave mirror with a focal length of 20 cm. Construct a scale diagram to correctly determine the location of the image and its height.

(indicate the scale used)