Introduction to Ray DiagramsIntroduction to Ray Diagrams

How to draw them for Curved How to draw them for Curved MirrorsMirrors

(please view this slide show in (please view this slide show in presentation view by pressing F5)presentation view by pressing F5)

Curved MirrorsCurved Mirrors

In the previous section you learned about In the previous section you learned about plane mirrorsplane mirrors– Mirrors that are flatMirrors that are flat

In this section you will begin to look at In this section you will begin to look at what happens to light when it reflects off what happens to light when it reflects off curved surfacescurved surfaces

Concave MirrorsConcave Mirrors

A mirror that has a surface that curves in like a A mirror that has a surface that curves in like a bowl, is called a bowl, is called a concave mirrorconcave mirror or or converging converging mirrormirror..– To remember the shape of a concave mirror, think of To remember the shape of a concave mirror, think of

the phrase: “You go into a cave.” The light goes into the phrase: “You go into a cave.” The light goes into the bowl of the mirror.the bowl of the mirror.

Concave Mirrors (cont’d)Concave Mirrors (cont’d)

We use concave mirrors for many different We use concave mirrors for many different reasons.reasons.– Examples include, microscopes, telescopes, Examples include, microscopes, telescopes,

flashlights, cosmetic mirrors, car headlights.flashlights, cosmetic mirrors, car headlights.

Curved Mirror TerminologyCurved Mirror Terminology

Remember all those definitions you did at Remember all those definitions you did at the first of this unit?the first of this unit?

Now you will start to understand what Now you will start to understand what some of those definitions meansome of those definitions mean

Curved Mirror Terminology (cont’d)Curved Mirror Terminology (cont’d)Curved mirrors follow the same laws of reflection as Curved mirrors follow the same laws of reflection as plane mirrorsplane mirrors– In this case you will be looking at a In this case you will be looking at a concave mirrorconcave mirror..

The difference is that when hitting a curved mirror with The difference is that when hitting a curved mirror with parallel rays of light, the light all reflect off the mirror to parallel rays of light, the light all reflect off the mirror to single point called the single point called the focal pointfocal point

focal point

concave mirror

Curved Mirror Terminology (cont’d)Curved Mirror Terminology (cont’d)

The middle part of the curved surface of a mirror is The middle part of the curved surface of a mirror is called a called a vertexvertex

The imaginary line drawn through the vertex at a right The imaginary line drawn through the vertex at a right angle to the surface of the mirror is called the angle to the surface of the mirror is called the principal principal axisaxis or or normalnormal

focal point

mirror

vertex

principalaxis

Curved Mirror Terminology (cont’d)Curved Mirror Terminology (cont’d)

The distance from the vertex to the focal The distance from the vertex to the focal point in called the point in called the focal lengthfocal length..

mirror

vertex

principalaxis

focal point

focal length

Curved Mirror Terminology (cont’d)Curved Mirror Terminology (cont’d)The distance between the vertex and the object being The distance between the vertex and the object being imaged in the mirror is represented by dimaged in the mirror is represented by doo

The distance between the vertex and the image created by The distance between the vertex and the image created by the mirror is referred as dthe mirror is referred as dii

Notice how the image is invertedNotice how the image is inverted

mirror

vertex

principalaxis

object

image

focal point

do

di

Curved Mirror Terminology (cont’d)Curved Mirror Terminology (cont’d)

A A real image real image is an image formed by light is an image formed by light rays that come from the location of the rays that come from the location of the imageimage– Meaning if a piece of paper was put at the Meaning if a piece of paper was put at the

spot where the real image forms, a focussed spot where the real image forms, a focussed image would appear on the paper.image would appear on the paper.

Ray Diagrams for Concave MirrorsRay Diagrams for Concave Mirrors

Ray diagrams allow a person to determine Ray diagrams allow a person to determine if an image will be formed by an object if an image will be formed by an object whose light is reflecting off a mirrorwhose light is reflecting off a mirror

The diagram also determines whether the The diagram also determines whether the image formed is real or virtualimage formed is real or virtual

Finally if an image is formed, the ray Finally if an image is formed, the ray diagram will show you where the image diagram will show you where the image will be locatedwill be located

Ray Diagrams for Concave Mirrors (cont’d)Ray Diagrams for Concave Mirrors (cont’d)

Usually to practice drawing a ray diagram Usually to practice drawing a ray diagram an arrow is used as the objectan arrow is used as the objectYou will need to draw two rays to find out You will need to draw two rays to find out where the image is located.where the image is located.– The place where the reflected rays intersect is The place where the reflected rays intersect is

the position of the imagethe position of the image– If there is no place where the reflected rays If there is no place where the reflected rays

overlap, then there is no real image formedoverlap, then there is no real image formed– However if the back reflecting rays insect However if the back reflecting rays insect

behind the mirror a virtual image is formedbehind the mirror a virtual image is formed

The following slides will illustrate how each The following slides will illustrate how each case occurscase occurs

Ray Diagrams for Concave Mirrors (cont’d)Ray Diagrams for Concave Mirrors (cont’d)

The image formed by a concave mirror The image formed by a concave mirror depends on how far away the object is depends on how far away the object is from the focal pointfrom the focal point

If the object is far away from the focal If the object is far away from the focal point, then the image formed is invertedpoint, then the image formed is inverted

mirror

vertex

principalaxis

focal point

object

invertedimage

focal point

mirror

vertex

principalaxis

Ray Diagrams for Concave Mirrors (cont’d)Ray Diagrams for Concave Mirrors (cont’d)

1. The first ray travels horizontally, parallel to the principal axis

2. This ray reflects off the mirror’s surface and travels through the focal point

3. The second ray travels through the focal point

4. This ray reflects off the mirror’s surface and travels horizontally, parallel to the principal axis

5. A third ray can be drawn to confirm the location of the image as shown. The incident ray is drawn from the object to the vertex. The reflected ray comes off the mirror at the same angle as the incident ray.

Ray Diagrams for Concave Mirrors (cont’d)Ray Diagrams for Concave Mirrors (cont’d)

The point where the two reflected rays cross is where the image forms

Notice how this image is larger and inverted.Since this image is on the same side of the mirror as the object, a real image is formed

This occurs when the object is at a greater distance from the mirror than the focal point

focal point

mirror

vertex

principalaxis

Ray Diagrams for Concave Mirrors (cont’d)Ray Diagrams for Concave Mirrors (cont’d)

focal point

mirror

vertex

principalaxis virtual

image

When the object is at a distance that is closer to the mirror than the focal point, something different happens to the rays.

These rays will never intersect

Only two rays can be drawn in this case

The only way to locate the image that is formed is by looking at the continuation of the reflected lines behind the mirror. They are drawn using dotted lines

Where the two dotted lines intersect is the location of the image. Since the image is behind the mirror, it is called a virtual image. It is upright and larger than the original image.

Ray Diagrams for Concave Mirrors (cont’d)Ray Diagrams for Concave Mirrors (cont’d)

focal point

mirror

vertex

principalaxis

These rays will never intersect

When the object is at the focal point, no image is formed.

Ray Diagrams for Concave Mirrors (cont’d)Ray Diagrams for Concave Mirrors (cont’d)

The closer the object gets to the focal point, the The closer the object gets to the focal point, the larger the image becomes.larger the image becomes.

Go to Go to www.explorelearning.comwww.explorelearning.com and login and login

Go to the “Ray Tracing (Mirrors)” Gizmo to see Go to the “Ray Tracing (Mirrors)” Gizmo to see how moving the object closer to the focal point how moving the object closer to the focal point makes it bigger.makes it bigger.– Choose concave mirror in the mirror optionsChoose concave mirror in the mirror options– You’ll have to move the focal point to the closest You’ll have to move the focal point to the closest

possible position to observe the difference effectivelypossible position to observe the difference effectively

MagnificationMagnification

You may have already noticed how the object You may have already noticed how the object and it’s reflected image are, in many cases, and it’s reflected image are, in many cases, not the same size.not the same size.When describing how much bigger or smaller When describing how much bigger or smaller the image is than the original object we use the the image is than the original object we use the term term magnifactionmagnifaction..The comparison between the object and it’s The comparison between the object and it’s image can be described in three waysimage can be described in three ways

1.1. same sizesame size2.2. enlarged (larger than the object)enlarged (larger than the object)3.3. Diminished (smaller than the object)Diminished (smaller than the object)

Magnification (cont’d)Magnification (cont’d)

Magnification can be calculated using the Magnification can be calculated using the following formulafollowing formula

o

i

h

hMor

heightobject

heightimageionmagnificat

o

i

d

dMor

distanceobject

distanceimageionmagnificat

It can also be calculated using distance from the It can also be calculated using distance from the image to the mirror and from the object to the mirrorimage to the mirror and from the object to the mirror

Convex MirrorsConvex Mirrors

A mirror with a surface curved outward is A mirror with a surface curved outward is called a called a convex mirrorconvex mirror or or diverging diverging mirrormirror..Instead of focussing light rays to a single Instead of focussing light rays to a single focal point, the convex mirror spreads focal point, the convex mirror spreads them outthem out– One can think of the rays being spread out One can think of the rays being spread out

from a single pointfrom a single point– This point is the focal point for the backside of This point is the focal point for the backside of

the mirrorthe mirror

Convex MirrorsConvex MirrorsWe use convex mirrors everyday.We use convex mirrors everyday.– They can used for store security, side view They can used for store security, side view

mirrors in cars, for safety at intersectionsmirrors in cars, for safety at intersections

Convex Mirrors (cont’d)Convex Mirrors (cont’d)Convex mirrors do not form a real image, only a Convex mirrors do not form a real image, only a virtual image.virtual image.

focal point

mirror

principalaxis

These rays will never intersect. Therefore, no real image will be formed.

virtualimage

Ray Diagrams for a Convex MirrorsRay Diagrams for a Convex Mirrors

focal point

mirror

principalaxis

1. Draw the first ray parallel to the principal axis from the object to the mirror’s surface. virtual

image2. Draw another line away from the mirror’s surface in line with the focal point.

3. Draw a dotted line from the surface of the mirror where the first line hits the mirror’s surface to the focal point.

4. Draw a second ray directly from the object to the mirror’s surface in line with the focal point.

6. Draw a dotted line from the surface of the mirror where the second ray hits the mirror’s surface parallel with the principal axis.

5. Another line is drawn away from the mirror’s surface parallel to the principal axis.

The point where the two dotted lines intersect is where the virtual

Ray Diagrams for Convex Mirrors (cont’d)Ray Diagrams for Convex Mirrors (cont’d)

Go to Go to www.explorelearning.comwww.explorelearning.com and login and login

Go to the “Ray Tracing (Mirrors)” Gizmo to Go to the “Ray Tracing (Mirrors)” Gizmo to see how moving the object closer to and see how moving the object closer to and further away from the mirror makes affects further away from the mirror makes affects the image formed.the image formed.– Choose convex mirror in the mirror optionsChoose convex mirror in the mirror options

Draw Ray DiagramsDraw Ray Diagrams

Go to the word document for this lesson Go to the word document for this lesson and print out the ray diagram pages.and print out the ray diagram pages.

Complete the ray diagrams for the Complete the ray diagrams for the concave and convex mirrors.concave and convex mirrors.– You only need to do rays for the tip of the You only need to do rays for the tip of the

arrow, just like you learned in the previous arrow, just like you learned in the previous slides.slides.

Questions from the TextbookQuestions from the Textbook

Go to page 433 in the book and answer Go to page 433 in the book and answer questions 4, 6, 8, 11 and 12 in the questions 4, 6, 8, 11 and 12 in the document for this lessondocument for this lesson