bcs g8 u2c05 j17 5 optical systems make use of mirrors and lenses.• mhr 183 object plane mirror...

$: BCS G8 U2C05 J17 5 Optical systems make use of mirrors and lenses.• MHR 183 object plane mirror image Figure 5.14 Only a small fraction of the light reflecting from an object enters$
Reflections of Reflections 5-6

In this activity, you will find out how many reflectionsyou can see in two plane mirrors.

Materials• 2 plane mirrors • masking tape• protractor • paper clip

Safety

• Handle glass mirrors and bent paper clips carefully.

What to Do1. Create a table to record your data. Give your table

a title.

2. Lay one mirror on top of the other with the mirror surfaces inward. Tape them together so they will open and close. Use tape to label them“L” (left) and “R (right).”

3. Stand the mirrors up on a sheet of paper. Using aprotractor, close the mirrors to an angle of 72°.

4. Bend one leg of a paper clip up 90° and place itclose to the front of the R mirror.

5. Count the number of images of the clip you see inthe R and L mirrors. Record these numbers in yourdata table.

6. Hold the R mirror still. Slowly open the L mirror to90°. Count and record the images of the paper clipin each mirror.

7. Hold the R mirror still. Slowly open the L mirror to120°. Count and record the images of the paperclip in each mirror.

What Did You Find Out?1. What is the relationship between the number of

reflections and the angle between the two mirrors?

2. How could you use two mirrors to see a reflectionof the back of your head?

Find Out ACTIVITY

All mirrors reflect light according to the law of reflection. Plane mirrors form an

image that is upright and appears to be as far behind the mirror as the object is in

front of it. Depending on the distance of the object, a concave mirror can form an

image that is inverted or right side up, and that can be larger or smaller than the

object. Convex mirrors form images that are upright and smaller than the object.

You can see yourself as you glance into a quiet pool of water or walkpast a shop window. You can see unusual reflections of yourself in thewavy mirrors at amusement parks. You can even see reflections ofyourself in a spoon. Most of the time, however, you probably look foryour image in a flat, smooth mirror called a plane mirror.

Using Mirrors to Form Images5.2

Key Termsconcaveconvergingconvexdivergingfocal point

182 MHR • Unit 2 Optics

Count the images in each mirror.

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Chapter 5 Optical systems make use of mirrors and lenses. • MHR 183

object plane mirror image

Figure 5.14 Only a small fraction of the light reflecting from an object enters the eye of the observer.

Did You Know?

Plane MirrorsLooking at yourself in a plane mirror, you can see that your imageappears to be the same distance behind the mirror as you are in frontof the mirror. How could you test this? Place a ruler between you andthe mirror. Where does the image touch the ruler? You also see thatyour image is oriented as you are and matches your size. This type ofreflection is where the expression “mirror image” comes from. If youmove toward the mirror, your image moves toward the mirror. If youmove away, your image also moves away.

How do reflected rays form an image that we can see in a mirror?Study Figure 5.14 to answer this question. Light from a lamp shines on a blueberry. This light reflects off all points on the blueberry, in all directions. In the figure, only the rays coming from one point areshown. All of the rays from the blueberry that strike the mirror reflectaccording to the law of reflection. The rays that reach your eye appearto be coming from a point behind the mirror. The same process occursfor every point on the blueberry. Your brain “knows” that light travelsin straight lines. Therefore, your brain interprets the pattern of lightthat reaches your eye as an image of a blueberry behind the mirror. In fact, it might even be possible to trick the observer into thinking the blueberry was behind a glass window, rather than in front of a very good mirror. A house of mirrors uses this trick to create a maze.

The mirror on the Hubble Space Telescope is one of thesmoothest mirrors ever made.If the mirror were as large asEarth, the biggest bump on itwould be only 15 cm tall.

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Notice that the points appear to be coming from behind themirror. Each point appears to be coming from a point that is as farbehind the mirror as the real point is in front of the mirror. Alsonotice that the three points are exactly the same distance apart in theimage as they are on the object, the bird. These observations explainwhy an image in a plane mirror is the same size as the object andappears to be the same distance from the mirror as the object.

Image orientation

A plane mirror produces an image withthe same orientation as the object. Ifyou are standing on your feet, a planemirror produces an image of youstanding on your feet. If you are doinga headstand, the mirror shows youdoing a headstand. However, there is adifference between you and theappearance of your image in the mirror.Follow the sight lines in Figure 5.16.The ray that diverges from the righthand of the boy converges at whatappears to be the left hand of hisimage. Left and right appear to bereversed by a plane mirror.

bird image of birdplane mirror

Figure 5.15 We know that whatwe see in a mirror is just animage. However, a pet bird willchatter for hours to a “friend” inthe mirror.

Image size and distance

Another important feature of images in plane mirrors is demonstratedin Figure 5.15. Rays are shown coming from three different points onthe bird. These rays reflect off the mirror and back to the bird’s eye.

e

image object

mirror

Figure 5.16 When the boy blinks his right eye, the left eye of hisimage blinks.

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Concave MirrorsA concave mirror is a mirror that curves inward. Concave mirrors,like plane mirrors, reflect light rays to form images. The difference isthat the curved surface of a concave mirror reflects light in a uniqueway. As shown in Figure 5.17, parallel light rays bounce off thecurved surface of a concave mirror and then meet at a single pointcalled the focal point. Light rays that are coming together at a focalpoint are described as converging.

The image formed by a concave mirror depends on how far theobject is from the focal point of the mirror (see Figure 5.18). If adistant object is reflected in a concave mirror, its image is small andupside down. As the object approaches the focal point, its imageremains inverted but gets ever larger. If the object is between the focalpoint and the mirror, then the image appears to be larger than theobject and is upright.

Concave mirrors have many uses (see Figure 5.19). If a brightlight is placed at the focal point, then all the light rays bounce off themirror and are reflected parallel to each other. This makes an intense,focussed beam of light. Spotlights, flashlights, lighthouses, and carheadlights use this kind of mirror. The largest telescopes all useconcave mirrors to collect light because the mirror concentrates thelight so effectively. Shaving mirrors and make-up mirrors are alsoconcave mirrors. They form an enlarged, upright image of a person’sface so it is easier to see small details.

Figure 5.17 Light rays collectedby a concave mirror converge on a focal point before spreading out again.

focalpoint

Figure 5.19 The boy is between the concave mirror and its focal point.Figure 5.18 The image formed by a concavemirror depends on how far away the object is.

focal point

focal point

focal point(a)

(b)

(c)

object

object

object

A

B

C

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Find out about the centre of curvature and radius ofcurvature for a concave lens.What is the relationshipbetween the radius ofcurvature and the focallength? If a person stands at the centre of curvature infront of a large concavemirror, where will his or herimage form and what will beits size and orientation? Visitwww.bcscience8.ca.


Figure 5.20 The reflected raysfrom a convex mirror diverge anddo not meet.

focalpoint

Figure 5.21 Convex mirrors are used in stores as security mirrors (A), and in cars as rearviewand side-view mirrors (B).

Convex MirrorsA convex mirror is a mirror that curves outwards. Convex mirrors alsoreflect light rays to form an image, but they do so in an opposite wayto concave mirrors. A convex mirror reflects parallel light rays as if theycame from a focal point behind the mirror (see Figure 5.20). Lightrays that spread apart after reflecting are described as diverging. Theimage formed is always upright and smaller than the actual object.

The reflection from a convex mirror has two main characteristics:1. Objects appear to be smaller than they are.2. More objects can be seen in a convex mirror than in a plane

mirror of the same size.Security mirrors, such as those in convenience stores, are large

convex mirrors. Convex mirrors make it possible to monitor a largeregion of the store from a single location. Convex mirrors can alsowiden the view of traffic that can be seen in rearview or side-viewmirrors of automobiles. However, because distances and sizes seen in a convex mirror are not realistic, most convex side-view mirrors carry a printed warning that the objects viewed are closer than they appear to be (see Figure 5.21).

Reading Check

1. What size does the image in a plane mirror appear to be?2. What distance from the mirror does an image in a plane mirror

appear to be?3. How is a concave mirror shaped differently from a plane mirror?4. What are some uses for concave mirrors? 5. How is a convex mirror shaped differently from a plane mirror?6. What are some uses for convex mirrors?

Conduct an Investigation 5-7on page 187

Suggested Activity

A B

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When you look across a lake, you might seethe reflection of the distant mountains andtrees in the water. The image of the treesand mountains appears to be upside down.However, when you look straight down atthe surface of the lake, you see an uprightreflection of yourself. Why would your imagebe upright while the image of the mountainsis upside down?

Pause and Reflect


Checking Concepts1. Describe how your image changes as you

move closer to:(a) a plane mirror(b) a concave mirror(c) a convex mirror

2. One side of a soupspoon is convex and theother is concave. Imagine you are havingsoup and you lift the spoon out of the soupbowl, holding some soup. Is the part of thespoon touching the soup convex or concave?

3. Do convex and concave mirrors obey the lawof reflection? Explain.

4. Explain the difference between divergent andconvergent light rays.

5. Draw and label a mirror that produces: (a) divergent light rays(b) convergent light rays

6. Suppose you find a shiny metal bowl that hasbeen left outside in the sunlight. (a) Are you more likely to see the reflection

of direct sunlight by viewing the outside or the inside of the bowl?

(b) Is it more dangerous to look at theoutside or the inside of the bowl? Explain.

Understanding Key Ideas7. Why is an image in a plane mirror the same

size as the object that is reflected?8. List several uses of:

(a) plane mirrors(b) concave mirrors(c) convex mirrors

9. (a) Draw a ray diagram that shows anarrangement of mirrors that would allowyou to see the back of your own head.Draw the diagram as if looking downfrom above. The rays should leave theback of your head and end in your eye.Show the normal and angles of incidenceand reflection.

(b) Will left and right be reversed in theimage? Explain.

10. Design and label an arrangement of mirrorsto do each of the following: (a) see over the top of a fence without

having to raise your eyes above the top of the fence

(b) read a book by reflected light without having the words backwards in a“mirror image”

(c) collect and concentrate the Sun’s lightinto a small space and then conduct thelight around two corners to a solar panel

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Observing Light Rays 5-8

In this activity, you will observe how light rays refractas they pass through lenses.

Materials• ray box• concave lens• convex lens• printed page

What to Do 1. Shine the ray box at a concave lens. Observe how

the rays are affected. Draw your observations.

2. Look through the concave lens at some printedtext. Observe the appearance of the print. Drawyour observations.

3. Shine the ray box at the convex lens. Observe howthe rays are affected. Draw your observations.

4. Look through the convex lens at some printed text.Observe the appearance of the print. Draw yourobservations.

What Did You Find Out?1. Compare what you observed about the appearance

of the text with each of the two lenses.

2. Which type of lens would be best used as amagnifying glass? Why?

3. What might the other kind of lens be used for?

Find Out ACTIVITY

A lens is a piece of transparent material that can bend, or refract, light rays in useful

ways to help form a well-focussed image. Concave lenses are thinner in the middle

than at the edge. They are used to diverge light rays. Convex lenses are thicker in the

middle than at the edge. They are used to converge light rays.

Light rays refract through a piece of glass in a predictable way. Recallfrom Section 5.1 that when a light ray passes from air into a densermaterial, such as glass, it bends toward the normal. When the light raypasses out of the glass, back into the air, it bends away from thenormal. Using these facts about light it is possible to design andconstruct lenses. A lens is a curved piece of transparent material, such as glass or plastic, that refracts light in such a way as to convergeor diverge parallel light rays. The image that a lens forms depends on the shape of the lens. Like curved mirrors, a lens can be convex or concave.

Using Lenses to Form Images5.3

Key Termsconcave lensconvex lensfocal lengthlens


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Concave LensesConcave lenses are lenses that are thinner inthe middle than at the edge. As shown inFigure 5.22, light rays that pass through aconcave lens diverge. The rays are refractedoutward, and never meet at a focal point. The image formed is always upright andsmaller than the actual object (see Figure 5.23and Table 5.1). Concave lenses are used insome types of eyeglasses and some telescopes,and are often used in combination with other lenses.

Distance of Object from Lens

Any location

Type of Image Formed

Smaller, upright

Table 5.1 Images Formed by Concave Lenses

do

di

object

ray 2

ray 1

image F

F

Figure 5.23 Concave lenses produce images that are upright and smallercompared to their objects.

Figure 5.22 Light rays diverge when they pass through aconcave lens.

Did You Know?

Lenses have been made andused for hundreds of years. In1303, French physician Bernardof Gordon wrote of the use of lenses to correct eyesight.Around 1610, Galileo used two convex lenses to make a telescope, with which hediscovered the moons of Jupiter.

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Raindrops take on aspherical shape as they fall,which gives them the shapeof a convex lens. A drop ofwater sitting on a glass slidehas a nearly spherical shape.Investigate whether a waterdroplet or a glass bead ofthe same size would make agood magnifying lens. Startyour search atwww.bcscience8.ca.

internet connect


Figure 5.25 An image formed by a convex lens may be inverted, or flipped upside down.

Convex LensesConvex lenses are lenses that arethicker in the middle than at theedge. As shown in Figure 5.24,light rays that pass through a convexlens come together, or converge.When parallel rays strike a convexlens from one side, they will allcome together at the focal point ofthe lens. Light passing through thethicker, more curved areas of thelens will bend more than lightpassing through the flatter areas. A light ray that passes straightthrough the centre of the lens is not refracted. The image formed by aconvex lens depends on the positions of the lens and the object (see Figure 5.25).

Figure 5.24 Light rays converge whenthey pass through a convex lens.

ray B

ray Aobject

focalpoint

onefocal

length

twofocal

lengths

imageoptical axis

ray Afocalpoint

optical axis

imageray B

onefocal

length

twofocal

lengths

object

ray Afocalpoint

optical axisobject

image

onefocal length

ray B

A

B

C

When the candle ismore than two focallengths away from thelens, its image isreduced and upsidedown.

When the candle isbetween one and twofocal lengths from thelens, its image isenlarged and upsidedown.

When the candle isless than one focallength from the lens,its image is enlargedand upright.

ds

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Distance of Object from Lens

More than two focal lengthsBetween one and two focal lengthsObject at focal pointLess than one focal length

Type of Image Formed

Smaller, invertedLarger, invertedNo imageLarger upright

Table 5.2 Images Formed by Convex Lenses

Reading Check

1. What happens to parallel light rays that strike a concave lens?2. What happens to parallel light rays that strike a convex lens?3. What type of image is formed by a concave lens? 4. What determines the type of image that is formed by a

concave lens?

Focal Length in Convex LensesConvex lenses and concave mirrors share a similar property in that thelight rays converge at the focal point. The distance from the centre ofthe lens or mirror to the focal point is called the focal length (seeFigure 5.26). There is a mathematical relationship linking the distanceof the object in front of the lens to the distance of the image formedby the lens. • If the object is more than two focal lengths in front of the lens, the

image is smaller than the object and inverted. • If the object is moved closer to the lens so that it is one to two focal

lengths away, the image is larger than the object and still inverted. • If the object is very close, less than one focal length away, the

image appears to be located on the other side of the lens and isboth upright and larger than the object.

As summarized in Table 5.2, the type of image a convex lens formsdepends on where the object is relative to the focal point.

Eyeglasses would morecorrectly be called“eyeplastics” these days.Glass refracts well but isheavy and can shatter.The highest quality of plastic in widespread use for glassesis polycarbonate plastic. Findout what properties it has that makes it so useful inlenses. Start your search atwww.bcscience8.ca.

Figure 5.26 The focallength of a convex lens

focallength

focalpoint

Find Out Activity 5-9 on page 194Find Out Activity 5-10 on page 195

Suggested Activities

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Checking Concepts1. What is a lens? 2. (a) Make a sketch of three parallel light

rays passing through a concave lens. (b) Make a sketch of three parallel light

rays passing through a convex lens.3. Describe the image formed by a concave

lens.4. As an object comes closer to a convex lens

what happens to: (a) the size of the image?(b) whether the image is upright or upside

down?(c) the location of the image?

5. List two factors that affect the way thatlight is refracted through a lens.

6. List two uses of convex lenses.7. List two uses of concave lenses.

Understanding Key Ideas8. What is the difference between the way

parallel light rays are affected by a concavemirror and a concave lens?

9. Does a concave lens affect light more like aconcave mirror or a convex mirror? Explainyour answer.

10. Explain why a drop of water placed on the page of a book magnifies printingbeneath it.

11. Reading glasses help people to see smallprint. What sort of lens would be used inthem?

The archer fish is a remarkable hunter thatcatches insects that are resting on branchesor reeds up to 2 m above the water. Thearcher fish sights the insect from beneath thewater and then shoots a stream out of its mouth at the insect. Light refracts when it passes from air into water, so the insectappears to be in a different place than it really is. Yet the archer fish is deadlyaccurate. How do you think this is possible?

Pause and Reflect

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Prepare Your Own SummaryIn this chapter, you investigated how opticalsystems make use of mirrors and lenses. Createyour own summary of the key ideas from thischapter. You may include graphic organizers or illustrations with your notes. (See ScienceSkill 10 for help with using graphic organizers.)Use the following headings to organize yournotes:1. The Ray Model of Light2. Convex Mirrors3. Concave Mirrors4. Convex Lenses5. Concave Lenses

Checking Concepts1. State the law of reflection.2. Use a ray diagram to explain why a light

appears dimmer the farther the observer is from it.

3. What is the difference between reflectionand refraction?

4. How is an opaque object different from atranslucent object in terms of its ability totransmit light?

5. How does the direction of a ray of lightchange as it passes from air into water?

6. (a) What are the three basic shapes of mirrors?

(b) With which shape of mirror do light rays converge?

7. How does the reflection from a convexmirror appear to make objects seem smaller?

Understanding Key Ideas8. Draw a diagram of a light ray reflecting

off the surface of a flat mirror. Label the normal, the incident ray, the reflectedray, the angle of incidence, and the angle of reflection.

9. Copy the diagrams below into yournotebook. Complete the missing parts of each diagram.

C h a p t e r

5

r = ?Draw the reflected ray.

Draw the normal.

Draw the two reflected rays. Compare the directions of the light striking and bouncing off the mirror.

r = ?

i = ?

i

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10. Making reference to the normal line,describe the change in the direction of a light ray that travels from: (a) air into water (b) glass into air

11. Draw a diagram to show how an image thesame size as an object can be produced byreflection from a flat mirror.

12. As an object moves closer to a convex lens,what happens to the size and orientation ofthe image?

13. Draw a ray diagram to show what happensto light rays as they pass through:(a) a convex lens(b) a concave lens

14. (a) How does the relative thickness of a convex lens affect its ability to refractlight?

(b) Draw a thin and a thick convex lens.Show how light rays pass through eachof them.

15. Draw ray diagrams to illustrate thedifference between opaque, translucent andtransparent.

16. Copy the following table into yournotebook. For each of the followingexamples, decide what kind of lens orlenses need to be used in the light fixtures.Use a diagram to show how the lens isaffecting the light.

17. A magnifying glass contains a lens that canfocus the light from the Sun at a singlepoint on the ground. (a) What shape of mirror can also do this? (b) Draw a ray diagram to show parallel

light from the Sun striking this mirrorand to show where the light rays converge.

(c) Which is better for focussing the Sun’slight at a point on the ground, a lens or a mirror? Explain.

18. Decide whether each of the following isopaque, translucent, or transparent.Explain your reasons.(a) your tooth(b) your skin(c) your fingernail(d) the lens of your eye

Suppose you have been given a concavemirror and you have been asked to find itsfocal point. Describe a procedure that youcould use to do this.

Pause and Reflect

Light Fixtures

(a) A reading light that lights one spot in the room whileleaving other areas dark

(b) An outdoor light that spreadsan even illumination over awide area

(c) A flashlight that spreads adiffuse, dim light over a widearea, while shining a brightfocussed beam in the middle

Type of Lens How the Lens Affects Light Rays

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