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Lesson 26: Reflection & Mirror Diagrams

The Law of Reflection

There is nothing really mysterious about reflection, but some people try to make it more difficult than itreally is.

● All EMR will reflect off of appropriate surfaces, but for the purposes of this lesson we will onlycare about visible light reflecting off of mirrors.

Drawings that show reflection always include a special linethat must be drawn first... the normal.

● ou might remember this word from when we studiedforces. !e say that a line drawn at "#$ to the surface isa normal line.

● !hen you want to figure out how something willreflect from a surface, draw a normal line to that boundary at that point.

The %aw of Reflection says &the angle of incidence equals the angle of reflection.'● These angles are always measured from the normal line so that we have a common reference.● (n Illustration 1 we see that the angle is )*$ coming in and )*$ reflecting off.● This is an e+ample of regular specular - reflection.

The only time you need to be really careful with the law of reflection is when the surface is somehowirregular.

● !e still draw normal lines, but we can end up with millions of them if the surface is reallyrandom.○ or e+ample a lake on a windy day will show a really blurred image because the surface

reflects the light in so many directions.

● !e won/t worry too much about this irregular diffuse- reflection.

Plane Mirror Diagrams

!e can use the %aw of Reflection to draw diagrams to predict the way an observer will see an image ina plane mirror.

● &0lane' in this case refers to boring, old fashioned, flat mirrors.

Doing problems involving plane mirrors is actually pretty easy since we only have to remember a fewthings1

1. The image will be the same size as the original object.2. The image will appear as far behind the mirror as the object is in front of the mirror.

2. The Law of Reflection. Any light beam that hits the mirror will bounce off at e+actly the sameangle. !e assume the mirror is perfectly flat in these situations. !e will have to make sure thatthe light rays reflected off the mirror do so at an angle that makes them hit the observer/s eye.

%et3s look at a simple e+ample to illustrate how we have to draw these diagrams.

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Illustration 1: Reflection diagram.


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Example 11 !etch a ray diagram that shows how light willtravel from the ob9ect to the eye by reflecting from the mirror

in Illustration 2. "dentif# the position of the image.

irst, measure how far the ob9ect is in front of themirror. Draw a :uick sketch Illustration 3- of theimage behind the mirror at the same distance 9ustmake sure it3s flipped around, and must be drawn witha dashed line-.

Illustration 4 shows how we draw a light ray a line-from the observer3s eye to an important part of theimage like the top-. The light ray should be dashedwhen it is behind the mirror to show that the light ray

isn3t really there.

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Illustration 2: An object in front of amirror. This diagram is edge-on.

Illustration 3: ho!ing the imagebehind the mirror.

Illustration 4: The first ra" sho!ing ho!the person sees the image.


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At the point where that light ray hit the mirror, bounceit back at the same angle law of reflection- so that it

hits the same spot on the original ob9ect as shown in Illustration #.

;ow we draw another separate light ray thatshows the path the light takes to get from the bottom of the ob9ect to the eye. (t should look like Illustration $ . This shows how the light rays fromthe ob9ect converge on the eye.

This gives you an idea of how the light rays are traveling from the ob9ect to you eye, and also why theimage appears to be behind the mirror.

●


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Curved Mirrors

Maybe you3ve gone into a mirror fun house that has all those weird mirrors that make you look 6# feettall, skinny in the middle and wide at the top.

● >bviously these are not regular, plane mirrors. (nstead, they3re all curved and bumpy andmisshaped.○ Don3t worry, we3re not going to be analy?ing mirrors that are that weird, but we will be

looking at curved mirrors.● (magine taking a giant metal ball and cutting a section out of it. ou spray some shiny paint on

the inside or outside and you have a curved mirror.○ The first kind we will be looking at is a conca$e con$erging mirror, which would mean that

you made the inside of the ball shiny.○ %ater we will look at con$ex di$erging mirrors, where the outside of the ball was made

shiny.

Concave Converging Mirrors

To be able to figure out how an image will be formed in one of these converging mirrors, you need to be aware of a few basic &parts'. @heck out Illustration & and the description of each part that follows.

%entre &%'The centre shown in the diagram is where the centre of the sphere would be. The diagram e+aggerates the shape ofthe mirror a bit to be able to use it in some of the diagrams later on, but you should be able to get the basic idea.%ike a regular circle, the distance from the centre to the surface of the mirror is the radius.

(ocus or (ocal )oint &('(f an ob9ect was infinitely far away from the mirror, the light from it would converge on this one point. (n thediagrams we are doing we will mostly be looking at how some light rays pass through or appear to pass through-this focal point. The focal point is e+actly in between the mirror and the centre. 8ince the distance between thecentre and the mirror is the radius, the distance from the focal point to the mirror is half of the radius. This distance

is referred to as the focal length.

)rinciple *xis &)*'The blue line is the principle a+is, a line that we will use as a reference point in our diagrams. (t passes through thecentre and is perpendicular to the surface of the mirror.

+ertex &+'!here the principle a+is meets the mirror surface.

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Illustration &: 'arts of a cur(ed mirror.

V PA


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There are three rules you need to use to figure out where the image of the ob9ect will appear. ou only need to use two of the three to actuallylocate the image.

● All of the rules involve what a ray will do when it leaves theob9ect.

● ou will need to have a ruler to draw the lines when you figureout these problems.

● !hen you sketch the curved mirror itself, you3ll find you don3thave to be too careful about making its shape perfect close enough will give you decentresults.

● The ob9ect we will be using in these e+amples is an arrow pointing up... that way we will havean easy time seeing if the image is flipped upside down or not.○ The image will appear where any two reflected rays cross.

Rule ,1- *n# ra# through the focal point will reflectparallel to the principle axis & Illustration 8'.

Don3t start worrying about how that ray of lightcame off the ob9ect and went straight through thefocus it 9ust did. %ight reflects off ob9ects at allsorts of angles, and if it will help us to find wherean image is, we might as well assume one raygoes right through the focus.

Rule ,2- *n# ra# parallel to the principle axis willreflect so that it passes through the focal point& Illustration 9'.

( know this sounds e+actly the same as the firstrule, but look at it carefully and you3ll see that itis the opposite.

;otice the spot where the reflected red ray iscrossing the reflected black ray from rule onethis shows me where the image will appear.

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rning!

If you use all three rules, you'llsometimes see that the don't allintersect at the same point and it mightseem you did something wrong. Don't

worry, it's just because our mirrordiagrams are not perfect.

Illustration ): *ight Ra" through the focus.

Illustration +: *ight Ra" parallel to the

principle a,is.


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8o how do we draw in the image=● 8ince all the rays were drawn from the tip of the ob9ect, this shows where the tip of the image

will be.● !e know that since the base of the ob9ect is on the principle a+is, the base of the image will

also appear on the principle a+is.

!e label the ob9ect as C>C and the image as C(C, as shown in Illustration 1.● !e draw the image as a solid line because the rays of light that make the image are actually

traveling through that point if ( was to hold a piece of paper right there, ( would see the imageappear there (t is a real image.

● Also notice that the image is upside down inverted - and slightly smaller diminished -compared to the original.○ This is not always the case with curved mirrors. ou might even find that your rays need to

be e+tended to behind the mirror to be able to be able to cross each other then the imagewould be a virtual image behind the mirror.

or any image, you will need to classify it as1

%haracteristic escription

Magnification 8ame 5 Enlarged 5 Diminished

Attitude Erect 5 (nverted

Type Real 5 irtual

Although we know where the image is, and that it is a real, inverted, smaller image, we can stillconfirm it using our last method

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Illustration 1: Image dra!n in diagram.

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Real light rays and images are drawnas solid lines, but virtual rays andimages are drawn as dotted lines.

Converging mirrors are sonamed because the lightrays that are reflected offthe mirror come together(converge) on the realside. It's ok to call thesemirrors either convergingor concave.


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Rule ,/- *n# ra# that passes through the centrewill reflect bac! through the centre.

Gnfortunately, this is the least reliable way todraw a ray, since we had to assume that if the

mirror was big enough it would have bounced the ray back. ;otice that it hits 9ustabout where the other two rays meet up.!e3re probably doing ok.

Convex Diverging Mirrors

The same set of rules shown above apply to diverging mirrors, it3s 9ust that things will look a bitdifferent since conve+ mirrors have their focal point and centre behind the mirror.

● Diverging mirrors typically make a diminished, virtual image of the original ob9ect.

%et3s look at an e+ample using the three rules covered above for converging mirrors.● The only difference is that ( will e+tend the rays behind the mirror as dotted lines to be able to

show how they &pass through the focal point' or &through the centre'.

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Illustration 11: ho!ing the ra" through thecentre.

Illustration 12: i(erging mirror.

Diverging mirrors are sonamed because the light

rays that are reflected offthe mirror go apart(diverge) on the real side.


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Gse Rule ,2 because it works wellfor this mirror- to draw the ray comingoff of the tip of the ob9ect parallel tothe principle a+is as shown in

illustration 62. !hen it hits the mirror,it bounces off so that a dotted linedrawn behind the mirror will passthrough the focal point .

Rule ,/ again, 9ust because it workswell for this mirror- is used in Illustration 14. This ray comes off of the tip of the ob9ect aiming straight for the centre. !here it hits the mirror itwill bounce back, but ( draw a dottedline behind the mirror to show wherethe ray !ould have gone.

;otice that there is now a place wherethe two dotted lines hit behind thediverging mirror. This is where theimage will appear.

● The image is $irtual it3s behind the mirror-, it is erectright side up-, and diminished

smaller-.

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Illustration 13: A ra" parallel reflects as though it came fromthe focus.

Illustration 14: *ight ra" through the centre.

Illustration 1#: Image sho!n behind the mirror.


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The Formulas

There are a couple of formulas you can use to figure out its position, attitude erect or inverted-, andmagnification.

Mirror Equation

The first is called the mirror equation... 6

f =

6

d o

6

d if I focal length m-

do I distance from mirror to ob9ect m-diI distance from mirror to image m-

Ultra-Special Notes for Signs Using the Mirror Equation:*n#thing in (ront of the 0irror &Real' )ositi$e *n#thing 3ehind the 0irror &+irtual' 4egati$e 5

This applies to the distances, and also applies to focal length...• a con$erging mirror with its focus in front has a positi$e focal length• a di$erging mirror with its focus behind the mirror has a negati$e focal length.

!e define which side is in front of the mirror by where we placed the ob9ect.• An ob9ect must always be in front of the mirror, otherwise it can not produce an image.

◦ (n Illustration 1$ the mirror must be converging, since the ob9ect must be on the realside.

◦ (n Illustration 1& we have a diverging mirror, again because of where we put theob9ect.

• ;otice how in both cases the positive side of the mirror is the side we have the ob9ect placed at.

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Illustration 1&: i(erging mirror

@

o

5

Illustration 1$: /on(erging mirror

@

o

5


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Example 21 A diverging mirror has a radius of *# cm. An ob9ect is placed 2# cm in front of the mirror.etermine where the image will appear.

8ince the radius is #.*# m which is the distance from the mirror to the centre-, the focal lengthis J#.6# m. This is because the focus is half ways between the verte+ and the centre, andnegative when the focus is behind the mirror of a diverging mirror.

6

f =

6

d o

+6

d i

6

d i=

6

f −

6

d o6

d i=

6

−#.6#−

6

#.2#

d i=−#.#4B m=−4.Bcm

The negative sign on the answer indicates that the image is virtual, behind the mirror.

Magnification Equation

The magnification equation is...

m=hi

ho=−d id o

8ame as mirror equation and...hi I height of the image m-

ho I height of ob9ect m-m I magnification how many times bigger or smaller-

Ultra-Special Notes for Using the Magnification Equation:8ame rules as for the mirror equation and...

Anything abo$e the 0rinciple A+is K )ositi$e

Anything below the 0rinciple A+is K 4egati$e 5

0agnification 6uantities1LmL 6 DiminishedLmL I 6 8ameLmL N 6 Enlarged

Example /1 or the same situation from E+ample *, determine how tall the image is if the ob9ect isB.#cm tall. Also determine the magnification.

hi

ho=−d id o

hi=−d i ho

d o

hi=−(−#.#4B)(#.#B#)

#.2#

hi=#.#6*B=#.#62 mThe height is positive so the image is erect, above the principle a+is.

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To calculate the magnification either distances or heights could be used. 8ince the distanceshave been through less calculations, we trust them more.

m=−d id o

m=−−#.#4B

#.2#

m=#.*BThe magnification is positive, verifying the image is erect.

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