Physics Optics: Plane Mirrors

a place of mindFA C U LT Y O F E D U C AT I O NDepartment ofCurriculum and PedagogyPhysicsOptics: Plane MirrorsScience and MathematicsEducation Research GroupSupported by UBC Teaching and Learning Enhancement Fund 2012-2014

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Plane Mirrors IIf you are standing 1 m in front of a plane mirror, what is thedistance between you and your reflected image?1mA. 0 mB. 0.5 mC. 1 mD. 1.5 mE. 2 md ?

SolutionAnswer: EJustification: For plane mirrors, the reflected image (a virtual image)and object are along the same line, perpendicular to the reflectivesurface. The image and object are equidistant from the mirror.If you are 3 m in front of the mirror, your reflected image will be located3 m behind the mirror. Thus, the distance between you and the imagewill be 6 m.1m1mThe reflected image’s distance fromthe mirror is constant, and does notchange if the observer moves fromleft to right.d 2m

Solution Cont’dThink about the image created here. Plane mirrors do not provide anymagnification, so the image must be the same size as the object. Wecan see that the image is created at the extension of the reflectedrays. From this, we know that the triangles created by the light raysare equal on both sides of the mirror, and the image and object areequidistant from the mirror.

Extend your Learning:ExperimentMeasure the imagedistance using two candlesand semi-reflective glass.

Extend your Learning:PredictThink about the word below. What would the image look likeif a mirror was placed along the edge AB? BD? CD? AC?ABCDWhat letters are unchanged if they are reflectedhorizontally? Vertically?Why are the letters on the front of an ambulance reversed?

Plane Mirrors IIIf you run towards a plane mirror at a speed of 2 m/s, at whatspeed does the apparent distance between you and your imagedecrease?A. 0.5 m/sB. 1 m/sC. 2 m/sD. 4 m/sE. 8 m/s

SolutionAnswer: DJustification: Your distance from the mirror is always equal to theapparent distance of your image from the mirror (see first question). Letthe initial distance between you and your image be d1. After you run for1 s at 2 m/s, the distance between you and your image is d2. You havemoved 2 m, and your image has moved 2 m, so the distance betweenyou and your image has decreased by 4 m – at a speed of 4 m/s.Your image approaches you at a speed of (d1 - d2)/(1s) 4 m/sd1d22mMirror2mYour initialpositionPosition after yourun for 1sImage position afteryou run for 1 sImage initialposition

Extend your Learning:Thought ExperimentThink about being in a car on the highway.When cars approach you in the other direction, it appears theyare going much faster than they actually are.When cars drive up beside you, they appear to be going slower.Why does this happen?What impact does the speed of your car have on how fast theother cars appear to be going?If the speed with which you run towards the mirror decreases byhalf, the speed with which the distance between you and yourimage decreases changes by what factor?

Plane Mirrors IIIA ray of light is approaching a set of three mirrors as shown inthe diagram. The light ray is approaching the first mirror at anangle of 45-degrees with the mirror surface.How many times will the ray reflect before it exits the system?A. 1B. 2C. 3D. 445 E. Infinitely many45 45

SolutionAnswer: BJustification: The light reflects twice before it finally exits the system.Draw a normal at the point of incidence to the first mirror; measure theangle of incidence (45 ); then draw a reflected ray at 45 from thenormal. The reflected ray will be parallel to the second mirror, and willnot hit it. The reflected ray will hit the third mirror at an angle of 45 ,and will reflect up and out of the mirror system.45 45 45 45 45 45

Plane Mirrors IVA corner mirror is created when two plane mirrors are connected ata 90 angle. A light ray is incident at an angle, α, to one face of acorner mirror as shown. It reflects off the second mirror and exitsthe systemWhat will the angle of reflection be at the second reflection?A. αB. 45 C. 90 - αD. 90 αPress for hint

SolutionAnswer: AJustification: By the law ofreflection, we know that thefirst ray reflects at an angleof α with the mirror, and thesecond ray is incident at anangle of β with the mirror.Given that the interior anglesof a triangle sum to 180 ,we know thatβ 180 - 90 - α.Therefore the incident and reflectedrays are parallel, and the angle ofreflection at the second mirror is α.ααβαβ 90o - α

Extend your Learning:SimulationTest out various incident rays in a corner reflector.

Extend your Learning:VideoTitle: Astronauts left reflectors and other PooP on the Moon! ft.MinutePhysics

Plane Mirrors VA horizontal light ray strikes a mirror such that the reflected rayis directed at a 60 angle with respect to the horizontal.What is the angle, a, that the mirror makes with the horizontal?A. 60 B. 45 C. 30 60oD. 20 E. Not enough informationa

SolutionAnswer: CJustification: Let’s divide this system into four angles: a, b, c, and d.1. a b (alternate angles)2. b c (opposite angles) a b c3. b d (law of reflection) a b d4. We know that c d 60 We can substitute a c and a d into c d 60 60oc d a a 2a 60 .dDividing both sides by 2, a 30 bac

Plane Mirrors VIA. 1 and 3B. 1 and 4C. 2 and 3A purple star is between two floating barriers, abovea plane mirror, as shown below.From which locations would an observer be able tosee the object?objectE. Not possible21mirrorbarrierbarrierD. All locations34

SolutionAnswer: AJustification: The diagram below depicts the reflections thatwould need to occur for each of the images to exist. The redrays pass directly through a barrier, which is impossible.Images 2 and 4 cannot exist.barrierbarrierobject2341mirrorimage

Solution Cont’dbarrierbarrierobject2134mirrorAnother way to think about this question is to figure out the wholepossible range of space an observer could stand in and still be ableto see the reflection. The blue regions represent the swept-out areasin which incident rays will reflect to the other side of one of thebarriers. In these regions, light rays have not collided with thebarriers. At these locations, an observer would be able to see theimage of the object.

Extend your Learning:VideoTitle: What is Parallax?Where do you observe parallax in everyday life?How can a plane mirror help you overcome parallax?

Plane Mirrors VIIYou are trying to buy a new mirror for your bedroom, and you wantto get one that will allow you to see your entire body at one time.What is the minimum length the mirror must be so that you can seeyour entire body?A. Whole heightB. Three quarter heightC. Half heightD. Quarter heightA. HB. ¾HC. ½HD. ¼H

SolutionAnswer: CJustification: The object andobserver are connected by areflection triangle. The angles ofincidence and reflection are equal. Ifthe object and observer areequidistant from the mirror, anisosceles triangle is created by theincident and reflected rays. The linenormal to the mirror bisects thedistance between the object andobserver. The image is formeddirectly behind the mirror, in line withthe object.ObjectθθObserverThe solution is continued on the next slide.

Solution Cont’dθθWhen you stand in front of a mirror, light bounces from your toeson to the mirror, and then up to your eyes. The light hits the mirrorhalf way between your eyes and your toes.The solution is continued on the next slide.

Solution Cont’dθθIn order to see your whole body, a mirror half your height isneeded.

Extend your Learning:ExperimentFind a mirror and test this out. If you don’t have a full-size mirror, usea smaller one and your head. Mark the top and bottom of yourreflection at a variety of distances from the mirror. What do younotice about the distance between the marks?

Plane Mirrors VIIISandy and Robin are in a pitch black room with a mirror.To see the best image of their faces, they should:A. Shine a light on the mirrorB. Shine a light in any direction in the roomC. Shine the light on their faces

SolutionAnswer: CJustification: Shining the light at the mirror will only createa reflection of the light. Shining a light anywhere in theroom will provide some illumination of their faces. This willcreate a reflected image. However, the best image will beproduced from shining the light directly on their faces.Think about the moon. The reason we can see it so clearlyon Earth is because the sun shines on it directly, and thatlight is reflected back to us.

Extend your Learning:VideoTitle: Future of Invisibility cloaks

Plane Mirrors IXTwo plane mirrors are joined at 90 degrees to create a rightangle mirror.How many images are produced when an object is placedbetween them?A. 1B. 2C. 3D. 4E. Infinitely manyNote: This is one example of an objectlocation, this occurs for all locations.

SolutionAnswer: CJustification: There is one virtual image directly behind each mirror(images 1 and 2). The light entering your eyes that appears to comefrom these images has undergone one reflection.ObjectImage 1ObserverImage 2The solution is continued on the next slide.

Solution Cont’dThe light that enters the eye that appears to come from the centerimage has undergone two reflections, one from each mirror.The third image is created here bythe red rays. Light travels from theobject to the mirror. It then reflects tothe second mirror. Image 3 formsbehind this second reflection.Image 1ObjectObserverAn imaginary line exists between theimage and the object, which passesthrough the vertex of the mirror.Image 2Image 3

Plane Mirrors XAn object (star) is placed in front of one or two mirrors, as seen below,and a number of images are formed in each system.Rank the number of images per system from least to most.12360 A. 1, 2, 3, 4B. 3, 4, 1, 2C. 2, 1, 4, 3D. 2, 3, 4, 1E. 3, 1, 4, 24

SolutionAnswer: BJustification: As we have discussed, a plane mirror produces a singleimage. Only one reflection occurs.When two mirrors are perpendicular to each other, three images areformed. (See previous question.)When two mirrors meet at an angle of 60, five imagesare formed. Four are individual reflections. TheI1fifth is a composite of reflections. I1 and I2 areimages formed by single reflections on each ofthe plane mirrors. I3 was found by reflecting I2across the extension of the top mirror. I4 wasObjectfound by reflecting I1 across the angled mirror.I5 is a composite of reflections from I3 and I4.I3I5I4I2The solution is continued on the next slide.

Solution Cont’dWhen two mirrors are parallel to each other (maybe you have seen thisin an elevator), the image is continuously reflected from mirror to mirror,and an infinite number of images are created.One mirrorTwo mirrors ata right angleTwo mirrors ata 60 angleTwo parallelmirrorsBy angling one of themirrors slightly, the pathof images will curve

Extend Your Learning: BuildLearn how to build your own kaleidoscope here.

Extend Your Learning: AnimateThis online simulator allows you to create and manipulate ananimated kaleidoscope.

Optics: Plane Mirrors Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement Fund 2012-2014 Department of Curriculum and Pedagogy a place of mind F A C U L T Y O F E D U C A T