PLANE MIRRORS. The simplest mirror is a plane mirror a flat, reflective surface, often consisting of a metal film covered in glass. 4/2/2018.

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1 4/2/208 UNIT 6 Geometri and physial optis AP PHYSICS 2 PLANE MIRRORS CHAPTER 22 Mirrors and lenses Plane mirrors The simplest mirror is a plane mirror a lat, reletive surae, oten onsisting o a metal ilm overed in glass. objet s s image Plane mirrors Plane mirror virtual image The image o the real objet seen in the mirror is loated where light releted rom the mirror to the eye o the observer seems to originate. This pereived image is behind the mirror and not on the surae o the mirror. Using the ray diagram, we ind that the image is exatly the same distane behind the plane mirror as the objet is in ront o it. A plane mirror produed a virtual image that is the same distane behind the mirror as the objet is in rom o it. VIRTUAL: The releted light reahing your eyes appears to originate rom the image behind the mirror. But no light atually leaves that image, you see light releted rom the mirror.

2 4/2/208 What does the image look like? The virtual image ormed by a plane mirror will be: The same size as the objet. Equidistant rom the mirror perpendiularly. Flipped let-to-right relative to the objet (mirror image) S S ASSUMPTION Treat your objets like a straight line, just or the sake o simpliying the physis. Avoid any details beyond distane between mirror and objet/image, and height o the objet/image. S S h h h h objet virtual image objet virtual image mirror mirror CURVED MIRRORS CURVED MIRRORS A urved mirror is ut rom a spherially shaped piee o glass baked by a metal ilm. Due to its geometry, a irularly urved mirror has a oal length that is one hal o its radius o urvature. normal Foal length (), is the distane between the enter o the mirror and the oal point. = 2 Law o reletion: Normal line is an extension o the radius o the irle. Thereore the enter o urvature will show you where to draw the normal line when a ray relets rom a urved mirror! 2

3 4/2/208 CONCAVE MIRROR normal Foal length Center o urvature Foal point Any ray o light parallel to the main axis, will relet through the oal point. Prinipal Rays (or Guiding Rays) Although there are essentially an ininite number o rays emanating rom the objet, we an use three prinipal rays to help us determine the loation o an image produed by a urved mirror. F-ray CONCAVE MIRROR C-ray P-ray Inverted Redued Real Real Images Rather than a virtual image (whih is ormed by virtual rays), a real image is ormed by real rays! It an only be produed by a onave mirror, and only i the objet is urther than the oal point. Sine the image is ormed by atual rays o light in ront o the mirror, it an be projeted onto a sreen. Image orientation: Upright, inverted IMAGE FINDINGS Image size: Enlarged, redued, same size Image type: Real, virtual You need to see it to believe it. 3

4 4/2/208 THE MIRROR EQUATION MAGNIFICATION + = Foal length is POSITIVE or onave mirrors. I S is negative, image is virtual Ratio o the image height (h ) and objet height (h) = CURVED MIRRORS VOCABULARY - oal length - enter o urvature s - distane rom the objet to the mirror. s - distane rom the image to the mirror. h - height o the objet. h - height o the image. m - magniiation o the image Convex mirrors are used as passengerside rearview mirrors and to provide visibility at blind spots, suh as hallway orners and driveway exits. Convex mirrors CONVEX MIRROR CONVEX MIRROR P-ray Center o urvature F-ray C-ray Foal point Upright Redued Virtual 4

5 4/2/208 THE MIRROR EQUATION + = Foal length is NEGATIVE or onvex mirrors. I S is negative, image is virtual WHITEBOARD Conave Mirror Assume a onave mirror ( = 2 m) Mirror : S = 3 Mirror 2: S = 2 Mirror 3: S =.5 Mirror 4: S = Mirror 5: S = /2 Assume h = 8 m Find: S, M, & h Determine: Image orientation: Image size: Image type: Conave Mirrors: Summary Objet Loation Image Orientation Image Size Image Type Beyond Inverted Redued Real At Inverted Same as objet Real Between and Inverted Enlarged Real At No image No image No image Closer than Upright Enlarged Virtual I the objet is urther than, the image will be inverted and real. I the objet is loser than, the image will be upright and virtual. WHITEBOARD Convex Mirror Assume a onvex mirror ( = 2 m) Mirror : S = 3 Mirror 2: S = 2 Mirror 3: S =.5 Mirror 4: S = Mirror 5: S = /2 Assume h = 8 m Find: S, M, & h Determine: Image orientation: Image size: Image type: Convex Mirrors: Summary Objet Loation Image Orientation Image Size Image Type Anywhere Upright Redued Virtual This is why onvex mirrors are used or seeing large areas at one! Real vs Virtual Images Real images are ormed by atual light rays (not virtual rays). They are able to be seen diretly with the human eye, and an also be projeted onto a sreen! Virtual images are ormed by virtual rays. A virtual image is the appearane o light originating rom a ertain loation, although the light never atually did (it was redireted by a mirror or lens to look like it did!) When a virtual image is ormed, it an be seen by the human eye. However, it annot be projeted onto a sreen! 5

6 4/2/208 Qualitative analysis o lenses LENSES A lens is a piee o glass or other transparent material with two urved suraes that produes images o objets by hanging the diretion o light through reration. CONVEX LENS CONVEX LENS Center o urvature Foal point A onvex lens made o glass is similar to a onave mirror where inident rays parallel to the prinipal axis interset at a oal point ater passing through the lens. How the rays onverge depends on the urvature o the surae o the lens. CONVEX LENS Seeing a sharp image on a sreen A sreen must be plaed where the image is loated to view a sharp image. F-ray C-ray P-ray Inverted Redued Real 6

7 4/2/208 Photography and ameras Light ield photography Light rom an objet enters the amera through the lens, whih ouses the light on a surae that has lightsensitive properties (an image sensor). In light ield photography, the image sensor reords all the light entering the amera, not just the light that would produe a sharp image on the oal plane. A photographer an hoose an objet to ous on ater the piture has been taken, beause the amera eetively ouses on all objets at one. CONCAVE LENS CONCAVE LENS Center o urvature For onave lenses, light seems to diverge rom a single point on the axis the virtual oal point. Foal point Foal point CONCAVE LENS THIN LENS EQUATION P-ray A thin lens has a radii o urvature muh larger than the size o the lens. F-ray C-ray Upright Redued Virtual + = 7

8 4/2/208 THIN LENS EQUATION The oal length is positive or onvex lenses and negative or onave lenses. The image distane s is positive or real images and negative or virtual images. Linear magniiation in lenses Lenses an produe images that are larger or smaller in size than the original objets. = Objets ar away rom the lens I an objet is extremely ar away along the prinipal axis, we an assume that rays rom the objet reahing the lens are parallel to the prinipal axis. Convex Lenses: Summary Objet Loation Image Orientation Image Size Image Type Beyond Inverted Redued Real At Inverted Same as objet Real Between and Inverted Enlarged Real At No image No image No image Closer than Upright Enlarged Virtual This is the same as or a onave mirror! This is why onvex lenses held lose to an objet make good magniying glasses! Conave Lenses: Summary Lenses with water Objet Loation Image Orientation Image Size Image Type Anywhere Upright Redued Virtual This is the same as or a onvex mirror! 8

9 4/2/208 APPLICATIONS OF CONVEX LENSES APPLICATIONS OF CONVEX & CONCAVE LENSES What do you need to do to see a virtual image? (reated by a lens) Look through the lens! Optis o the human eye Light rom an objet enters the ornea and passes through a transparent lens. An iris in ront o the lens widens or narrows, like the aperture on a amera that regulates the amount o light entering the devie. The retina plays the role o the ilm. Optis o the human eye When the eye looks at distant objets, musles around the lens o the eye relax, and the lens beomes less urved. As the objet moves loser, the eye musles ontrat, inreasing the urvature o the lens and reduing the oal length. Corretive lenses: nearsightedness myopia (nearsightedness) hyperopia (arsightedness). 9

10 4/2/208 Corretive lenses: arsightedness myopia (nearsightedness) LENSES PRACTICE hyperopia (arsightedness). Coneptual Exerise 22. Coneptual Exerise 22.3 You plae a lamp in ront o a mirror and tilt it so that the top and the bottom o the lamp are at dierent distanes rom the mirror, at the position shown. Where do you see the image o the lamp produed by the mirror? You hold a onvex mirror 0.7R behind a penil. A. Approximately where is the image o the penil? B. What are the properties o the image? Example 22.4 Example 22.5 You plae a andle 0.80 m rom a onave mirror with a radius o urvature o 0.60 m. Where should you plae a paper sreen to see a sharp image o the andle? S + S = S = A riend's ae is 0.60 m rom a onvex mirror with a 0.50-m radius. Where does the image o her ae appear to you when you look at the mirror? S + S = S = S = S S = 0.48 m S = S S = 0.76 m 0

11 4/2/208 Example 22.6 You use a onave mirror with a radius o urvature o 0.32 m or putting on makeup or shaving. When your ae is 0.08 m rom the mirror, what are the image size and magniiation o a m-diameter birthmark on your ae? S + S = S = S S = S = 0.6 m m = S S m = m = 2 h = m h h = h = m h = 0.6 m Upright Enlarged Virtual WHITEBOARD - LENSES You take a piture o a arpenter ant with an old ashioned amera with a lens 8 m rom the ilm. a) At what plaes an the 4.0 m oal length onvex amera lens be loated so you see a sharp image o the ant on the ilm? b) What is the magniiation o the ant? ) I the length o the arpenter ant is 2.5 m, what is the size o the image? S + S = S = S S = 4 8 S = 5.4 m m = S S m = m = 3.5 h = m h h = h = 8.75 m Inverted Enlarged Real WHITEBOARD - LENSES WHITEBOARD - LENSES A seret agent uses a amera with 5 m oal length lens to photograph a doument whose height is 0 m. a) What is the magniiation so that an image 2.5 m high is produed on the sreen? (note: the real image is inverted) b) At what distane rom the lens should the agent hold the amera? A 20 m tall bottle o water is plaed in ront o onave lens o oal length 30 m. a) At what distane must the bottle o water be plaed so the image will be virtual and 0.25 times the original size? b) What is the distane to the image? ) what is the height o the image? a)m=-0.25, b) s=25 m a)s=90 m, S =-22.5 m, h =5 m

12 4/2/208 WHITEBOARD - LENSES 2 LENS APPLICATION - TELESCOPE You use a onvex lens o oal length +0.0 m to look at a tiny inset on a book page. The lens is 5.0 m rom the paper. A. Where is the image o the inset? B. I the inset is.0 m in size, how large is the image? A ommon telesope has two onvex lenses separated by a distane slightly less than the sum o their oal lengths. a)s =-0 m, B) m=2, h =2 m The irst lens reates an real image o the distant objet. The seond lens takes the image reated by the irst lens as the objet and reates a virtual and enlarged image o the original objet WHITEBOARD I - TELESCOPES A.2-m-tall lion stands 50 m rom the irst lens o a telesope. Loate the image o the Lion reated by the irst lens (=20 m). Image Findings S + S = S = S m = S S m = Inverted Redued Real S = m = h = m h S = m h = h = 0.48 m WHITEBOARD II - TELESCOPES A.2-m-tall lion stands 50 m rom the irst lens o a telesope. Loate the NEW image o the Lion reated by the seond lens (=5 m). Image, magniiation, height o the image. Lenses are separated 8 m New Lens S = 24.5 m m S = 4. 42m S + S = S = S S = S = 38.0 m m = S S m = m = 8.62 h = m h upright Enlarged Virtual h = m h = 4.5 m 2

13 4/2/208 2 LENS APPLICATION - MICROSCOPE A ommon telesope has two onvex lenses separated by a small distane. The irst lens produes an inverted, enlarged, and real image o a small objet. The seond lens takes the image reated by the irst lens as the objet and reates a virtual and enlarged image o the original objet. WHITEBOARD I - MICROSCOPES A ompound mirosope has an objetive lens o oal length 0.80 m and an eye piee o oal length.25 m. The lenses are separated by 8 m. i a red blood ell is loated 0.84 m in ront o the objetive lens. Loate the image o the ell reated by the irst lens. Image Findings S + S = S = S S = S = 6.8 m m = S S m = m = 2 upright Enlarged Real Lenses are separated 8 m New Lens S = 8 m 6.8 m S =. 2 m WHITEBOARD II - MICROSCOPES A ompound mirosope has an objetive lens o oal length 0.80 m and an eye piee o oal length.25 m. The lenses are separated by 8 m. i a red blood ell is loated 0.84 m in ront o the objetive lens. Loate the image o the ell reated by the seond lens. Image Findings S + S = S = S S =.25.2 m = S S m = 30.2 m = 25 Inverted Enlarged Virtual S = 30 3