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4/5/2017 AP PHYSICS 2 PLANE MIRRORS UNIT 6 Geometric and physical optics CHAPTER 22 Mirrors and lenses Plane mirrors The simplest mirror is a plane mirror—a flat, reflective surface, often consisting of a metal film covered in glass. Plane mirrors s s’ PLANE MIRROR The image of the real object seen in the mirror is located where light reflected from the mirror to the eye of the observer seems to originate. This perceived image is behind the mirror and not on the surface of the mirror. Using the ray diagram, we find that the image is exactly the same distance behind the plane mirror as the object is in front of it. 1 4/5/2017 Plane mirror virtual image What does the image look like? The virtual image formed by a plane mirror will be A plane mirror produced a virtual image that is the same distance behind the mirror as the object is in from of it. The same size as the object. Equidistant from the mirror perpendicularly. Flipped left-to-right relative to the object (mirror image) S S’ VIRTUAL: The reflected light reaching your eyes appears to originate from the image behind the mirror. But no light actually leaves that image, you see light h h’ object virtual image mirror reflected from the mirror. CURVED MIRRORS CURVED MIRRORS A curved mirror is cut from a spherically shaped piece of glass backed by a metal film. CONCAVE MIRROR Focal length Center of curvature Due to its geometry, a circularly curved mirror has a focal length that is one half of its radius of curvature. 𝑐 𝑓= 2 Focal point f c 2 4/5/2017 Principal Rays (or Guiding Rays) normal f Although there are essentially an infinite number of rays emanating from the object, we can use three principal rays to help us determine the location of an image produced by a curved mirror. c And don’t forget, the center of curvature will show you where to draw the normal line when a ray reflects from a curved mirror! c CONCAVE MIRROR f Real Images Rather than a virtual image (which is formed by virtual rays), a real image is formed by real rays! F-ray C-ray P-ray Inverted Reduced Real It can only be produced by a concave mirror, and only if the object is further than the focal point. Since the image is formed by actual rays of light in front of the mirror, it can be projected onto a screen. You need to see it to believe it. Convex mirrors Convex mirrors are used as passengerside rearview mirrors and to provide visibility at blind spots, such as hallway corners and driveway exits. CONVEX MIRROR Center of curvature Focal point 3 4/5/2017 CONVEX MIRROR P-ray F-ray C-ray Upright Reduced Virtual THE MIRROR EQUATION CURVED MIRRORS VOCABULARY f - focal length c - center of curvature s - distance from the object to the mirror. s’ - distance from the image to the mirror. h - height of the object. h’ - height of the image. m - magnification of the image THE MIRROR EQUATION The focal length is positive for concave mirrors and negative for convex mirrors. + = MAGNIFICATION • Ratio of the image height (h’) and object height (h) The image distance is positive for real images and negative for virtual images. IMAGE FINDINGS Image orientation: Upright, inverted Image size: Enlarged, reduced, same size = Image type: Real, virtual 4 4/5/2017 Concave Mirrors: Summary Convex Mirrors: Summary Object Location Image Orientation Image Size Image Type Beyond c Inverted Reduced Real Object Location Image Orientation Image Size Image Type At c Inverted Same as object Real Anywhere Upright Reduced Virtual Between c and f Inverted Enlarged Real At f No image No image No image Closer than f Upright Enlarged Virtual This is why convex mirrors are used for seeing large areas at once! If the object is further than f, the image will be inverted and real. If the object is closer than f, the image will be upright and virtual. Real vs Virtual Images Real images are formed by actual light rays (not virtual rays). They are able to be seen directly with the human eye, and can also be projected onto a screen! LENSES Virtual images are formed by virtual rays. A virtual image is the appearance of light originating from a certain location, although the light never actually did (it was redirected by a mirror or lens to look like it did!) When a virtual image is formed, it can be seen by the human eye. However, it cannot be projected onto a screen! Qualitative analysis of lenses A lens is a piece of glass or other transparent material with two curved surfaces that produces images of objects by changing the direction of light through refraction. CONVEX LENS Center of curvature Focal point 5 4/5/2017 CONVEX LENS A convex lens made of glass is similar to a concave mirror where incident rays parallel to the principal axis intersect at a focal point after passing through the lens. How the rays converge depends on the curvature of the surface of the lens. CONVEX LENS F-ray Inverted Reduced Real P-ray Photography and cameras Light from an object enters the camera through the lens, which focuses the light on a surface that has lightsensitive properties (an image sensor). Light field photography In light field photography, the image sensor records all the light entering the camera, not just the light that would produce a sharp image on the focal plane. A photographer can choose an object to focus on after the picture has been taken, because the camera effectively focuses on all objects at once. c f C-ray Seeing a sharp image on a screen A screen must be placed where the image is located to view a sharp image. f c CONCAVE LENS Center of curvature Focal point Focal point 6 4/5/2017 CONCAVE LENS CONCAVE LENS For concave lenses, light seems to diverge from a single point on the axis—the virtual focal point. P-ray F-ray C-ray THIN LENS EQUATION c f f c Upright Reduced Virtual THIN LENS EQUATION A thin lens has a radii of curvature much larger than the size of the lens. The focal length f is positive for convex lenses and negative for concave lenses. The image distance s’ is positive for real images and negative for virtual images. = + Linear magnification in lenses Lenses can produce images that are larger or smaller in size than the original objects. = Objects far away from the lens If an object is extremely far away along the principal axis, we can assume that rays from the object reaching the lens are parallel to the principal axis. 7 4/5/2017 Convex Lenses: Summary Concave Lenses: Summary Object Location Image Orientation Image Size Image Type Beyond c Inverted Reduced Real Object Location Image Orientation Image Size Image Type At c Inverted Same as object Real Anywhere Upright Reduced Virtual Between c and f Inverted Enlarged Real At f No image No image No image Closer than f Upright Enlarged Virtual This is the same as for a convex mirror! This is the same as for a concave mirror! Converging lenses and converging mirrors have the same image properties. This is why convex lenses held close to an object make good magnifying glasses! Diverging lenses and diverging mirrors have the same image properties. Lenses with water Ray diagrams for various lenses Ray diagrams for various lenses Optics of the human eye Light from an object enters the cornea and passes through a transparent lens. An iris in front of the lens widens or narrows, like the aperture on a camera that regulates the amount of light entering the device. The retina plays the role of the film. 8 4/5/2017 Optics of the human eye When the eye looks at distant objects, muscles around the lens of the eye relax, and the lens becomes less curved. As the object moves closer, the eye muscles contract, increasing the curvature of the lens and reducing the focal length. Corrective lenses The two most common vision abnormalities corrected with lenses are myopia (nearsightedness) and hyperopia (farsightedness). Corrective lenses (Cont'd) LENSES PRACTICE Conceptual Exercise 22.1 You place a lamp in front of a mirror and tilt it so that the top and the bottom of the lamp are at different distances from the mirror, at the position shown. Where do you see the image of the lamp produced by the mirror? Conceptual Exercise 22.3 You hold a convex mirror 0.7R behind a pencil. A. Approximately where is the image of the pencil? B. What are the properties of the image? 9 4/5/2017 Example 22.4 You place a candle 0.80 m from a concave mirror with a radius of curvature of 0.60 m. Where should you place a paper screen to see a sharp image of the candle? Example 22.5 A friend's face is 0.60 m from a convex mirror with a 0.50-m radius. Where does the image of her face appear to you when you look at the mirror? 1 1 1 + = 𝑆 𝑆′ 𝑓 1 1 1 = − 𝑆′ 0.3 0.8 1 1 1 + = 𝑆 𝑆′ 𝑓 1 1 1 = − 𝑆′ −0.25 0.6 1 1 1 = − 𝑆′ 𝑓 𝑆 𝑆 ′ = 0.48 𝑚 1 1 1 = − 𝑆′ 𝑓 𝑆 𝑆 ′ = −0.176 𝑚 Example 22.6 You use a concave mirror with a radius of curvature of 0.32 m for putting on makeup or shaving. When your face is 0.08 m from the mirror, what are the image size and magnification of a 0.0030-m-diameter birthmark on your face? 1 1 1 + = 𝑆 𝑆′ 𝑓 1 1 1 = − 𝑆′ 0.16 0.08 1 1 1 = − 𝑆′ 𝑓 𝑆 𝑆 ′ = −0.16 𝑚 WHITEBOARD - LENSES You take a picture of a carpenter ant with an old fashioned camera with a lens 18 cm from the film. a) At what places can the 4.0 cm focal length convex camera lens be located so you see a sharp image of the ant on the film? b) What is the magnification of the ant? c) If the length of the carpenter ant is 2.5 cm, what is the size of the image? Upright Enlarged Virtual 𝑆′ 𝑚=− 𝑆 𝑚=− −0.16′ 0.08 h′ = 𝑚 ∙ ℎ 𝑚=2 h′ = 2 ∗ 0.003 ℎ′ = 0.006 𝑚 ℎ′ = 0.6 𝑐𝑚 1 1 1 + = 𝑆 𝑆′ 𝑓 1 1 1 = − 𝑆 𝑓 𝑆′ 1 1 1 = − 𝑆 4 18 𝑆 = 5.14 𝑐𝑚 𝑚=− 𝑆′ 𝑆 𝑚=− 18 5.14 Inverted Enlarged Real 𝑚 = −3.5 h′ = 𝑚 ∙ ℎ h′ = −3.5 ∗ 2.5 ℎ′ = −8.75 𝑐𝑚 10 4/5/2017 WHITEBOARD - LENSES A secret agent uses a camera with 5 cm focal length lens to photograph a document whose height is 10 cm. a) What is the magnification so that an image 2.5 cm high is produced on the screen? (note: the real image is inverted) b) At what distance from the lens should the agent hold the camera? a)m=-0.25, b) s=25 cm WHITEBOARD - LENSES A 20 cm tall bottle of water is placed in front of concave lens of focal length 30 cm. a) At what distance must the bottle of water be placed so the image will be virtual and 0.25 times the original size? b) What is the distance to the image? c) what is the height of the image? a)S=90 cm, S’=-22.5 cm, h’=5 cm WHITEBOARD - LENSES You use a convex lens of focal length +10.0 cm to look at a tiny insect on a book page. The lens is 5.0 cm from the paper. A. Where is the image of the insect? B. If the insect is 1.0 cm in size, how large is the image? Telescopes A common telescope has two convex lenses separated by a distance slightly less than the sum of their focal lengths. a)S’=-10 cm, B) m=2, h’=2 cm WHITEBOARD - TELESCOPES A 1.2-m-tall lion stands 50 m from the first lens of a telescope. Locate the image of the Lion created by the first lens (f=20 cm). Image, magnification, height of the image. 1 1 1 + = 𝑆 𝑆′ 𝑓 1 1 1 = − 𝑆′ 𝑓 𝑆 1 1 1 = − 𝑆′ 20 5000 𝑆 ′ = 20.08 𝑐𝑚 𝑚=− 𝑆′ 𝑆 𝑚=− 20.08′ 5000 Inverted Reduced Real 𝑚 = −0.004 h′ = 𝑚 ∙ ℎ h′ = −0.004 ∗ 120 ℎ′ = 0.48 𝑐𝑚 11 4/5/2017 WHITEBOARD - TELESCOPES A 1.2-m-tall lion stands 50 m from the first lens of a telescope. Locate the NEW image of the Lion created by the second lens (f=5 cm). Image, magnification, height of the image. 1 1 1 + = 𝑆 𝑆′ 𝑓 𝑚=− 𝑆′ 𝑆 1 1 1 = − 𝑆′ 𝑓 𝑆 𝑚=− −38.10′ 4.42 1 1 1 = − 𝑆′ 5 4.42 𝑚 = 8.62 𝑆 ′ = −38.10 𝑐𝑚 WHITEBOARD - TELESCOPES LENS 1 LENS 2 S = 5000 cm F = 20 cm S’ =20.08 cm S = 4.42 cm F = 5 cm S’ =-38.1 cm m = -0.004 h = 120 cm h’ = 0.482 cm m = 8.62 h = 0.482 cm h’ = 4.155 cm Angular magnification The angular magnification M of an optical system is defined as: upright Enlarged Virtual h′ = 𝑚 ∙ ℎ h′ = 8.62 ∗ 0.48 cm ℎ′ = 4.15 𝑐𝑚 Angular magnification and magnifying glasses The impression of an object's size is quantified by its angular size: Angular size of the object as seen with the unaided eye The maximum angular size of an object viewed by the unaided eye is: 12