Optics-Image Formation Lab - University of Michigan



Instructor Outline: Optics-Image Formation UM Physics Demo Lab 07/2013Lab length: 70 minutesLab objective: To instruct the students about geometrical optics: ray tracing and the formation of real and virtual images by a pinhole and a thin converging lens. Also to demonstrate practical instruments based on a single thin lens: light house, slide projector and camera.Materials40-Watt “candle” lamp on wooden basePower stripMesh stand for candle lampCookie sheet pinhole projectorWhite cardboard projection screenDesk lamp with 100 watt soft white bulb (“slide projector” light source)Transparency-film “slide”Hand-held magnifying glassReading glassesCalculator2 Meter sticksClear plastic ruler4 Large binder clips (support legs for pinhole projector and screen)Small rubber bandExploration: 15 minutes - Group Lab WorkThe students first trace three rays from an object through a pinhole and predict that the pinhole should produce an inverted real image. They then observe the images produced by a glowing filament through a small, medium and large pinhole and compare the brightness and focus of the three images. Next they explore the depth of field and magnification by varying the distance of the lamp to the projector.Analysis: 5 minutes – LectureThe concepts of reflection, refraction, refractive index, focal length, depth of field and magnification are discussed. Real and virtual images are also discussed.Exploration: 20 minutes – Group Lab WorkThe students first measure the focal length of a thin converging lens by measuring the image distance for a distant lamp. Next they predict what will happen when they place the lamp near the focal point of the lens and then observe that placing the lamp near the focal point of the lens will project the image of the lamp filament on a distant wall. Finally they design and test a “slide projector” made from a 100 watt desk lamp, a transparency film slide and a magnifier.Analysis: 5 minutes – LectureThe Thin Lens Equation is introduced and related to the thin-lens Exploration results. The f/number and diopter scale are defined.Application: 25 minutes – Group Lab WorkThe students apply the thin lens equation for the magnifying glass with a screen to lamp distance of 1.5 meters and verify that there are two locations that produce an image of the lamp and that the focal length predicted by the thin lens equation is in reasonable agreement with that obtained by measuring the image distance for the distant lamp. Next they compute the f/number and diopter magnification for the magnifying glass and the f/number for a pinhole camera. They then observe that the virtual magnified image of a magnifying glass is produced for objects inside the focal point of the lens. Finally, they measure the diopter magnification for a pair of reading glasses, again using the distant lamp method.Suggested Demos:6A61.10 Pin Hole CameraHome-made shoe box pinhole camera with five-LED flashlight.Concepts developed:The Law of Reflection states that the angle of reflection is equal to the angle of incidence for a reflected ray of light. The angles are defined with respect to the direction perpendicular to the reflecting surface called the normal.Images where the light actually emanates from the location of the image are called real images. Images where the light only appears to emanate from the image location but does not actually do so are called virtual images. The image of a lamp filament projected by a thin converging lens is real. The image in a plane mirror is virtual.Ray tracing demonstrates that pinholes can produce an inverted, real image. Small pinholes produce well focused, dim images. Large pinholes produce bright, poorly focused images. The depth of field for a point pinhole is infinite, and real pinholes have a very large depth of field. The f/number of a pinhole or lens is defined as the ratio of its focal length to its diameter. The focal length of a pinhole is the distance from the pinhole to the image screen. A true pinhole (geometric point) therefore has an “infinite” f/number (f/∞) (owing to a zero diameter) and real pinholes have very large f/numbers. Convex lenses can focus parallel light rays to a common focal point and can therefore produce real images. Concave lenses always produce diverging rays and can only produce virtual images.The speed of light in a material such as glass, water or plastic is slower than it is in vacuum. The ratio of (speed of light in vacuum)/(speed of light in matter) is called the refractive index of the material.The direction of a light ray changes as it enters a material with a higher refractive index such that its angle with the normal decreases. This is how lenses change the direction of light rays and is described by Snell’s Law.The Thin Lens Equation relates the image distance (i), object distance (o) and focal length (f) for a thin lens and is stated as: 1/i + 1/o = 1/f. This equation predicts that light from very distant objects (0→∞) will converge to form a real image at the focal point of a converging lens and that interchanging the image and object distances will again result in a focused image. It also predicts that an object placed at the focal point of the lens (o=f) will project an image “to infinity” (1/i→0 so i→∞), that is, to a very distant screen (slide projector). Real images produced by a thin converging lens are inverted (“upside-down”) Objects viewed with image distances less than the focal length of the lens will produce an upright (“right-side-up”) virtual image of the object—this how a converging lens is used as a “magnifying glass”. The thin lens equation also works for diverging lenses which have a negative focal length.The magnification for any thin lens or pinhole is defined as –(i/o) where the minus sign predicts that real images are inverted and virtual images (which have negative image distances) are upright.The speed of light, and hence the index of refraction, is different in optical materials such as glass or plastic for different wavelengths of light. This effect is called dispersion. Blue light (short wavelength) is refracted (bent toward the normal) more than red light (long wavelength). This is how a prism separates white light into its component colors. ................
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