ࡱ> UWTy` ,@jbjb dd:*8$*D*`z"******>@@@@@@,'Ry!~l*****l*********>*r*>***n 3***0*!*!******Experiment #10: Mirrors And Lenses I. INTRODUCTION Light is an electromagnetic wave just like radio waves, microwaves, T.V. signals, and waves produced by our audio generator. The difference is that light is of very high frequency, and is visible to earthlings! Since it is visible, we use optical elements such as mirrors and lenses to manipulate and study light, in contrast to the way we used resistors, capacitors, and the oscilloscope to control and study other types of signals. In this lab, we will explore some important properties of mirrors and lenses as fundamental optical components. II. MIRRORS Flat or Plane mirrors are common in our daily lives. They reflect light without changing the relative orientation or size of the object being reflected. What is changed is the apparent location of the original object. An image that is formed appears to be virtually as far behind the mirror as the object is in front of it. We all, generally, realize that when we look in the mirror our head is still on our shoulders and not inside the wall or mirror. Locating, and describing, image formations is a very important aspect of optics, and the main thrust of this lab.  Fig. 1. A Concave Mirror and the Focal Point Usually optical elements are curved rather than flat. Spherical curvature of mirrors is common and useful. A mirror that bulges inward is called a concave mirror. These mirrors are used in some cosmetic kits and reflecting telescopes. An outwardly bulging mirror is termed a convex mirror and is commonly used for car and truck side mirrors, usually labeled, "Objects are closer than they appear." (Remember the great T-Rex chase scene in Jurassic Park ?) The surface of a spherical mirror is a small section of a large sphere, and therefore, has a center of curvature (C). The distance from C to the mirror along the axis is the radius of curvature (R). Figure 1 shows a concave mirror. The focal length (f), is the characteristic parameter of a lens or mirror. It is a measure of the converging or diverging power of the optical element. It describes the distance required for the lens or mirror to direct, or "focus", light rays incident parallel to the mirror's axis to a point. This point is called the focal point (F). Conversely, a point source of light rays located at the focal point will be converted to parallel or collimated light. The focal length f of a spherical mirror is defined as: f =  EQ \F(R,2)  Warning: This relationship does not hold for lenses. Having an object or an image exactly at the focal point is a special case of the many possible locations. However, the focal length remains the characteristic parameter of the way a lens or mirror operates on the rays from an object placed at any location, since it describes the converging or diverging strength of the optical element. Diagrams of the interaction between light and elements such as lenses or mirrors, often use ray diagrams, such as that in Figure 2.  EMBED Word.Picture.6  Figure 2. A Real Image Produced By A Concave Mirror Rays of light from the object interact with the mirror surface, and then travel off to form the image. Note that there are an infinite number of rays from the object, but we have chosen two specific ones for use in our ray diagram. These two special rays follow the definition of the focal length, and make it easy for us to locate the image. Ray 1 is incident parallel to the axis and therefore gets directed through the focal point by the mirror. Ray 2 is incident through the focal point and must be reflected parallel to the axis by the mirror. The location at which these two rays intersect is where the image lies. In fact, all of the rays emanating from each point on the object are brought into focus at this location. The location of the object relative to the mirror is represented by the variable p, and the image distance is the variable q. Equation 1 shows the relationship between p, q, and f. (1)  EQ \F(1,p) +  EQ \F(1,q) =  EQ \F(1,f)  Knowledge of any two of these variables gives us the third. Once we know these parameters, we can gain information as to what modifications were introduced by the mirror in forming the image. The magnification (m) refers to the relative size of the image with respect to the object, i.e.: magnification, by definition, is =  EQ \F(size of the image,size of the object)  A very useful theoretical formula for magnification is: (2) m = -  EQ \F(q,p)  Values of m greater than 1 indicate that the image is larger (magnified) than the object and for values of m less than 1 the image has been minified (made smaller). The sign of m is dependent on the signs of p and q, and tells if the image is erect (the same direction) or inverted with respect to the objects orientation. A positive m indicates an erect image, and a negative m says that the image is inverted. Some sign conventions and definitions that must be introduced: (1) The focal length f is positive (+) for a concave mirror and negative (-) for a convex mirror. (2) p and q are positive (+) for real objects and real images, and they are negative (-) for virtual objects and virtual images. A real image is defined as one in which the rays physically converge to a particular location, thus forming a real focused image. The image formed by the converging lens in Figure 2 is real because the rays intersect the space. In the lab you can locate a real image by using a screen to find where they rays come into focus. It is important to note that the light rays do not somehow end at the point where the image is "in focus", but continue to travel through space representing that image. Indeed, when we see an image, or an object for that matter, we are seeing the rays propagating away from it. A virtual image is defined as one in which the rays do not physically converge to a particular location, but instead diverge as if they were coming from a focused image. Consider the image formed by the diverging lens in Figure 3.  Figure 3. A Virtual Image Produced By A Convex Mirror Since the mirror reflects all incident light rays, none can exist on the right side of Figure 3. Although no rays can physically pass through the focal point of a diverging lens, we can still make use of the definition of the focal length to locate and describe the image in a ray diagram. Ray 1 is incident parallel onto the mirror and upon reflection it gets diverged as if it had been physically directed through the focal point. Ray 2 is incident directly towards the focal point, and gets reflected parallel to the axis just as the ray incident through the focal point in Figure 2 did. These rays will never intersect. However, they propagate as if they were coming from an image on the right side of the mirror exactly the same way the mirror in the bathroom presents an image of your face that appears to be behind the glass surface. To locate the image in the diagram we simply trace the path of the reflected rays back to the point where they intersect, to a point where a real image cannot be formed, but a virtual image can. Now we can use equations 1 and 2, along with careful use of the sign conventions, to quantitatively describe the image. III. LENSES A large part of the previous discussion can be applied to the treatment of lenses. The primary differences are that lenses transmit and refract light rather than reflect it. Lenses have spherical curved surfaces and either converge or diverge incident light. A converging lens will direct collimated incident light through the focal point, and a diverging lens will diverge collimated incident light as if it were coming directly from the focal point on the incident side of the lens. See Figure 4. A lens has an equivalent focal point on each side where for a mirror there was only one. This simply indicates that a lens will transmit in either direction with the same properties, where a mirror can only operate on light incident from one side.  Figure 4. Convex and Concave Lenses and their Focal Lengths For many lenses, including those that we will use, we can neglect the thickness and apply the thin lens formula to relate object and image locations to the focal length of the lens. Interestingly this is the same formula that applied to mirrors:  EQ \F(1,p) +  EQ \F(1,q) =  EQ \F(1,f)  With the following, similar sign conventions: 1) f is positive (+) for a converging lens and negative (-) for a diverging lens. 2) p and q are positive for real objects and images and negative for virtual objects and images. As was the case for mirrors, an image is described as either erect or inverted, magnified or minified, and real or virtual. These terms are defined in the same way as before and the equation for the magnification is the same: m = -  EQ \F(q,p)  Figure 5 shows a ray diagram for a common use of a converging lens. Note that a real, inverted image is formed.  Figure 5. Real Image Produced By a Convex Lens IV. PROCEDURE: (GROUP WRITE-UP) Equipment: Two convex lenses of different focal lengths (approx. 5 cm. to 10 cm.), One concave mirror (approx. focal length 10 to 20 cm.), Optical bench, with Optical mounts, Light bulb source unit, Viewing screen. A. Lens optics: Perform steps 1 through 7 on two lenses of different focal lengths. 1. Selection of Lenses One can get a rough idea of the approximate focal length of lenses by using the following simple technique. Hold the lens with your thumb and index finger by the edges so that it is parallel to the ceiling, directly below an operating light fixture and about waist high. Hold a piece of paper directly below and parallel to it. Move the lens, or the piece of paper, vertically up and down until you see a roughly focused image of the light fixture on the paper. The distance between that image and the lens is approximately the focal length (f ). You are looking for lenses with two different focal lengths differing by a factor of at least two, in a range from approx. 5 cm. to approximately 10 cm. 2. Measurement of Focal Lengths Place the light source (object) at one end of the bench. Place the screen near the other end of the bench. Place the shorter focal length lens, installed in a lens mount, on the bench between the object and the screen. Starting with the lens near to the object, experimentally locate it to produce a focused image on the screen. Using your experimentally determined values for p and q, and the thin lens equation, calculate the focal length of the lens. Starting with the lens near to the screen, repeat the steps above. Repeat the procedure with the longer focal length lens. First Lens Tested p _________ q _________ f _________ (Shorter focal length lens.) First Lens Tested p _________ q _________ f _________ (Shorter focal length lens.) Second Lens Tested p _________ q _________ f _________ (Longer focal length lens) Second Lens Tested p _________ q _________ f _________ (Longer focal length lens) 3. Description of Images Describe the images produced in Step 2 as erect or inverted, real or virtual, and magnified or minified. Justify your conclusions. First Lens: _______________________________________________ _______________________________________________ _______________________________________________ Second Lens: _______________________________________________ _______________________________________________ _______________________________________________ 4. Theoretical Calculations of Image Distance (q) Using your experimental values of f from Step #2, calculate the theoretical values of q, if the lens is located a distance 3/2 f from the object. 1st Lens: p = 3/2 f _____ Theoretical q _____ 2nd Lens: p = 3/2 f _____ Theoretical q _____ 5. Experimental Determination of Image Distance (q) Place the lens a distance p = 3/2 f from the object. Move the viewing screen to experimentally determine the value of q. 1st Lens: p = 3/2 f _____ Experimental q _____ 2nd Lens: p = 3/2 f _____ Experimental q _____ Question 1: How do your results from Steps 4 and 5 compare? ____________________________________________________________________________________________________________________________________________________________________________________ 6. Theoretical Calculations of Image Magnification Using your experimental data from Step 5, calculate the theoretical magnification of the object. First Lens: Theoretical Magn. _______________________________ Second Lens: Theoretical Magn. _______________________________ 7. Experimental Determination of Image Magnification Returning to the distances for p and q in Step 5, as needed, measure and record the lengths of the object arrows and the image arrows. Calculate the experimental magnification. First Lens: Object Arrow: ________ Image Arrow: ________ Second Lens: Object Arrow: ________ Image Arrow: ________ First Lens: Experimental Magn. _____________________________ Second Lens: Experimental Magn. _____________________________ Question 2: How do your results from Steps 6 and 7 compare? ____________________________________________________________________________________________________________________________________________________________________________________ B. Mirror Optics: Experimental Measurement of Focal Length 1. Take the larger diameter of the two lenses that you worked with above, and place it a distance exactly equal to f from the object. Question 3: What does this do to the light that is transmitted from the object through the lens? ____________________________________________________________ ________________________________________________________________________________________________________________________ 2. Place the concave mirror about 40 cm away from the lens. Tilt it slightly so that the reflection is not directly back down the axis, this allows viewing of the reflected image. 3. Determine the focal length of the mirror by using a piece of paper to locate the image produced by the mirror. 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Page NumberJOJ times^``dh pCJEH,:(  Dz Ez Fz Gz Hz Iz Jz Kz Lz Mz Nz6 !#*/,29,:`c7 z #$4\]j   t{|$  34  !=!>!m!!#"$" # #)#*#################################$$$$$$E%^% (!(D(*****E+c+d++++,-,.,K,,,-P--- .C.D.y. / /C/D/y/z//+0,0b0c0000111'2(2n2o2223333'4(4n4o4444555l6m66777A8B88888X99:::(:):-:0p@ʀ0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0p@0q0p0o %2,@>BDH"))16<,@?ACEFGIJ+@@ Dr!!!)!.!;!#&#,:1:111111111 !!:-:@0 ,: @UnknownGTimes New Roman5Symbol3 Arial;Helvetica9New York3Times"(˘˘f/ f $+xx4:4+L P182B12.961College of Sciences Tony DiMAuro