Part I: Converging Lenses 2mm uncert. Measurement 1 neg. if inverted mm Quantity Object distance Image distance Object height Image height Magnification (d) Magnification (h) 1/Obj. Dist. 1/Im. Dist. 1/Focal Length Focal Length Unit cm cm cm cm 1/cm 1/cm 1/cm cm - - . . . ... Value 25 7.5 3.7 -0.9 -0.3 -0.2432432432 0.04 0.1333333333 0. 1733333333 5.780346821 Uncertainty 0.2 0.2 0.2 0.2 0.008352245207 0.05563019069 0.00032 0.003555555556 0.003569926513 Measurement 2 Quantity Object distance Image distance Object height Image height Magnification (d) Magnification (h) 1/Obj. Dist. 1/Im. Dist. 1/Focal Length Focal Length Unit : cm cm cm cm 1/cm 1/cm 1/cm cm - . . ... Value 11.2 41.4 8 -1.1 3.696428571 -0.1375 0.08928571429 0.02415458937 0. 1134403037 Uncertainty 0.2 0.2 0.2 0.2 0.06838046368 0.02523522154 0.00159438775 0.000116688837 0.001598652119 Does your first measurement of focal length agree with the expected value of 5cm, to within uncertainty? Does your first pair of magnifications agree with each other, to within uncertainty? Does your second measurement of focal length agree with the expected value of 5cm, to within uncertainty? Does your second pair of magnifications agree with each other, to within uncertainty?Introduction In this lab, we will investigate the properties of lenses and lens system. We will begin with a single lenses, then make more complicated instruments with multi-lens systems. "W" "" "'3\"! Back to Top . Optical Bench - Lamp . Objects: 0 Arrow slide 0 Wingdings slide 0 Eye chart . Lens Kit: 0 5cm Converging Lens (Red Tape) 0 10cm Converging Lens (Yellow Tape) 0 20cm Converging Lens (Green Tape) 0 10cm Diverging Lens (Black Tape) - Projecting screen . Record data in this Google Sheets data table For students: this background section is unusually long in part because this is an undercovered subject in a typical physics curriculum, and some 7345 may find the more thorough overview heipfui. Feel free to skim more than usuai if you feei you understand lenses fairiy weii. Basics of Lenses There are two basic components to build optical instruments: mirrors and lenses. In this lab, we will only be dealing with lenses. 1 A converging lens takes incoming parallel light (resulting from an object "at infinity") and focuses it at some pont, known as the focal point. The distance to this focal point is the focal length, and our sign convention is that this is positive. Geometrically, a converging lens is "convex" (bulging outwards in the middle). A diverging lens takes incoming parallel light and splits it apart, as though the light came from a fixed point behind the lens. That point is the focal point of the diverging lens, and negative the distance from the lens to the focal point is the focal length, f. Geometrically, a diverging lens is "concave" (wider on the edges than in the middle). In general, understanding how lenses make images requires a whole bunch of complicated geometry, because you have to consider the refraction of the light as it comes in, the motion of the light inside the lens, and the refraction of the light when it leaves. A customary approximation is to assume the lens is very thin, and therefore to neglect that middle part, treating the lens as "plane-like" (except insofar as the changed angle from refraction is concerned). 1 In this case, if you place an object on one side of a parabolic lens, 2 there will somewhere be an "image" formed. This is where the object appears to be if you look at it through the lens. The image can appear either in front of or behind the lens. If the image appears in front of the lens (i.e., opposite side of the lens from the object), then the image is reai - if you put a screen at that location, you will actually see the image there, because the light beams pass through that point. If the image is behind the lens (i.e., same side as the object), then the image is virtuai - although the image appears to be there, no light rays actually pass through that point, and hence you cannot project such an Image. The distance between the lens and the object defines the object distance do, and the distance between the lens and the image defines the image distance (1,. Similarly, the height of the object we call ho, and the height of the object we call hi. These distances and heights can be positive or negative; we choose the signs on these quantities according to the following conventions: 0 Object distance, do: 0 This is positive if the object is "behind" the lens (same side as the light comes from), and negative if it is "in front" of the lens. [The latter is uncommon, but can "effectively" occur in composite lens systems, as you will see in this lab.] 0 Why this makes sense: The "normal" position for the object is what we call "positive." 0 Image distance, di: 0 This is positive if the image is "in front of" the lens (opposite side of the lens from the light source), and hence a real image. It is negative if it is I'behind" the lens, hence virtual. 0 Why this makes sense: A real image (that we can actually project) is what we call "positive." 0 Focal length, f: o This is positive if the focal point is in front of the lens (i.e., if the lens is convex/converging), and negative if the focal point is behind the lens (i.e., if the lens is concave/diverging). 0 Why this makes sense: A real focal point (where light actually focuses) is what we call "positive." - Object height, ho: a This is basically always positive, by definition. 3 0 Why this makes sense: Usually in pictures our "object" is an upright arrow, and upright is naturally "positive." 0 Image height, by: a This is positive if the orientation is the same as the object (the image is "upright"), and negative if the orientation is flipped (the image is "inverted"). 0 Why this makes sense: Hopefully obvious. Be aware that several of these conventions change for mirrors. 4 We won't be dealing with curved mirrors in the lab, but you will probably see them in the course. (Those conventions also make sense if you think about them, though.) Be aware that several of these conventions change for mirrors. 4 We won't be dealing with curved mirrors in the lab, but you will probably see them in the course. (Those conventions also make sense if you think about them, though.) Properties of Single-Lens Images Under the thin lens approximation that we made, one can derive (with ray-tracing diagrams) the thin lens equation: 1 1 1 += m do d'i f This equation only works if do and (i.- use the sign convention dened above. (It also works with mirrors, if you use the mirror sign conventions.) The image from the lens may be magnified (larger) or demagnied (smaller), and may be upright or inverted. The magnification for a projected image is dened as the ratio of image size hi to object size ho (again, with signs as defined above): m: (2)