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Lab 11 Lenses, Imaging and Intensity 4/14/11 Andrew Do Ashley Schreckengast Courtney Stewart Daniel Trujillo Aim: For unit 11 lab we will be looking at lenses. We will look at magnification with diverging and converging lenses and the position and size of images produced by these lenses. We will use the lens equation to find the position of our images and the magnification equation to find the degree of magnification of our image. Then we will test the difference in the intensity of radiation with regards to moving towards and away from a set source and with light bulbs of different wattage. Procedure: Distances used in calculations that utilize the thin-lens equation or the magnification equation are defined as positive or negative based on a certain set of rules. In simple terms, if the absolute value of the magnification is greater than 1 (ǀmǀ > 1), the image is bigger. If the absolute value of the magnification is less than 1 (ǀmǀ < 1), the image is smaller. If the magnification is greater than 0, m > 0, or positive it is upright. If the image is less than 0, m < 0, or negative the image is inverted. In experiment one, the measurement of focal length of a convex lens; we used an optical bench, light bulb, convex lens, and two different screens to measure the object distance and image distance in order to calculate the focal length of the utilized convex lens. Then the object size and image size were measured to determine the magnification of the convex lens. This was repeated for a second lens. In experiment two, the combination of two convex lens, we used the previous lenses with the aforementioned equipment to make a combination of lens. It should be noted that the focusing characteristics of a combination of lens can be calculated from the thin lens equation by assuming that the image of the first lens acts as the object for the second, and so forth. The net magnification is simply the product of the magnifications of each lens, as determined in experiment one. Using the experiment, you can measure the image distance and size of the image to determine magnification with the thin-lens equation and compare this to the product magnification you determine from experiment one. In experiment three, determination of focal length for a diverging lens, one must go to lengths to find the focal length of a diverging lens since the image formed by a diverging lens is virtual. To do so, one must combine the diverging lens with a converging lens to create a real image and use the thin-lens equation. You will use the set-up for experiment two, but replace one convex lens with a diverging lens. You then measure all the distances from the figure below. Using these measurements and the thin-lens equation we could then determine the focal length. Then we could measure the image size and calculate the magnification. In experiment four, variation of intensity with distance, we observed the variation of intensity with distance by measuring the relative intensity impinging from opposite sides onto a photometer using the optical bench, photometer, and two bulbs of varying wattage on either side of the photometer. We would move the bulbs up and down the bench until they appeared to match in intensity upon the photometer and would record their positions. One bulb was a constant 100 watts, and the other was varied in wattage. What we should determine is the truth that the intensity from the source decreases as the inverse square of the distance when the intensities at the photometer are equal. In this case, the following relationship should hold. P100 = Pb 4πR1002 4πRb2 P(100) is the wattage of the 100 watt bulb, P(b) is the wattage of the second bulb, R(100) is the distance of the 100 watt bulb from the photometer and R(b) is the distance of the second bulb from the photometer. Using this relationship, we can calculate the position at which the second bulb should be placed when the intensities of the photometer are equal and can compare this to what we measured. Data: Experiment No. 1: Measurement of Focal Length of a Convex Lens Thin Convex Lens Object Distance: 22.5 cm Image Distance: 16.5 cm f-1 = d0-1 + di-1 f-1 = 22.5-1 + 16.5-1 Focal Length: 9.5 cm Object Size: 2.5 cm Image Size: -1.6 cm m = - di/do m = -16.5/22.5 Magnification: -0.73 Thick Convex Lens Object Distance: 15.5 cm Image Distance: 7 cm f-1 = d0-1 + di-1 f-1 = 15.5-1 + 7-1 Focal Length: 4.82 cm Object Size: 2.5 cm Image Size: -1.2 cm m = - di/do m = -7/15.5 Magnification: -0.45 Experiment No. 2: Combination of Two Convex Lenses (work shown below) Measured: Calculated: Image Distance: 20cm 23.8cm Magnification: 1.28 0.33 Object lens 1 Lens 1 lens 2 Lens 2 image Hi = 3.2 cm d01 = 6.5 cm d = 7.5 cm di2 = 6 cm 1/d02 = 1/f2 – 1/di2 d02 = -16.3 cm di1 = d – d02 di1 = 7.5 + 16.3 = 23.8 cm 1/f1 = 1/do1 + 1/di2 f1 = 3.12 cm m = hi/ho = 3.2/2.5 = 1.28 mcalc = m1 * m2 = -0.73 * -0.45 = 0.33 Experiment No. 3: Determination of “f” for a diverging lens(work shown below) Focal Length: 4.702 Magnification: 0.44 D(o1) = 6.5 D = 18 D (i2) = 17 1/d02 = 1/f2 – 1/di2 d02 =6.5 cm di1 = d – d02 di1 =11.5 cm 1/f1 = 1/do1 + 1/di2 f1 = 4.7 cm H(i1) = 2.5 H(i2) = 1.1 m = hi/ho = 1.1/2.5 = 0.44 Experiment No. 4: Variation of Intensity with Distance Wattage of Bulb 100W 75W 60W 40W Position 19 cm 16 cm 13 cm 10 cm P100/(4𝜋*(R100)2) = Pb/(4𝜋*(Rb)2) Calculated Position 19 cm 16.5 cm 14.7 cm 12 cm 1/Rb = √100/(192 * Pb) 1/R75 = √100/(192 * 75) R75 = 16.5 cm 1/R60 = √100/(192 * 60) R60 = 14.7 cm 1/R40 = √100/(192 * 40) R40 = 12 cm Conclusion: In this lab we studied convex and concave lenses. A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. We setup two lenses a certain distance apart and shine a light through a paper with a design on it, which in turn created a shadow on another paper, and the purpose of this experiment was to find the length in which the shadow became clear, by moving the lenses closer or farther apart. Overall the experimentation was a success and the uses of concave or convex lenses made more sense. Although the possibility of human error was minimal, there was a chance that the bulbs we used were mislabeled and we lacked the proper equipment to properly test the wattage of the light bulbs, another possibility was an error in the calculation part of the experiment in which a rounding error or simple algebraic miscalculation had occurred. Our results that we obtained were anticipated and we accepted as correct.