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The analysis  x of the light emitted from a distant object can give the scientist an insight into many of physical  xproperties of that object. For example, you have already determined the quantitative relationship  xbetween color and temperature. So far the transmission of light through a medium has been  xignored because for the most part the light travels through mostly empty space. However, the  xlight that is analyzed on the surface of the earth, or even in one of the orbiting satellites, does  xtravel through the earth's atmosphere and this must be taken into account in the scientist's  x<analysis. The objective of this experiment is to simulate the transmission of light, from a point  xsource such as a star, through the earth's atmosphere. More specifically (as usual), you are to  xdetermine the mathematical (or functional) relationship between the intensity of the light source  xand the thickness or depth of the earth's atmosphere. In other words, as the detector that  x<measures the intensity of the light from a distant object gets deeper into the earth's atmosphere  xl(or closer to the earth's surface), how does the intensity change? This attenuation, or extinction  xof light as the astronomers refer to it, is extremely important. For example, the extinction of  xultraviolet (UV) light by the ozone layer is a crucial health issue. Normally the UV is attenuated  xso greatly that it only causes sunburn problems. However, as the ozone layer is depleted the UV  xintensity can reach a level that may lead to a serious risk of cancer. The predominant range of  xtransmitted radiation is in the visible range of the spectrum. This of course raises the interesting  xquestion of which came first our vision or the transmission of this particular part of the overall electromagnetic spectrum.  X0 xX Experimental Apparatus: A 100 watt light bulb, circular aperture, clamps, support rod,  X0 xgraduated cylinder, pipette, colored water, PASCO photo detector, DataMonitor (DM) and  X0CricketGraph (CG).  X0 Implementation: The experimental apparatus is set up as shown in figure 1.  l \p 6 #A\  P /P# Figure 1 y!! $!yl ddOBJECT #0001! y#XN\  P XP# Figure 1 dXB)0*0*0*(3@$!-!*R$!XԌ x`Be sure to align the photo detector with the center of the bottom of the graduated cylinder. The  x8circular aperture must be close to the top of the cylinder and also in the center of the top  X0 xopening. In DM  follow the same procedures as in the previous light experiments (refer to the  X0 xappendix on Tips for the Use of DM). In this experiment, label the independent variable as depth  xhmeasured in cm. With the light on and the cylinder completely empty of water, adjust the  xsensitivity or the gain of the detector so that the maximum reading is slightly below 9.995 volts.  x0Measure the background (lights out) and record this in your lab notebook. With the pipette add  xa fixed amount of colored water to establish a depth of 10 mm in the cylinder. Refer to the  XL0 xAppendix to review the measurement of depth. Record the average intensity for ten readings and  xthe corresponding depth of 10 mm. Now add more water such that the depth is increased to 16  X 0 xmm. Measure and record the average intensity for ten readings. Also examine the standard  xdeviation to assure yourself that your data are consistent (i.e. the standard deviation should be  xsmall relative to the average or mean value). Continue this procedure, increasing the depth in  X 0 x6 mm increments, until you have obtained at least twenty data points or until you have reached background.  X0 xH Analysis: Enter your data into CG and be sure to clearly label your columns in the data sheet.  X` xPlot the corrected intensity (I IBG) versus the depth of the colored water. Make sure the origin  Xp0 xof your graph is set at (0, 0). Examine the shape of this distribution and refer to your reference  xcurves to formulate your hypothesis about the relationship between the intensity and the depth  xof the water. You have observed this distribution before. Perform the appropriate mathematical  xtransformations and plot your data to test your hypothesis. Discuss your results with your partner and your instructor. What is the significance of the slope of your "simple fit" to this distribution?  X0 x Conclusions: Formulate a simple mathematical relationship between the intensity of the light  x0source and the depth of the colored water. Discuss the significance of the parameters obtained  xin the "simple fit". How might this effect (the decreasing intensity as the atmosphere gets thicker) be accounted for in the analysis of the light from stars and planets? "u0*0*0*"  `< #[\  P #P# Appendix How to Read the Graduated Cylinder   X0d#XN\  P XP#    yAE  \\hEy dFigure 1  d   The figure above is a representation of the graduated cylinder, which is used to measure  xTeither the volume or, as in the case of this experiment, the depth of a fluid. The crosssectional  x0area of the cylinder is constant so the correlation between depth and volume is a linear one, i.e. one can read the depth of the fluid directly as shown in the figure. XX` ` Vol. = (area) x (depth)(#`  x A volume reading of 10 ml corresponds to a depth of 2 cm. Therefore, each dotted line in the  XE0diagram, the smallest division on the cylinder, corresponds to a depth of 2 mm (1 mm = 10é3 m).     ( s]   X0` (##,(\  P6Q,P#8 January 1996#XP\  P6QXP#у