PHYS 1400: Physical Science Laboratory Manual ILLUMINATION AND DISTANCE
INTRODUCTION How bright is that light? You know, from experience, that a 100W light bulb is brighter than a 60W bulb. The wattage measures the energy used by the bulb, which depends on the bulb, not on where the person observing it is located. But you also know that how bright the light looks does depend on how far away it is. That 100W bulb is still emitting the same amount of energy every second, but if you are farther away from it, the energy is spread out over a greater area. You receive less energy, and perceive the light as less bright. But because the light energy is spread out over an area, it’s not a linear relationship. When you double the distance, the energy is spread out over four times as much area. If you triple the distance, the area is nine Twice the distance, ¼ as bright. Triple the distance? 11% as bright. times as great, meaning that you receive only 1/9 (or 11%) as much energy from the light source. To quantify the amount of light, we will use units called lux. The idea is simple: energy emitted per second (Watts), spread out over an area (square meters). However, a lux is not a W/m2! A lux is a lumen per m2. So, what is a lumen? Technically, it’s one candela emitted uniformly across a solid angle of 1 steradian. That’s not helping, is it? Examine the figure above. The source emits light (energy) in all directions simultaneously. But we are focused on that cone of light (that’s the solid angle): how much total energy (per second) is radiated within that cone? That would be measured in lumens. When the light strikes a surface (look at the spheres), the energy is spread out over the area. That would be measured in lux, and the greater the distance, the bigger the sphere, the larger the area, and the same number of lumens is a decreasing number of lux. Or, the bulb appears dimmer the farther away you are.
OBJECTIVES EQUIPMENT ๏ Become familiar with units which describe the brightness or intensity of ๏ Optics bench a light source ๏ Point source ๏ Measure the brightness of a point source as a function of distance ๏ Magnetic component holder ๏ Prepare a graph to analyze the relationship mathematically ๏ Vernier LabQuest ๏ Compare the experimental plot to a predicted inverse-square graph ๏ Light Sensor ๏ Examine the experimental set up and suggest possible improvements ๏ Rod & clamp
PROCEDURE ๏ Place the Parallel Ray Lens over the light source, and set the source on the bench. ๏ Clamp the light sensor to the rod as shown in the photograph. ๏ The light sensor should be carefully aligned with the point source. The sensor tip should be positioned at the end of the optics bench in order to make accurate distance measurements. ๏ Connect the sensor to the LabQuest, and turn on the unit. Switch the sensor range to the 0-6000 lux setting. ๏ With the light source off, measure the background light level. The room will never be completely dark, and other lab tables will have sources as well. Watch the light level in the Meter tab, and record the value. ๏ Under the Sensor menu of the Meter tab, choose the Data Collection option. Select Place the magnetic component holder at the end of the optics bench to Events with Entry as the data collection properly position and align the light sensor. mode. The Number of Columns should be 1. Give it the name Distance, with units of cm. Tap OK to continue. PHYS 1400: Physical Science Laboratory Manual ๏ Position the light source at the 4 cm mark on the bench. Switch it on. ๏ To begin data collection, tap the GO button. You should notice a small KEEP icon appear directly next to it. To record data, tap the KEEP icon. When you are asked for the event name, type in 4 (for the distance to the source) and tap OK. Data collection resumes, and you can adjust the position of the source to 6 cm. When the source is in the new position, KEEP this new illumination data and type in 6 for the event name. Move only the light source, and not the light sensor or the optics bench. ๏ Continue to increase the distance by 2 cm increments, tapping KEEP to record the light level. Continue taking data until the light source is 40 cm from the light sensor. When you have completed the data collection, tap STOP, and the File Cabinet icon to save the trial. ๏ As you collect data, also record the values in your notebook. You do not need to write down every value. You may record data in your notebook at 4 cm intervals , but you must collect data at 2 cm intervals. DATA & ANALYSIS If you have not already, organize your data into a neat table in your lab notebook. RECORDED SOURCE PREDICTED RECORDED SOURCE PREDICTED DISTANCE DISTANCE BRIGHTNESS BRIGHTNESS BRIGHTNESS BRIGHTNESS BRIGHTNESS BRIGHTNESS (cm) (cm) (lux) (lux) (lux) (lux) (lux) (lux)
4 Lo 24 (1/36)Lo
8 (1/4)Lo 28 (1/49)Lo
12 (1/9)Lo 32 (1/64)Lo
16 (1/16)Lo 36 (1/81)Lo
20 (1/25)Lo 40 (1/100)Lo 1. Subtract the background light level from the mean for each of your data:
2. Predict the brightness using the inverse-square rule. Calculate those values as shown on the sample table above. Use do = 4 cm, and the source brightness at the 4 cm distance as your value for Lo in each case.
3. If you have not already, carefully sketch the Illumination vs Distance graph in your notebook. Use the LabQuest to fit the curve of the data. Under the Analyze menu of the Graph tab, tap Curve Fit. Choose the Power equation:
and record the resulting coefficients A and B in your notebook. 4. A perfect inverse square curve will have a coefficient B = –2. Does your data match the inverse-square curve perfectly? Is your actual curve above or below the prediction? That is, are the predicted brightness values consistently greater (above) or smaller than (below) the data values? 5. Why might your curve be brighter (above) the predicted curve? Can you think of any reasons why it might be dimmer (below) the prediction? (At this point, you might want to re-examine the output of the lightbulb over a longer than 3-second interval.) 6. Suggest some techniques which could be used to improve the results of this experiment.