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You probably have noticed that a light appears to be brighter when you are close to it, and dimmer when you are farther away. If you are reading this page illuminated by a single light bulb, the amount of the light that strikes this page will increase as the page is brought closer to the light source. Using a Light Sensor, you can determine how the brightness of light varies with distance from the source and compare that result to a mathematical model.
There are several ways to measure the brightness of light. Since this experiment can be performed with any of several different light sensors, each of which measure slightly different quantities, we will just use the word intensity to describe the relative brightness of the light, although the term may not be strictly appropriate for your sensor. Regardless of the way light is measured, the same relative changes with distance are observed, and that is what you will study today. In this experiment you will measure light intensity at a variety of distances from a small source of light, and see how the intensity varies with distance.
Light Intensity and Photos
Light Intensity and Photos
In the images, the light sources moves from 1.0 m to 4.0m in 0.5m increments. The settings were:
F2.4
1/90s
4.30 mm
ISO 400
Light Intensity Experimentation
Light Intensity Experimentation
Suppose a small light source is placed at the center of two transparent spheres. One sphere has a radius R, and the other a radius 2R. Energy in the form of light leaves the source at a rate P. That same power P passes through the surface of the inner sphere and reaches the outer sphere. Intensity is the power per unit area. What is the intensity at each sphere? Solve this problem by considering the following:
How does the power passing through the inner sphere compare to the power reaching the outer sphere?
How do the surface areas of the two spheres compare?
In general, then, how will the intensity vary with distance from the source?
Since most light bulbs that you use are not true point sources of light, how do you think the answer to Question 1 would change if a typical light bulb were used?
Accounting for ambient conditions.
How do various data collection techniques affect the quality of data?
How can you linearize your data? Importance of the intercepts?
Does your equipment limit your perfection?
Using LoggerPro on Your Computer:
Using LoggerPro on Your Computer:
Procedure:
On your computer, open the file 29 Light Brightness Dist
Open ... Experiments ... Physics with Vernier ... 29 Light Brightness Dist
This will set your collection to Event With Entry.
Place the Light Sensor a certain distance from the light bulb filament and note the value of intensity in the Meter window. Make sure that the intensity changes as you move the sensor, otherwise you may need to switch to a less sensitive scale or use a less intense light source. Move the sensor away from the bulb and watch the displayed intensity values.
What is your prediction for the relationship between intensity and the distance to a light source?
Click COLLECT to begin data collection. Place the Light Sensor 2 cm from the light bulb filament. Important: The distance must be measured carefully. Be sure you measure from the filament of the lamp to the sensor on the Light Sensor.
Wait for the intensity value displayed on the screen stops changing in a single direction. Click, KEEP then type the distance between the Light Sensor and the light source and click OK to record the value of intensity. A point will be plotted on the graph.
Move the Light Sensor farther away from the light source and repeat Step 4.
Repeat Step 4 moving the sensor in significant increments until the Light Sensor is not measuring significant changes in the intensity from the light source.
Click STOP when you have finished collecting data. In your data table, record the intensity and distance data pairs displayed in the table (or, if directed by your instructor, print a copy of the table).
Analysis:
Examine the graph of light intensity vs. distance. Does it appear to be consistent with the model you predicted in the Preliminary Questions? How can you tell?
Fit a model to your data.
Click the Curve Fit button, . Select inverse square from the list of curve fits displayed then click TRY FIT .
A best-fit curve will be displayed on the graph. The curve should closely match the data.
How well does the power regression fit your experimental data? Does your data approximately follow an inverse square function? Does the equation agree with your model of light intensity using the concentric spheres?
List some reasons why your experimental setup might not match the relationship you predicted in the Preliminary Questions between intensity and distance.
Using the LabQuest 2:
Using the LabQuest 2:
Using the LabQuest 2, determine the relationship between the distance (m) and the intensity of the light (lux).
Practical Skills:
Events with Entry Data Collection
Inverse square graphing
Linearization of data
Adjusting for ambient conditions
Ranges of data v. precision
Light Meter
Light Meter
Similar to the LabQuest2 data collection, determine the relationship btwn position v. intensity using the Light Meter.
Joly Photometer - PIVOTInteractives
Joly Photometer - PIVOTInteractives
Using the instructions within the PIVOTInteractives activity, determine the relative distance v. intensity of various bulbs.
Practical Skills:
Uncertainty in Measurements
Judgement of data
Linearization of Data
Exploring Error Bars with Desmos (Link above)
Light Intensity Simulation:
Light Intensity Simulation:
Using the simulation at FLUX Simulator
Select a power on the dial.
Move the detector a position of your choice. Record both the position and the intensity. As shown in the table to the right.
Collect a minimum of 6 data points. Your position readings don't have to change consistently (every 0.5 m) but they should be significant.
Linearization of the graph:
Create a new column to calculate the inverse square of the distance. The spreadsheet formula is shown in cell E12 and D12.
Display the trendlines for both sets of data (raw and processed).
Compare the accuracy of the simulated results to those of the experimental results above.
Outline benefits of collecting both types of data.
Possible Extensions / IA Ideation:
Possible Extensions / IA Ideation:
Confirm the relationship between intensity and distance by finding the linear plot of I = k • 1/d2. Use Logger Pro to verify the inverse square relationship between intensity and distance. Enter the data, then create a modified column of data with the heading “Distance^–2” to represent 1/d2. Graph intensity vs. distance^–2. A straight line that passes through the origin would verify the inverse square relationship.
If you have a window facing the sun, it may be interesting to try an experiment to measure the intensity of the sun. If your sensor has a range switch set it to the 150,000 lux range and load the calibration for that setting. Place the Light Sensor 10 cm from a 150 W clear light bulb and measure the intensity. Point the Light Sensor at the sun and measure the intensity of the sun relative to the light bulb. How many light bulbs would you have to place 10 cm from the Light Sensor to be equal to the intensity of the sun? Use the mathematical relationship found in this lab to calculate the intensity of the sun if it was placed 10 cm from the Light Sensor. Determine how many of these light bulbs would be equivalent to this value.
Use the Light Sensor to measure the intensity of the sun over the period of an entire school day.
Use the Light Sensor to examine sunglasses. By what percentage is the sun’s intensity reduced when sunlight passes through the lens of sunglasses?
Use the sensor to compare other light sources to the light source that you used in the lab. For instance, how does intensity vary as you move away from a long fluorescent bulb or a circular fluorescent bulb?
Inverse Square Law Theory
Inverse Square Law Theory
While the area may expand, the total energy passing per second (POWER) is constant. Therefore, the power at r, 2r and 3r is the same. Another form of the equation is P = IA
Intensity of light is measured in [W/m^2] or Power per area. Some additional relationships can be
Possible Question:
At a distance of 2 m a candle has an intensity of I. Determine the relative intensity at the following distances:
4 meters - 0.25I
8 meters - 0.0625I
1 meter - 4I
0.5 meter - 16I
General Resources:
General Resources:
Kognity Textbook Chap 4 - Use you ACS Login
IB Physics Site: Topic 4 - Comprehensive notes
IB Physics Site: Topic 4 - More notes
Topic 4 Flashcards - Vocab Devo.
Physics Classroom - Intensity and the Decibel Scale
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