# The Camera

 Materials: Microsoft Excel program (available in the Math or Science Computer Lab) Time Allotment: 4 Class Days

### Purpose:

The purpose of this lab is to utilize a spreadsheet to answer a variety of questions pertaining to the formation of images by camera lenses. Through this activity, you will learn to use a spreadsheet and gain an understanding of the physics of cameras.

### Overview:

All cameras are equipped with lenses which serve to produce images of the world upon a thin sheet of photo-sensitive film. Light from the surroundings passes through the camera lens and then through a small opening known as the aperture; the light ultimately converges upon the film to produce the image. The focusing of a camera involves controlling the distance from the lens to the film (the image distance) such that a focused image is formed at the film location. As the subject of a photograph is moved farther or closer to the photographer (and thus, the lens), the distance from the lens to the film must be adjusted (through the focusing procedure) in order to obtain a focused image at the film location. To put it mildly, cameras and photography involve a wealth of physics which is applicable to our current unit of study - refraction and lenses.

A spreadsheet is a type of computer application which allows the user to modify a given parameter and measure the effect of such a modification upon other relevant parameters. In this lab, you will use a spreadsheet file to observe the effect of object distance and height upon image distance and height. You will use the file to ask and answer a variety of what if? type questions. The first several questions involve the determination of a precise image distance value and the last several questions involve the determination of a range of object distances which provide suitable image distance values. Your objective is to use the spreadsheet program to arrive at reasonable answers. You will be required to provide charts (graphical representations) which provide evidence for at least two of the investigations and to interpret these charts as a demonstration of your understanding.

1. Open the Microsoft Excel spreadsheet. A blank spreadsheet page will appear.
2. Choose Open from the File menu. A directory dialogue box will appear. Find the folder titled Science and open the spreadsheet file titled Camera Lens by double-clicking upon it.

### Note:

The Microsoft Excel software is available in the Science Computer lab (Room 159) and on most computers in the Math Computer lab. If the Microsoft Excel spreadsheet file is inaccessible from the Math Computer lab, then you will have to open the program in the Science Computer lab and save it to a floppy disk.

### Guided Explorations:

In each of these guided explorations, you will enter data for the input parameters in the first column of the spreadsheet (note that you must use metric units only; the spreadsheet will automatically convert to English units to assure that you have entered realistic values). All the blue-bordered cells must be filled in; the spreadsheet program will calculate all other cells. The increment value merely allows the user to control the increment at which the object distance values are increased in each successive calculation. This increment value can be either a positive or a negative value. The spreadsheet will automatically update the output parameters after you press the Return or Enter key. You will use the spreadsheet data values and spreadsheet charts (where instructed) to arrive at an answer to the questions. For at least two of the following investigations, you will generate charts (graphs) of the data in order to verify your findings.

1. A photographer is on vacation with a 35-mm (focal length) camera lens. If the photographer is taking a picture of a 1.6-meter tall person (object height) standing 5-meters away (object distance), how far from the lens must the film be located (image distance) in order to obtain a focused image? _____________ How tall will the image be (image height) on the photographic film? _____________ Suppose that in the process of developing the photographic film, the image on the film is magnified by four times as it is placed upon the photograph. How big will the image of the person be on the photograph? ______________

2. A photographer is on vacation with a 35-mm (focal length) camera lens. If the photographer is taking a picture of a 1000-meter high cliff from a distance of 1400 meters, how far from the lens must the film be located in order to obtain a focused image? _____________ How tall will the image of the cliff be on the photographic film? _____________ Suppose that in the process of developing the photographic film, the image on the film is magnified by four times as it is placed upon the photograph. How big will the image of the cliff be on the photograph? ______________

3. A photographer is on vacation with a 35-mm (focal length) camera lens. If the photographer is taking a picture of a 2.0-meter tall moose standing 50-meters away, how far from the lens must the film be located in order to obtain a focused image? _____________ How tall will the image of the moose be on the photographic film? _____________ Suppose that in the process of developing the photographic film, the image on the film is magnified by four times as it is placed upon the photograph. How big will the image of the moose be on the photograph? ______________

4. If the same photographer in the question above uses a 200-mm zoom lens to take the picture of the same moose from the same distance away, then how far from the lens must the film be located in order to obtain a focused image? _____________ How tall will the image of the moose be on the photographic film? _____________ Suppose that in the process of developing the photographic film, the image on the film is magnified by four times as it is placed upon the photograph. How big will the image of the moose be on the photograph? ______________ How many times bigger is the image of the moose when taken with a 200-mm zoom lens compared to the normal 35-mm lens? ______________

5. Suppose that two objects which are different distances from the camera lens are simultaneously focused if they have image distances which are within 0.02 mm apart. Use -2 as the increment value, 35-mm as the focal length and 1000 meters as the object distance. Determine the range of object distances (with 1000 meters as the upper limit of the range) which will lead to the simultaneous focusing of all objects within the range. State and explain your answer.

6. Determine the range of object distances for which two objects will be simulatneously focused if the upper limit of the range is 100 meters. Use -0.25 meters as the increment value, 35-mm as the focal length and 100 meters as the image distance. State and explain your answer.

7. Determine the range of object distances for which two objects will be simulatneously focused if the upper limit of the range is 10 meters. Use -0.05 meters as the increment value, 35-mm as the focal length and 10 meters as the image distance. State and explain your answer.

8. Summarize your results of investigations #5, 6, and 7 by filling in the table below.

 Focal Length (mm) Upper Limit of Range (m) Range of Objects in Focus (m) Image Distance (m) 35 mm 1000 m ______________ __________ 35 mm 100 m ______________ __________ 35 mm 10 m ______________ __________

9. Repeat the procedure described in investigations #5, 6, and 7 using a 200-mm camera lens. That is, use 200 mm as the focal length and determine the range of objects which can be legitimately focused (i.e., within an image distance of 0.02 mm). You may need to adjust the increment value for each investigation in order to determine the lower limit of the range. Summarize your results of this investigation in the table below.

 Focal Length (mm) Upper Limit of Range (m) Range of Objects in Focus (m) Image Distance (m) 200 mm 1000 m ______________ __________ 200 mm 500 m ______________ __________ 200 mm 100 m ______________ __________ 200 mm 50 m ______________ __________ 200 mm 10 m ______________ __________

10. Based on your findings from investigations #1-9, which type of lens (35 mm or 200 mm) would you used if you wished to magnify the images of objects? _____________ Explain your answer using some comparative data values to provide support.

11. Based on your findings from investigations #1-9, which type of lens (35 mm or 200 mm) would you used if you wished to obtain a large depth of field (i.e., have objects of widely varying distances still be in focus)? _____________ Explain your answer using some comparative data values to provide support.

12. Now you will make a spreadsheet chart for any two of the investigations which you conducted in questions #5, 6, 7, or 9. Your chart will plot the image distance along the vertical axis and the object distance along the horizontal axis. Reset the input parameters to the desired values and then follow the procedure listed below to construct both charts. Once you have constructed a chart, print it out and use it for the Conclusion section.

1. Select the two columns of data which you wish to chart. To select the first column (object distance in m), click on its column heading. To select the second column (image distance in mm), hold down the Control key and click on its column heading.
2. Select New from the File menu. Select Chart and click OK. Select X-Values for XY Chart and click OK.
3. Label the axis of the chart and title the chart:
1. Click on the vertical axis and select Attach Text from the Chart menu. Click on Value (Y) Axis and click OK; Type "image distance (mm)" and press the Return key.
2. Click on the horizontal axis and select Attach Text from the Chart menu. Click on Category (X) Axis and click OK; Type "object distance (m)" and press the Return key
3. Click on the chart title (above the graph). Select Attach Text from the Chart menu. Click on Chart Title and click OK. Type a descriptive name of the chart (e.g., "Depth of Field for 35 mm Lens")
4. Format text by clicking on the text and selecting either Font or Text from the Format menu; format the text (color, font, size, alignment, etc.) however you wish.
5. Consider other options for the text and the chart by clicking on the chart or some text and selecting options from the Format menu.

### Conclusion:

As a conclusion (on a separate page of paper), elaborate on the two different charts which you have created. Discuss the meaning of each chart, including the following in your discussion:

• Explain the input parameters for the two charts which you are discussing.
• In general, how would you describe the relationship between the object distance and the image distance for a camera lens?
• For what object distance values (large or small) is there a large (or small) depth of field - i.e., a large range of object distance for which the images are simultaneously focused? Indicate this on the chart by circling or labeling the range of object distances.
• How do your two charts compare to one another? What significance does this have to the art of photography?
• Include a single calculation for each of the two investigations in which you use the lens equation to calculate the image distance (in mm) for any given two values of object (in m) and focal length (in m). Be cautious of units. Show all your work.

Do a bang-up job!