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In an experiment to measure the focal length of a concave mirror, an approximate value for the focal length was found - Leaving Cert Physics - Question 3 - 2007
Question 3
In an experiment to measure the focal length of a concave mirror, an approximate value for the focal length was found. The image distance v was then found for a rang... show full transcript
Worked Solution & Example Answer:In an experiment to measure the focal length of a concave mirror, an approximate value for the focal length was found - Leaving Cert Physics - Question 3 - 2007
Step 1
How was an approximate value for the focal length found?
Answer
An approximate value for the focal length was found by determining the relationship between the object distance (u) and the image distance (v) for the concave mirror. By focusing an image of a distant object on a screen, the image distance was measured while varying the object distance. The data collected allowed for the identification of a trend that demonstrated how the focal length relates to the distances u and v through the mirror formula: By arranging the measurements on a graph with 1/v on the y-axis and 1/u on the x-axis, the focal length (f) could then be extrapolated from the slope of the line.
Step 2
What was the advantage of finding the approximate value for the focal length?
Answer
The advantage of finding the approximate value for the focal length is mainly twofold: first, to facilitate the later finding of the image when conducting the experiment, and second, to confirm the results and the magnitude of the final answer. It serves as a useful reference point, particularly when making subsequent detailed measurements, ensuring accuracy in further calculations.
Step 3
Describe, with the aid of a labelled diagram, how the position of the image was found.
Answer
To find the position of the image formed by the concave mirror, an experimental setup is required:
- Apparatus: The setup includes an object (e.g., a window or a distant lamp), a concave mirror, and a screen.
- Arrangement: The object should be positioned on one side of the mirror, while the screen is placed on the same side to observe and locate the image.
In the diagram:
- Label the concave mirror, object, and screen.
- Draw arrows indicating the light rays reflecting from the mirror to the screen, demonstrating how the image is formed. When the object is adjusted closer or further from the mirror, the image can be seen on the screen.
This method allows for visual confirmation of the position of the image.
Step 4
Calculate the focal length of the concave mirror by drawing a suitable graph based on the recorded data.
Answer
To calculate the focal length:
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Calculate 1/u and 1/v Values: Convert the distances to their reciprocals:
- For each value of u, calculate (\frac{1}{u}) and (\frac{1}{v}).
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Label Axes: Label the x-axis as (\frac{1}{u} (m^{-1})) and the y-axis as (\frac{1}{v} (m^{-1})).
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Plot at Least Five Points: Plot the calculated values on a graph.
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Fit a Straight Line: Draw a straight line to fit the data points, ensuring that it represents the relationship well.
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Extrapolate to Axes: Check where the line intersects the axes, particularly at (\frac{1}{u} = 0) to find the focal length.
- Use the formula, substituting the point where the line crosses the y-axis:
Ultimately, the data suggests a focal length of approximately 12.0 cm.