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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 using the following steps:
- Setup of Experiment: An object (e.g., a candle) was placed in front of the concave mirror, and a screen was used to capture the image formed by the mirror.
- Measurement of Distances: The distance from the object to the mirror (u) and the distance from the image to the mirror (v) were measured at various points as the object distance was varied.
- Recording Data: The values of u and v were recorded in a table as shown in the provided data.
- Graphical Interpretation: A graph of 1/v against 1/u was plotted. The focal length can be approximated from where this line intersects the axes.
Step 2
What was the advantage of finding the approximate value for the focal length?
Answer
The advantages of finding the approximate value for the focal length include:
- Ease of Experimentation: Knowing a rough estimate of the focal length allows for a more manageable approach when placing the object. It helps avoid placing it too close or too far from the mirror.
- Verification of Results: It enables confirmation of the expected results before the final analysis is done, thereby ensuring that the magnitude of the final focal length is reasonable.
Step 3
Describe, with the aid of a labelled diagram, how the position of the image was found.
Answer
In this part, a labelled diagram is created to illustrate the arrangement of the apparatus:
- Diagram Description:
- Label the parts: concave mirror, object (candle), image (on the screen).
- Draw the light rays: one ray parallel to the principal axis reflecting through the focus, and another ray directed towards the focus reflecting parallel to the principal axis.
- Indicate the focal point and the distances u and v.
Arrangement: The object was placed in line with the mirror and a screen to capture the formed image. By adjusting the distance until a clear image was observed, the position was documented.
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, follow these steps:
- Graph Preparation: Plot the graph of 1/v (y-axis) against 1/u (x-axis) using the recorded values for u and v.
- Transformation of Data: Convert the distances to their reciprocal values:
- Calculate 1/u for the values of u.
- Calculate 1/v for the values of v.
- Plot the Points: Mark at least five points on the graph based on the 1/u and 1/v calculations.
- Draw the Best Fit Line: Extend the line to find where it intersects the axes.
- Calculate the Focal Length: The focal length (f) is calculated using the formula derived from the graph's linear approximation: f = rac{1}{ rac{1}{u} + rac{1}{v}} Using the data, an average focal length can be found from the intersection points. Estimate using the graph: average f is approximately 12.0 ± 0.1 cm.