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In an experiment to measure the focal length of a converging lens, a student measured the image distance v for each of four different values of the object distance u - Leaving Cert Physics - Question 2 - 2012
Question 2
In an experiment to measure the focal length of a converging lens, a student measured the image distance v for each of four different values of the object distance u... show full transcript
Worked Solution & Example Answer:In an experiment to measure the focal length of a converging lens, a student measured the image distance v for each of four different values of the object distance u - Leaving Cert Physics - Question 2 - 2012
Step 1
Describe, with the aid of a labelled diagram, how the student obtained the data.
Answer
The student set up the apparatus using a converging lens, a ray box, and a screen to capture the image. The apparatus was arranged such that the object (a candle) was placed at various distances from the lens. Each time, the image was focused on the screen by adjusting the position of the lens.
A labelled diagram would show:
- The ray box emitting light rays towards the lens.
- The lens bending the rays to create an image on the screen.
- The distances labeled for both the object distance (u) and image distance (v).
The student repeated this process for multiple object distances and recorded the corresponding image distances.
Step 2
Why is it difficult to measure the image distance accurately?
Answer
Measuring the image distance accurately can be difficult because:
- The image may not be sharply defined, especially if the object is not perfectly aligned.
- If the image is virtual, it cannot be captured on a screen, complicating the measurement.
- There could be parallax errors when taking measurements from different angles, leading to incorrect readings.
Step 3
Using all the data in the table, find the value for the focal length of the lens.
Answer
To find the focal length (f) of the lens, we can use the lens formula:
rac{1}{f} = rac{1}{u} + rac{1}{v}
Using the values from the table:
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For u = 12.0 cm and v = 64.5 cm: rac{1}{f} = rac{1}{12.0} + rac{1}{64.5} o f = 10.12 cm
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For u = 18.0 cm and v = 22.1 cm: rac{1}{f} = rac{1}{18.0} + rac{1}{22.1} o f = 9.92 cm
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For u = 23.6 cm and v = 17.9 cm: rac{1}{f} = rac{1}{23.6} + rac{1}{17.9} o f = 10.18 cm
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For u = 30.0 cm and v = 15.4 cm: rac{1}{f} = rac{1}{30.0} + rac{1}{15.4} o f = 10.60 cm
The average focal length: f_{avg} = rac{10.12 + 9.92 + 10.18 + 10.60}{4} = 10.10 cm
Step 4
Why is it difficult to measure the image distance when the object distance is less than 10 cm?
Answer
When the object distance is less than 10 cm, measuring the image distance becomes challenging because:
- The image may become very close to the lens, resulting in a virtual image that cannot be projected onto a screen.
- The lack of clear image formation makes it hard to determine the exact position of the image.
- Additional difficulty arises from distortion and aberration, which can skew measurements when working with short distances.