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In an experiment to determine the focal length of a concave mirror a student first found the approximate focal length of the mirror - Leaving Cert Physics - Question 2 - 2019
Question 2
In an experiment to determine the focal length of a concave mirror a student first found the approximate focal length of the mirror. He then placed an object in fron... show full transcript
Worked Solution & Example Answer:In an experiment to determine the focal length of a concave mirror a student first found the approximate focal length of the mirror - Leaving Cert Physics - Question 2 - 2019
Step 1
How did the student find the approximate focal length?
Answer
The student found the approximate focal length by capturing the image of a distant object. By placing a distant object in front of the concave mirror, he ensured that the rays of light coming from the object were effectively parallel before hitting the mirror. This is vital because parallel rays reflect through the focal point, allowing him to observe the distance at which the image forms compared to the object distance.
Step 2
Why did the student find the approximate focal length at the start of the experiment?
Answer
The student found the approximate focal length at the start of the experiment to ensure that he could observe a clear image formed by the mirror. By using a distant object, he effectively set the stage for accurately locating the focal point. This also helped to confirm that the image could form on a screen, giving a tangible comparison against which other measurements can be assessed.
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, a diagram should show the concave mirror with an object placed at a certain distance 'u'. The setup involves:
- Drawing the concave mirror with its focal point labeled.
- Illustrating the object (e.g., an arrow or a block) placed at distance 'u' with respect to the mirror.
- Drawing the incident rays coming from the object towards the mirror. One ray should be drawn parallel to the principal axis and reflecting through the focal point, while another should pass through the center of curvature (C) and reflect back on itself.
- Indicating where the reflected rays meet or diverge to represent the position of the image formed (at distance 'v').
- Noting the appropriate measurements of u and v to capture the relationship.
This diagram provides a visual understanding of the optical principles at play.
Step 4
State two precautions that should be taken when measuring v.
Answer
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Error of Parallax: Ensure that the observer's eye is directly in line with the measurement mark on the scale to avoid parallax errors, which can lead to incorrect readings.
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Distance to the Mirror: Carefully measure the distance from the center of the mirror to the object and the image to ensure accuracy in finding the focal length. Any inaccuracies in distance can lead to incorrect calculations.
Step 5
Use all of the data to calculate the focal length of the mirror.
Answer
To calculate the focal length using the formula:
rac{1}{f} = rac{1}{u} + rac{1}{v}
Using the provided data for u and v values:
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For u = 20.0 cm and v = 61.0 cm:
rac{1}{f} = rac{1}{20} + rac{1}{61}
The calculation yields an f value. -
For u = 30.0 cm and v = 29.5 cm:
rac{1}{f} = rac{1}{30} + rac{1}{29.5} Calculate accordingly. -
For u = 40.0 cm and v = 24.0 cm:
rac{1}{f} = rac{1}{40} + rac{1}{24} Again, calculate for f. -
For u = 50.0 cm and v = 20.5 cm:
rac{1}{f} = rac{1}{50} + rac{1}{20.5} Calculate.
Finally, average the calculated focal lengths from all measurements, ensuring correct substitution has been made, which leads to an average focal length of approximately 14.9 cm.