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A student carried out an experiment to measure the focal length of a concave mirror - Leaving Cert Physics - Question 3 - 2010
Question 3
A student carried out an experiment to measure the focal length of a concave mirror. The student placed an object in front of the mirror so that a real image was for... show full transcript
Worked Solution & Example Answer:A student carried out an experiment to measure the focal length of a concave mirror - Leaving Cert Physics - Question 3 - 2010
Step 1
Draw a labelled diagram showing how the apparatus was arranged.
Answer
To draw the apparatus, include the following components:
- A concave mirror, represented as a curved line.
- An object placed in front of the mirror, marked as 'object'. Use a cross to denote the object.
- An image appearing behind the mirror labeled 'image'.
- A ray diagram illustrating the reflection of light, showing how light rays converge to form the image.
- Label the optical bench with a straight line along which the distances will be measured. Include the correct arrangement of distances u (object distance) and v (image distance).
- Ensure that the diagram is detailed, showing measurements with a meter stick and the screen position.
Step 2
Mark the distances u and v on your diagram.
Answer
In the diagram:
- Mark the distance from the mirror to the object as 'u'. This is the object distance.
- Mark the distance from the mirror to the image as 'v'. This is the image distance.
- Ensure to place both measurements in the correct orientation, with u being positive in front of the mirror and v being negative behind the mirror.
Step 3
How was the position of the real image located?
Answer
To locate the real image, the screen was adjusted until a clear (inverted) image was obtained. This was done by focusing the image formed by the concave mirror onto a screen. Adjust the position of the screen gradually until the image is sharpest, indicating the correct distance from the mirror.
Step 4
Calculate the value for the focal length f of the mirror using the data.
Answer
To calculate the focal length (f), we use the mirror formula:
rac{1}{f} = rac{1}{u} + rac{1}{v}
Using the data from the table:
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For u = 20 cm, v = 65 cm: rac{1}{f} = rac{1}{20} + rac{1}{65} = rac{65 + 20}{1300} = rac{85}{1300} Thus, f = 15.29 cm.
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For u = 30 cm, v = 32 cm: rac{1}{f} = rac{1}{30} + rac{1}{32} = rac{32 + 30}{960} = rac{62}{960} Thus, f = 15.48 cm.
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For u = 50 cm, v = 23 cm: rac{1}{f} = rac{1}{50} + rac{1}{23} = rac{23 + 50}{1150} = rac{73}{1150} Thus, f = 15.75 cm.
Finally, to find the average focal length: f_{avg} = rac{15.29 + 15.48 + 15.75}{3} = 15.51 ext{ cm}
Step 5
Why did the student repeat the experiment?
Answer
The student repeated the experiment to ensure greater accuracy. Repeating the experiment helps to minimize errors, allowing for a more reliable result. This also aids in obtaining an average value from multiple trials, providing a better estimate of the focal length.