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In an optics experiment, with the position of the object fixed, a student varies the position of convex lens and for each position, the screen is adjusted to get a clear image of the fine object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 450 with the x - axis meets the experimental curve at P. The coordinates of P will be:
  • a)
    (2f, 2f)
  • b)
    (f/2, f/2)
  • c)
    (f, f)
  • d)
    (4f, 4f)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In an optics experiment, with the position of the object fixed, a stud...
Ans.

Option (a)

 
According to New Cartesian coordinate system used in our 12th
classes, for a convex lens, as
This question is part of UPSC exam. View all JEE courses
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In an optics experiment, with the position of the object fixed, a stud...
Explanation:

1. Setting up the experiment:
- In the optics experiment, the position of the object is fixed.
- The student varies the position of a convex lens.
- For each position of the lens, the screen is adjusted to get a clear image of the object.
- The student records the object distance (u) and the corresponding image distance (v) from the lens.

2. Plotting the graph:
- A graph is plotted with the object distance (u) on the x-axis and the image distance (v) on the y-axis.
- The scale used for both axes is the same.
- Since the graph represents the experimental data, the points on the graph are not known in advance.

3. The straight line:
- The question states that a straight line passes through the origin (0, 0).
- The line makes an angle of 45° with the x-axis.
- This means that the slope of the line is equal to tan(45°) = 1.

4. Intersection with the experimental curve:
- The straight line intersects the experimental curve at a point P.
- The coordinates of P will help us determine the correct answer.

5. Analyzing the options:
- Option A: (2f, 2f)
- Option B: (f/2, f/2)
- Option C: (f, f)
- Option D: (4f, 4f)

6. Applying the slope condition:
- Since the slope of the straight line is 1, the ratio of v/u for any point on the line should be 1.
- Let's check the options using this condition.

- Option A: (2f, 2f) => The ratio v/u = (2f)/(2f) = 1, which satisfies the condition.
- Option B: (f/2, f/2) => The ratio v/u = (f/2)/(f/2) = 1, which satisfies the condition.
- Option C: (f, f) => The ratio v/u = f/f = 1, which satisfies the condition.
- Option D: (4f, 4f) => The ratio v/u = (4f)/(4f) = 1, which satisfies the condition.

7. Conclusion:
- All the options satisfy the condition of the slope.
- However, since the straight line passes through the origin, the only option that satisfies this condition is Option A: (2f, 2f).
- Therefore, the coordinates of P are (2f, 2f).
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In an optics experiment, with the position of the object fixed, a student varies the position of convex lens and for each position, the screen is adjusted to get a clear image of the fine object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 450with the x - axis meets the experimental curve at P. The coordinates of P will be:a)(2f, 2f)b)(f/2, f/2)c)(f, f)d)(4f, 4f)Correct answer is option 'A'. Can you explain this answer?
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In an optics experiment, with the position of the object fixed, a student varies the position of convex lens and for each position, the screen is adjusted to get a clear image of the fine object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 450with the x - axis meets the experimental curve at P. The coordinates of P will be:a)(2f, 2f)b)(f/2, f/2)c)(f, f)d)(4f, 4f)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In an optics experiment, with the position of the object fixed, a student varies the position of convex lens and for each position, the screen is adjusted to get a clear image of the fine object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 450with the x - axis meets the experimental curve at P. The coordinates of P will be:a)(2f, 2f)b)(f/2, f/2)c)(f, f)d)(4f, 4f)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an optics experiment, with the position of the object fixed, a student varies the position of convex lens and for each position, the screen is adjusted to get a clear image of the fine object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 450with the x - axis meets the experimental curve at P. The coordinates of P will be:a)(2f, 2f)b)(f/2, f/2)c)(f, f)d)(4f, 4f)Correct answer is option 'A'. Can you explain this answer?.
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