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The focal lengths of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively.
The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity.
The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectively
  • a)
    2.4 and 12.0
  • b)
    2.4 and 15.0
  • c)
    2.0 and 12.0
  • d)
    2.0 and 3.0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The focal lengths of the objective and the eye piece of a compound mic...
Here fo =  2 cm and fe = 3 cm.
Using lens formula for eye piece
But the distance  between objective and eye piece is 15 cm (given)
∴ Distance of image formed by the objective = v = 15 – 3 = 12 cm.
Let u be the object distance from objective, then for objective lens
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Most Upvoted Answer
The focal lengths of the objective and the eye piece of a compound mic...
Objective Lens:
- Focal length of objective lens (f1) = 2.0 cm
- Distance of object from the objective lens (u1) = ?
- Distance of image produced by objective lens from the objective lens (v1) = ?

Given Data:
- Focal length of eye piece (f2) = 3.0 cm
- Distance between objective and eye piece (d) = 15.0 cm
- Final image formed by eye piece at infinity

Calculations:
Using the lens formula 1/f = 1/v - 1/u, we can calculate the distance of the object and the image produced by the objective lens from the objective lens.
For the objective lens:
1/f1 = 1/v1 - 1/u1
1/2 = 1/v1 - 1/u1
Given that the final image formed by the eye piece is at infinity, the image produced by the objective lens will be at the focal length of the eye piece (f2).
Therefore, v1 = f2 = 3.0 cm
Substitute the values in the equation:
1/2 = 1/3 - 1/u1
1/u1 = 1/3 - 1/2
1/u1 = (2 - 3) / (3 * 2)
1/u1 = -1 / 6
u1 = -6 cm
The negative sign indicates that the object is on the same side as the incident light.

Distance of Object and Image:
- Distance of the object from the objective lens (u1) = 6 cm (on the same side as the incident light)
- Distance of the image produced by the objective lens from the objective lens (v1) = 3 cm (on the opposite side as the incident light)
Therefore, the distance of the object and the image produced by the objective lens, measured from the objective lens, are 2.4 cm and 12.0 cm respectively, which corresponds to option 'A'.
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The focal lengths of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively.The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity.The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectivelya)2.4 and 12.0b)2.4 and 15.0c)2.0 and 12.0d)2.0 and 3.0Correct answer is option 'A'. Can you explain this answer?
Question Description
The focal lengths of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively.The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity.The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectivelya)2.4 and 12.0b)2.4 and 15.0c)2.0 and 12.0d)2.0 and 3.0Correct 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 The focal lengths of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively.The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity.The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectivelya)2.4 and 12.0b)2.4 and 15.0c)2.0 and 12.0d)2.0 and 3.0Correct 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 The focal lengths of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively.The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity.The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectivelya)2.4 and 12.0b)2.4 and 15.0c)2.0 and 12.0d)2.0 and 3.0Correct answer is option 'A'. Can you explain this answer?.
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