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Q77
(NDA-II/2009)
Science & Technology › Basic Science (Physics, Chemistry, Biology) › Geometrical optics
Answer Verified
Ln object is placed at a distance of 12 cm from a anvex lens on its principal axis and a virtual image f certain size is formed. If the object is moved further cm away from the lens, a real image of the same ize as that of the virtual image is formed. Which ne of the following is the focal length of the lens?
Result
Your answer:
—
·
Correct:
B
Explanation
The correct answer is Option 2 (16 cm). This problem utilizes the lens formula 1/f = 1/v - 1/u and the magnification formula m = f / (f + u).
In the first case, the object distance (u₁) is -12 cm. Since the image is virtual, the magnification (m₁) is positive. In the second case, the object is moved 8 cm further away, so u₂ = -(12 + 8) = -20 cm. Here, a real image of the same size is formed, meaning the magnification (m₂) is negative and equal in magnitude to m₁ (m₁ = -m₂).
- Case 1: m₁ = f / (f - 12)
- Case 2: m₂ = f / (f - 20)
Equating them as m₁ = -m₂:
f / (f - 12) = -[f / (f - 20)]
1 / (f - 12) = -1 / (f - 20)
f - 20 = -f + 12
2f = 32
f = 16 cm.
Options 1, 3, and 4 are incorrect as they do not satisfy the condition of equal magnification magnitude at these specific object distances.
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