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प्रश्न
Solve Numerical example.
A convex lens held some distance above a 6 cm long pencil produces its image of SOME size. On shifting the lens by a distance equal to its focal length, it again produces the image of the SAME size as earlier. Determine the image size.
उत्तर
For a convex lens, it is given that the image size remains unchanged after shifting the lens through a distance equal to its focal length. From given conditions, it can be inferred that the object distance should be u = `-"f"/2`.
Also, h1 = 6 cm, v1 = v2
From the formula for thin lenses,
`1/"f"=1/"v"-1/"u"`
i.e., `1/"v"=1/"f"+1/"u"`
∴ `1/"v"=1/"f"+(-2/"f")`
∴ v = – f
Now, magnification of the lens is,
m = `"h"_2/"h"_1="v"/"u"=(-"f")/(-"f"/2)` = 2
∴ h2 = h1 × 2 = 6 × 2 = 12 cm
The size of the image formed will be 12 cm.
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