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Question
A card sheet divided into squares each of size 1 mm2 is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 cm) held close to the eye.
- What is the magnification produced by the lens? How much is the area of each square in the virtual image?
- What is the angular magnification (magnifying power) of the lens?
- Is the magnification in (a) equal to the magnifying power in (b)? Explain.
Solution
(a) For magnification by the magnifying lens.
Let us use lens formula,
u = −9 cm, f = +9 cm
`1/"v" - 1/"u" = 1/"f"`
`1/"v" - 1/(-9) = 1/9`
`1/"v" = 1/9 - 1/9` = 0
Image position v = ∞
Magnification, `"m" = "v"/"u"` = ∞
A large image will be formed.
(b) Angular magnification, m = `"D"/"u" = 25/9` = 2.8
(c) No, the linear magnification by a lens and the magnifying power (angular magnification) of a magnifying glass have different values.
The linear magnification is calculated using m = `"v"/"u"`, whereas angular magnification is m = `"D"/"u" = β/α`, the ratio of the angle subtended by the image of the object at eye lens 'β' to the angle subtended by the object assumed to be at least distance at eye lens 'α'.
The linear magnification and angular magnification in a microscope have similar magnitude when the image is at least a distance of distinct vision, i.e., 25 cm.
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