Question:
A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm. (a) What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass? (b) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?
Answer:
Focal length of the magnifying glass (f)= 5 cm
Least distance of distance vision (d) = 25 cm
Closest object distance (u) = ?
Using lens formula
1/v - 1/u = 1/f
or, 1/u = 1/f +1/v = 1/-25 -1/5 = -5-1/25 = -6/25
u = -25/6 = -4.16 cm
Hence a person can read a book at closest distance is -4.16 cm
For the object at the farthest distance (u1) and image distance (v1) =∞
1/v1 - 1/u1 = 1/f1
1/u1 = 1/v1 + 1/f1 = 1/∞ -1/5 = -1/5
u1 = -5 cm
Hence a person can read a book at closest distance is -5 cm
(b)
Maximum angular magnification is
amax = d/u = 25/25/6 =25 x 6/25 = 6
Minimum angular magnification is
amax = d/u = 25/5 =5
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