(a) Focal length of the magnifying glass, f = 5 cm
Distance vision has the least distance, d = 25 cm
Closest object distance = u
Image distance, v = -d = -25 cm
Applying the lens formula we have:
Where, f0 = focal length of the objective lens
v0 = Distance of image formation
u0 = Distance of object from objective
⇒ u = -25/6
⇒ u = 4.16 cm
Hence, the closest distance at which the person can read the book is 4.167 cm.
For the object at the longest distance (u’), the image distance (v’) = ∞
Again using equation (1), we get,
By solving the above equation we get,
u’ = – 1/5
Therefore, u’ = -5 cm
Hence, the farthest distance at which the person can read the book is 5 cm.
(b) Maximum angular magnification is given by the relation:
αmax = d/|u′|
Hence the maximum magnification is 5.
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