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?
Given:
(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:
…(1)
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′|
= 25/5
= 5
Hence the maximum magnification is 5.