Answer :

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, f_{0} = focal length of the objective lens

v_{0} = Distance of image formation

u_{0} = 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:

α_{max} = d/|u′|

= 25/5

= 5

Hence the maximum magnification is 5.

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