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 1

(i)

Given: the focal length of the magnifying glass is 5 cm and the least distance of vision is 25 cm .

The lens formula is given as

1 f = 1 v − 1 u

Where, f is the focal length of the magnifying glass, v is the least distance of vision and u is the object distance.

When the man keeps the magnifying glass close to the page, the images are formed at his near point. So,

v=−25 cm

By substituting the given values in the above expression,

1 5 = 1 −25 − 1 u 1 u = 1 −25 − 1 5 = −5−1 25 u=−4.167 cm

Thus, the closest distance at which the person can read the book is 4.167 cm.

When the man keeps the magnifying glass far from the page, the images are formed at the far point of the eye. So,

v=∞

By substituting the given values in the above expression,

1 u ′ = 1 ∞ − 1 5 =− 1 5 u ′ =−5 cm

Thus, the farthest distance at which the person can read the book is 5 cm.

(ii)

The angular magnification is given as,

α= d | u |

Where, d is the near point of the eye.

Maximum angular magnification occurs when the magnifying glass is placed close to the book.

So,

| u |=4.167 cm

By substituting the given values in the above expression,

α max = 25 4.167 =6

Minimum angular magnification occurs when the magnifying glass is placed at the farthest distance from the book.

So,

| u |=5 cm

By substituting the given values in the above expression,

α min = 25 5 =5

Thus, the values of maximum and minimum angular magnification are 6 and 5 respectively.