Question

An object is located to the left of a convex lens whose focal length is 39 cm . The magnification produced by the lens is m1 = 3.1. To increase the magnification to 4.5, should the object be moved closer to the lens or farther away? Calculate the distance through which the object should be moved.

Answer 1

Focal length, f = 39 cm
magnification, m1 = 3.1
Consider the object distance as u and the image distance as v.
- (v / u) = 3.1
v = - 3.1 * u
Using the formula, 1 / f = 1 / u + 1 / v,
1 / 39 = 1 / u + 1 / (- 3.1 * u)
1 / 39 = 1 / u * (1 - 0.323)
u = 39 * 0.677
= 26.42 cm

New magnification, m2 = 4.5,
(- v' / u') = 4.5
Where v' and u' are the new image and object distances
Using the formula, 1 / f = 1 / u' + 1 / v',
1 / 39 = 1 / u' - 1 / (4.5 * u')
1 / 39 = 1 / u' * (1 - 0.0.222)
u' = 39 * 0.788
= 30.33 cm

u' - u = 30.33 - 26.42
= 3.9 cm away from the lens