Question

A macro lens is designed to take very close-range photographs of small objects such as insects and flowers. At its closest focusing distance, a certain macro lens has a focal length of 42.0 mm and forms an image on the photosensors of the camera that is 1.29 times the size of the object. 1) How close must the object be to the lens to achieve this maximum image size? (Express your answer to three significant figures.)

2)

What is the magnification if the object is twice as far from the lens as in part (1)? (Express your answer to three significant figures.)

Answer 1

m = magnification = 1.29

f = focal length = 42 mm

d_i = image distance

d_o = object distance

magnification is given as

m = - d_i/d_o

1.29 = - d_i/d_o

d_o = - d_i/1.29                                                         eq-1

Using the lens equation

1/f = 1/d_o + 1/d_i

1/42 = 1/(- d_i/1.29 ) + 1/d_i

d_i = - 12.18 mm

using eq-1

d_o = - d_i/1.29

d_o = - (- 12.18)/1.29

d_o = 9.44 mm

2)

f = focal length = 42 mm

d_i = image distance

d_o = object distance = 2 x 9.44 = 18.88 mm

Using the lens equation

1/f = 1/d_o + 1/d_i

1/42 = 1/(18.88 ) + 1/d_i

d_i = - 34.4 mm

magnification is given as

m = - d_i/d_o = - (- 34.4)/18.88 = 1.82