Question

A photographer uses his camera, whose lens has a 50mm focal length, to focus on an object 5.0m away. He then wants to take a picture of an object that is 60cm away.

How far must the lens move to focus on this second object?

Answer 1

f₂ = 0.019 m

Step-by-step explanation:

Let's analyze this exercise a bit, when taking a picture the image should always be in the same place, position of the CCD, let's use the builder's equation to find this distance from the image (i)

1 / f = 1 / o + 1 / i

Where f is the focal length and "o, i" are the distances to the object and image, respectively

1 / i = 1 / f - 1 / o

Let's reduce the magnitudes to the SI system

f = 50 mm = 0.050 m

o = 5.0 m

Let's calculate

1 / i = 1 / 0.050 - 1 / 5.0 = 20- 0.2 = 19.8

i = 0.020 m

Now the object is 60 cm, rotates the lens and has a new focal length

o₂ = 60 cm = 0.60 m

1 / f = 1 / 0.60 + 1 / 0.020 = 1.66 + 50 = 51.66

f₂ = 0.019 m