Question

The focal length of the lens of a simple digital camera is 6.5 mm, and it is originally focused on a mountain 1 km away. In what direction must the lens be moved to change the focus of the camera to a person 2.0 m away?

A. It does not make any difference.

B. sideways from the CCD sensors

C. away from the CCD sensors

D. towards the CCD sensors

Answer 1

C. away from the CCD sensors

when the lens is focused on a mountain 1 km away,

u = 1 km = 1000 m
f = 6.5 mm = 0.0065 m
let v is the image distance.

use, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/0.0065 - 1/1000

v = 0.00650 m

= 6.50 mm

when the lens moved to change the focus of the camera to a person 2.0 m away
u = 2.0 m
f = 6.5 mm = 0.0065 m
let v is the image distance.

use, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/0.0065 - 1/2

v = 0.006521 m

= 6.521 mm

so, image distance is increased by 6.521 - 6.5 = 0.021 mm

so, the lens should move away from the CCD sensor.