Question

A camera with a 90-mm-focal-length lens is focused on an object 1.30 m from the lens. To refocus on an object 6.50 m from the lens, by how much must the distance between the lens and the sensor be changed

Answer 1

The distance between the lens and the sensor must be changed by 5.454-mm

Step-by-step explanation:

`(1)/(S) +(1)/(S^')} = (1)/(f)`

Given;

the focal length = 90-mm

object distance = 1.30 m= 1300-mm

`(1)/(S^')} = (1)/(f) - (1)/(S) \\\\(1)/(S^')} = (1)/(90) - (1)/(1300)\\\\(1)/(S^')} = (121)/(11700) \\\\S{^'} = (11700)/(121) =96.694-mm`

When the object is refocused from the lens;

New object distance = 6.50 m = 6500-mm

`(1)/(S^')} = (1)/(f) - (1)/(S) \\\\(1)/(S^')} = (1)/(90) - (1)/(6500)\\\\(1)/(S^')} = (641)/(58500) \\\\S{^'} = (58500)/(641) =91.264-mm`

determine how much the distance between the lens and the sensor be changed; = Δs'

Δs' = (96.694 - 91.264)mm = 5.454-mm

Therefore, the distance between the lens and the sensor must be changed by 5.454-mm