The focal length of the lens of a simple film camera is 40.0 mm.By what amount should the distance between the lens and the film be increased or decreased to change the focus from a person who is 25 m from the lens to one who is 4.0 m from the lens?
A)0.2 mm
B)0.3 mm
C)0.4 mm
D)0.5 mm
E)0.7 mm

Question

Quizplus · Accepted Answer

To solve this problem, we use the lens formula: $ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} $, where $f$ is the focal length of the lens, $d_o$ is the object distance, and $d_i$ is the image distance. We need to find the change in image distance ($d_i$) when the object distance changes from 25 m to 4 m.First, for the object at 25 m:Given $f = 40.0$ mm and $d_o = 25000$ mm (since 1 m = 1000 mm), we find $d_i$ using the lens formula.$ \frac{1}{40} = \frac{1}{25000} + \frac{1}{d_i} $Solving for $d_i$, we get $d_i \approx 40.16$ mm.Next, for the object at 4 m:Given $d_o = 4000$ mm, we use the lens formula again.$ \frac{1}{40} = \frac{1}{4000} + \frac{1}{d_i} $Solving for $d_i$, we get $d_i \approx 40.40$ mm.The change in $d_i$ is $40.40 - 40.16 = 0.24$ mm, which is closest to 0.3 mm.

The Focal Length of the Lens of a Simple Film