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) $0.3 \mathrm {~mm}$
B) $0.5 \mathrm {~mm}$
C) $0.4 \mathrm {~mm}$
D) $0.2 \mathrm {~mm}$
E) $0.7 \mathrm {~mm}$

Question

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) $0.3 \mathrm {~mm}$
B) $0.5 \mathrm {~mm}$
C) $0.4 \mathrm {~mm}$
D) $0.2 \mathrm {~mm}$
E) $0.7 \mathrm {~mm}$

Quizplus · Accepted Answer

The lens equation is:$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$where f is the focal length, d_o is the object distance, and d_i is the image distance.When the person is 25 m from the lens, d_o = 25 m. When the person is 4.0 m from the lens, d_o = 4.0 m.We want to find the change in the image distance, d_i, when the object distance changes from 25 m to 4.0 m.$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$$$\frac{1}{40 \mathrm {~mm}} = \frac{1}{25 \mathrm {~m}} + \frac{1}{d_i}$$$$d_i = 40.4 \mathrm {~mm}$$$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$$$\frac{1}{40 \mathrm {~mm}} = \frac{1}{4 \mathrm {~m}} + \frac{1}{d_i}$$$$d_i = 40.7 \mathrm {~mm}$$The change in the image distance is:$$d_i - d_i = 40.7 \mathrm {~mm} - 40.4 \mathrm {~mm} = 0.3 \mathrm {~mm}$$Therefore, the distance between the lens and the film should be increased by 0.3 mm to change the focus from a person who is 25 m from the lens to one who is 4.0 m from the lens.

The Focal Length of the Lens of a Simple Film 0.3 mm0.3 \mathrm {~mm}0.3 mm

The Focal Length of the Lens of a Simple Film $0.3 \mathrm {~mm}$