A 1.7-m tall woman stands 8.0-m in front of a camera with a 5.0-cm focal length lens.What is the size of the image formed on film?
A)23.5 cm
B)2.7 cm
C)1.1 cm
D)68.0 cm
E)0.37 cm

Question

A 1.7-m tall woman stands 8.0-m in front of a camera with a 5.0-cm focal length lens.What is the size of the image formed on film?
A)23.5 cm
B)2.7 cm
C)1.1 cm
D)68.0 cm
E)​0.37 cm

Quizplus · Accepted Answer

First, we need to calculate the distance the image is formed from the lens using the thin lens equation: 
1/f = 1/di + 1/do where f = 0.05m (converted from cm), di is the distance of the image from the lens, and do is the distance of the object from the lens. Since the object is far away (8.0m >> 0.05m), we can approximate do to be 8.0m. Solving for di, we get di = 0.0498m (or 4.98 cm).

Next, we can use similar triangles to find the height of the image. The ratio of the image height (hi) to the object height (ho) is equal to the ratio of the image distance (di) to the object distance (do). 
hi/ho = di/do 
hi/1.7m = 0.0498m/8.0m 
Solving for hi, we get hi = 0.011 m (or 1.1 cm).

Therefore, the size of the image formed on film is 1.1 cm, which is Choice C.

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