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A camera is focused on the image of a building formed by a water-filled spherical flask acting as a convex lens. The height of the building's window appears as H = 50 mm on the photograph, while the image of that same window formed by the flask appears as h = 6 mm on the photograph. Both images subtend the same viewing angle from the camera lens. If the camera lens is at distance d1 from the flask and the flask forms the window image at distance d2 from the flask center on the camera side, find d2 in cm given that d1 = 25 cm.

1. 3.0
2. 3.2
3. 3.5
4. 4.0

Correct answer: 3.0

Solution

The viewing angle to the real window from the camera lens = H / d1 (proportional). The viewing angle to the flask image from the camera lens = h / d2. Since both are captured in the same photograph and the ratio of their heights equals H:h = 50:6, and the camera focuses on d2 (sharp image), while the building is at a much larger distance. The ratio H/h = d1/d2 => d2 = d1 * h/H = 25 * 6/50 = 3.0 cm.

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