Final answer:
The image formed by the 200 mm focal length telephoto lens photographing mountains 10 km away is at the focal point on the opposite side of the lens, approximately 0.200 m from it.
The height of the image of a 1000 m high cliff can be calculated by using the magnification equation which relates to the object height and distances involved.
Step-by-step explanation:
In the scenario provided, a 200 mm focal length telephoto lens is used to photograph mountains that are 10.0 km away. To answer the questions:
- (a) The image location in terms of a lens equation, given the object distance (10.0 km) is extremely far away, will basically be at the focal point on the opposite side of the lens. Thus, the image is formed at a distance equal to the focal length of the lens from the lens itself, which is 0.200 m (200 mm converted to meters).
- (b) The height of the image of the 1000 m high cliff can be found using the lens magnification equation. Magnification is the ratio of the height of the image to the height of the object and is also equal to the negative ratio of the image distance to the object distance (given by the formula M = -I/O where I is image distance and O is object distance). As the object distance is much greater than the image distance, the magnification will be very small and negative, leading to a small inverted image. The exact height of the image can be calculated using the magnification and the object's actual height.
The 100 yards mentioned in the hypothetical ski lift question is not related to this photography scenario. It could refer to a horizontal distance or be a typographical error, depending on the context of that particular problem.