A photographer wishes to take a photograph of the Eiffel Tower (300 m tall ) from across the Se

step 1 In this problem we use a camera to take a picture of the Eiffel Tower. So the Eiffel Tower is he

A photographer wishes to take a photograph of the Eiffel...

A photographer wishes to take a photograph of the Eiffel Tower $(300 \mathrm{~m}$ tall $)$ from across the Seine River, a distance of $300 \mathrm{~m}$ from the tower. What focal length lens should she use to get an image that is $20 \mathrm{~mm}$ high on the film?

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Key Concepts

Thin Lens Equation

The thin lens equation relates the focal length of a lens to the distances of the object and the image from the lens. It is given by 1/f = 1/v + 1/u, where f is the focal length, u is the object distance, and v is the image distance. This relationship is fundamental in optics and is used to determine how images are formed by lenses in many applications including photography.

Magnification

Magnification in optics is the ratio of the size of the image to the size of the object. It can also be expressed in terms of the distances from the lens, where magnification m = v/u. This concept is crucial in understanding how a lens scales objects onto a film or sensor, allowing photographers to control the size of the captured image relative to the actual object.

Focal Length

The focal length of a lens is a measure of its ability to converge or diverge light, and it directly influences the field of view and the scale of the image projected onto the film or sensor. In photography, selecting the appropriate focal length is key to achieving the desired composition and magnification of the subject in the final image.

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