A person on a safari wants to take a photograph of a...

A person on a safari wants to take a photograph of a hippopotamus from a distance of $75.0 \mathrm{~m}$. The animal is $4.00 \mathrm{~m}$ long and its image is to be $1.20 \mathrm{~cm}$ long on the film. (a) What focal length lens should be used? (b) What would be the size of the image if a lens of $50.0-\mathrm{mm}$ focal length were used? (c) How close to the hippo would the person have to be to capture a $1.20-\mathrm{cm}$ -long image using a $50.0-\mathrm{mm}$ lens?

A person on a safari wants to take a photograph of a hippopotamus from a distance of $75.0 \mathrm{~m}$. The animal is $4.00 \mathrm{~m}$ long and its image is to be $1.20 \mathrm{~cm}$ long on the film. (a) What focal length lens should be used?
(b) What would be the size of the image if a lens of $50.0-\mathrm{mm}$ focal length were used? (c) How close to the hippo would the person have to be to capture a $1.20-\mathrm{cm}$ -long image using a $50.0-\mathrm{mm}$ lens?

Key Concepts

Thin Lens Equation

The thin lens equation, stated as 1/f = 1/do + 1/di, relates the focal length of a lens (f) to the distances of the object (do) and the image (di) from the lens. This fundamental concept in geometric optics allows one to predict where an image will form given a lens and an object, or determine the focal length required to produce an image at a specific distance.

Magnification

Magnification (m) is defined as the ratio of the image size to the object size, and is also given by the ratio of the image distance to the object distance (m = di/do). This concept is crucial when determining how much larger or smaller an image will appear compared to the actual object, which is particularly important in photography and optical instrumentation.

Image Formation

Image formation involves the process by which lenses or mirrors converge or diverge light rays to produce an image of an object. Understanding how the object distance, image distance, and focal length interact is essential for controlling the size, orientation, and clarity of the resulting image.

Focal Length Determination

Determining the focal length of a lens is a key aspect in optical design, as it defines the lens's ability to converge or diverge light. In practical applications like photography, selecting the appropriate focal length is necessary to achieve the desired image size and quality, based on the distance to the subject and the dimensions of the image sensor or film.