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 camera's image sensor. (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 (1/f = 1/do + 1/di) relates the focal length of a lens (f) to the distances of the object (do) and its image (di) from the lens. This fundamental relationship in optics allows one to determine the necessary lens properties to form a clear image on an image sensor or screen, by accounting for how light rays converge or diverge after passing through the lens.

Magnification

Magnification in optics is defined as the ratio of the image size to the object size and is also given by m = -di/do, where di is the image distance and do is the object distance. This concept describes how much larger or smaller an image appears compared to the actual object, and is essential in applications like photography, where achieving the desired image scale is crucial.

Object and Image Distance Relationships

Understanding the relationship between the object distance and the image distance is key in optical systems. These distances, interconnected through the thin lens equation, determine the position and scale of the image. Adjusting either the object distance or the focal length of the lens directly influences the image distance, which in turn affects the magnification and clarity of the image captured.

Lens Selection and Focal Length Determination in Photography

In photography, choosing the appropriate lens focal length is critical for capturing images with the desired composition and scale. By applying the thin lens equation and the concept of magnification, one can calculate the ideal focal length needed to obtain a specific image size from a particular object at a given distance. This process aids photographers in selecting the right lens for different shooting scenarios, ensuring that images are sharp and properly scaled.

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