Consult Interactive Solution 26.117 at www.wiley.com/...

Consult Interactive Solution $26.117$ at www.wiley.com/ college/cutnell to review the concepts on which this problem depends. A camera is supplied with two interchangeable lenses, whose focal lengths are $35.0$ and $150.0 \mathrm{~mm}$. A woman whose height is $1.60 \mathrm{~m}$ stands $9.00 \mathrm{~m}$ in front of the camera. What is the height (including sign) of her image on the image sensor, as produced by (a) the $35.0$ -mm lens and (b) the $150.0-\mathrm{mm}$ lens?

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Key Concepts

Thin Lens Equation

The thin lens equation (1/f = 1/do + 1/di) is a fundamental relation in geometrical optics that connects the focal length of a lens with the distances of the object (do) and the image (di) from the lens. This equation is key to calculating where an image will form when an object is placed at a certain distance from a lens.

Magnification

Magnification in lens optics is defined as the ratio of the image height to the object height (m = hi/ho), which can also be expressed as m = -di/do based on the thin lens formula. This concept is used to determine the size and orientation (inversion) of the image relative to the object.

Optical Sign Conventions

Optical sign conventions provide a systematic way to assign positive or negative values to various distances (such as object distance, image distance, and focal length) in optical calculations. They are crucial for correctly applying formulas like the thin lens equation and for understanding the nature of the image (whether it is real or virtual, upright or inverted).

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