A camera is supplied with two interchangeable lenses, whose...

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 -mm lens?

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Key Concepts

Image Formation in Lenses

Understanding image formation involves combining the thin lens equation and the concept of magnification. This process explains how a lens projects an image onto a sensor or film, defining characteristics such as size, inversion, and clarity.

Sign Conventions in Geometric Optics

Consistent sign conventions are used to assign positive or negative values to distances in optical formulas. These conventions help determine whether the resulting image is real or virtual and whether it is inverted or upright.

Thin Lens Equation

This formula 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/d_o + 1/d_i, and it is central in understanding how lenses form images by connecting these three quantities.

Magnification

Magnification in lens systems describes the ratio of the image size to the object size, typically expressed as m = -d_i/d_o. It not only indicates the scale change of the image relative to the object but also brings information about image orientation, such as inversion.

Focal Length

The focal length is a critical property of a lens that indicates its converging or diverging power. It determines how much an incoming beam of light will be bent and is key to calculating both the image location and its size.

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