The Ortiz family is viewing slides from their summer...

The Ortiz family is viewing slides from their summer vacation trip to the Grand Canyon. Their slide projector has a projection lens of $10.0-\mathrm{cm}$ focal length and the screen is located $2.5 \mathrm{~m}$ from the projector. (a) What is the distance between the slide and the projection lens? (b) What is the magnification of the image? (c) How wide is the image of a slide of width $36 \mathrm{~mm}$ on the screen? (See the figure with Problem 18.)

The Ortiz family is viewing slides from their summer vacation trip to the Grand Canyon. Their slide projector has a projection lens of $10.0-\mathrm{cm}$ focal length and the screen is located $2.5 \mathrm{~m}$ from the projector. (a) What is the distance between the slide and the projection lens? (b) What is the magnification of the image?
(c) How wide is the image of a slide of width $36 \mathrm{~mm}$ on the screen? (See the figure with Problem 18.)

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Key Concepts

Thin Lens Equation

The thin lens equation relates the focal length of a lens to the distances from the lens to the object and to the image. It is expressed as 1/f = 1/d? + 1/d?, where f is the focal length, d? is the object distance from the lens, and d? is the image distance from the lens. This equation is central in geometrical optics and is used to determine the positions and characteristics of images formed by lenses.

Magnification

Magnification is a measure of how much larger or smaller the image is compared to the object. It is defined as the ratio m = -d?/d? for a thin lens, where the negative sign indicates image inversion. Magnification also relates to the sizes of the image and object, as m = image size / object size. This concept is essential in understanding how lenses can project images that are scaled versions of the original objects.

Image Size Determination

Once magnification is known, the physical dimensions of the projected image can be calculated by multiplying the object’s dimensions by the magnification factor. This method is widely used in projection optics to determine how large an image will appear on a screen, given the size of the object and the setup of the optical system.

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