A slide projector needs to create a 98 -cm-high image of a...

A slide projector needs to create a 98 -cm-high image of a 2.0-cm-tall slide. The screen is $300 \mathrm{cm}$ from the slide.
a. What focal length does the lens need? Assume that it is a thin lens.
b. How far should you place the lens from the slide?

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Key Concepts

Thin Lens Equation

The thin lens equation relates the object distance, the image distance, and the focal length through the formula 1/f = 1/d_o + 1/d_i. This equation is fundamental in geometrical optics for finding the focal length if the distances of the object and its corresponding image are known.

Magnification

Magnification in lens systems is defined as the ratio of the height of the image to the height of the object, and it is also equal to -d_i/d_o. This concept helps to link the physical size of the produced image with the original object size, allowing for the determination of object or image distances when combined with other relationships.

Object and Image Distance Relationships

In many optical systems, especially projection setups, the distance between the object and the screen is fixed. This constraint, which sets the sum of the object distance and image distance, is critical when applying the thin lens equation and magnification to solve for unknown distances and the required focal length.

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