A converging lens (f=25.0 cm) is used to project an image of an object onto a screen. The object

step 1 So we have an object here and we have a screen here and the lens can be placed anywhere in betwe

A converging lens (f=25.0 cm) is used to project an image of...

A converging lens $(f=25.0 \mathrm{cm})$ is used to project an image of an object onto a screen. The object and the screen are $125 \mathrm{cm}$ apart, and between them the lens can be placed at either of two locations. Find the two object distances.

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Key Concepts

Quadratic Equation in Lens Systems

When the two relationships from the thin lens equation and the fixed total distance between the object and the screen are combined, the result is a quadratic equation. Solving this quadratic can yield two valid solutions, representing the two distinct positions where the lens can form a sharp image on the screen.

Object and Image Distance Relationship

In setups where the object and the screen are fixed at a specific separation, the object and image distances are interdependent, given by do + di = constant. This relationship is crucial when determining the possible positions of a lens that will project a clear image on the screen.

Thin Lens Equation

The thin lens equation 1/f = 1/do + 1/di relates the focal length (f), the object distance (do), and the image distance (di) of a lens. This equation is central to understanding how lenses form images and is widely applied in designing optical systems.

Converging Lens

A converging, or convex, lens is one that bends incoming parallel light rays so that they meet at a single point known as the focal point. Such lenses have a positive focal length and are used to form real images by bringing light together in systems like cameras, projectors, and eyeglasses.

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