When a converging lens is used in a camera (as in Figure...

When a converging lens is used in a camera (as in Figure $26.26 b)$, the film must be at a distance of $0.210 \mathrm{~m}$ from the lens to record an image of an object that is $4.00 \mathrm{~m}$ from the lens. The same lens and film are used in a projector (see Figure $26.27 b$ ), with the screen $0.500 \mathrm{~m}$ from the lens. How far from the projector lens should the film be placed?

Key Concepts

Thin Lens Equation

The thin lens equation (1/f = 1/d_o + 1/d_i) is the fundamental relationship in geometrical optics that relates a lens's focal length (f) to the distances of the object (d_o) and the image (d_i) from the lens. This equation is used to determine image positions, check the possibility of a real or virtual image formation and is essential in solving problems involving image formation by lenses.

Focal Length

The focal length is a central property of a lens, defining the distance at which parallel rays of light converge (or appear to diverge) after passing through the lens. It determines the scale of magnification and image formation in both cameras and projectors and remains constant for a given lens, regardless of the object or image distances.

Object and Image Distance

Object distance and image distance refer to the separations between the lens and the object and between the lens and the image, respectively. Correctly identifying and manipulating these distances using the thin lens formula is critical for designing and understanding optical systems that form clear images.

Reversibility of Light Paths

In optical systems, the principle of reversibility states that light rays follow the same path in reverse. This concept underpins the ability to interchange the roles of the object and image in systems like cameras and projectors, allowing adjustments in placements to achieve proper image formation on film or a screen.

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