When a diverging lens is held 13.0 cm above a line of print, as in Figure 26.29, the image is 5.

step 1 So in figure 26 .29, we have a converging lens being used as a magnifying class. And what we see

When a diverging lens is held 13.0 cm above a line of print,...

When a diverging lens is held $13.0 \mathrm{cm}$ above a line of print, as in Figure $26.29,$ the image is $5.0 \mathrm{cm}$ beneath the lens. (a) Is the image real or virtual? (b) What is the focal length of the lens?

Key Concepts

Sign Conventions in Lens Equation

Correct application of sign conventions is critical when using the lens formula. Typically, distances are measured from the lens: object distances are positive if the object is on the incoming light side, while image distances are positive for real images (formed on the opposite side from the object) and negative for virtual images (formed on the same side as the object). The focal length for diverging lenses is also taken as negative.

Lens Formula

The lens formula is used to relate the object distance (d?), the image distance (d?), and the focal length (f) of a lens through the equation 1/f = 1/d? + 1/d?. This formula is essential for calculating unknown parameters in imaging systems and understanding how changes in one affect the others.

Diverging (Concave) Lens

A diverging lens is one that spreads out light rays that are initially parallel. It always forms a virtual, upright, and typically reduced image of an object, regardless of the object's position relative to the lens. Understanding the nature of image formation by diverging lenses is essential for analyzing many optical systems.

Virtual Image

A virtual image is formed where light rays appear to diverge from a point behind the lens, even though they do not actually converge there. In diverging lens systems, the image is always virtual because light rays diverge upon passing through the lens, and the brain traces them backward to an apparent origin.

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