An object of height 3.00 cm is placed 12.0 cm from a diverging lens of focal length -12.0 cm.

step 1 Okay, so in drawing this array diagram to scale, we can figure out that the image height is half

An object of height 3.00 cm is placed 12.0 cm from a...

Key Concepts

Ray Diagram Construction

Constructing a ray diagram involves drawing key rays from the object through the lens that help determine the image location, size, and orientation. For diverging lenses, typical rays used include a ray parallel to the principal axis (which appears to diverge from the focal point) and a ray directed toward the lens’s center (which continues in a straight line). These diagrams visually represent the paths of light and the formation of the virtual image, making it easier to apply the lens equation and magnification concepts.

Magnification

Magnification relates the height of the image to the height of the object and is given by the relation m = -di/do. The negative sign indicates that a negative image distance corresponds to an upright image when dealing with diverging lenses. It also provides information about the relative sizes of the image and the object, demonstrating whether the image is reduced or enlarged.

Lens Equation

The lens equation (1/f = 1/do + 1/di) is a fundamental relation in geometric optics that relates the focal length, object distance, and image distance of a lens. In this formula, the sign conventions are crucial: for diverging lenses, the focal length is negative, and the resulting image distance is also negative, indicating that the image is virtual and located on the same side of the lens as the object.

Diverging Lenses

A diverging lens is a type of lens that causes parallel rays of light to spread out, or diverge, after passing through it. Unlike converging lenses, which can produce real images, diverging lenses always form virtual, upright, and reduced images. This characteristic is essential when analyzing the image properties in optical systems involving diverging lenses.

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