A diverging lens has a focal length of 15.0 cm . An object placed near it forms a 2.0 -cm-high i

step 1 Because this is a diverging lens, focal length is negative 15 centimeter, image distance is give

A diverging lens has a focal length of 15.0 cm . An object...

A diverging lens has a focal length of $15.0 \mathrm{cm} .$ An object placed near it forms a 2.0 -cm-high image at a distance of $5.0 \mathrm{cm}$ from the lens. a. What are the object position and object height? b. The diverging lens is now replaced by a converging lens with the same focal length. What are the image position, height, and orientation? Is it a virtual image or a real image?

A diverging lens has a focal length of $15.0 \mathrm{cm} .$ An object placed near it forms a 2.0 -cm-high image at a distance of $5.0 \mathrm{cm}$ from the lens.
a. What are the object position and object height?
b. The diverging lens is now replaced by a converging lens with the same focal length. What are the image position, height, and orientation? Is it a virtual image or a real image?

Key Concepts

Thin Lens Equation

The thin lens equation (1/f = 1/do + 1/di) relates the focal length of a lens to the distances from the lens to the object and the image. It is fundamental in geometrical optics for determining where an image forms and requires careful application of sign conventions to correctly determine whether images are real or virtual.

Sign Conventions

Sign conventions in optics help assign positive or negative values to the focal length, object distance, and image distance. They are essential for consistently applying the thin lens equation, particularly in distinguishing real images from virtual ones and understanding the behavior of converging versus diverging lenses.

Magnification

Magnification describes the ratio of the image size to the object size and is expressed as m = hi/ho = -di/do. This concept is critical as it indicates whether the image is enlarged or reduced compared to the object, and whether the image is upright or inverted based on the sign of the magnification.

Lens Types and Image Formation

Different types of lenses, such as converging and diverging lenses, produce images with distinct characteristics. A diverging lens generally forms a virtual, upright, and diminished image, while a converging lens can form real or virtual images depending on the object's position relative to the lens's focal point. Understanding the inherent behavior of each lens type is key to predicting image location, size, and orientation.

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