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Understanding the lens formula is critical for predicting how lenses will affect light passing through them. The formula \[\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\]is the foundation for finding where an image will form relative to a lens. Here, \(f\) represents the focal length of the lens, \(v\) is the image distance from the lens, and \(u\) is the object distance from the lens.

To apply the lens formula for a diverging lens, we note that its focal length \(f\) is negative because diverging lenses spread out light rays. Similarly, the object distance \(u\) is negative if the object is placed in front of the lens, following sign convention in optics. To find the image distance \(v\), you simply rearrange the formula:
\[\frac{1}{v} = \frac{1}{f} + \frac{1}{u}\]
Once you substitute the given values and solve for \(v\), you can determine the location of the image which, for a diverging lens, will always be virtual and on the same side as the object.

Ray tracing is a method used to visually determine the path of light through lenses and mirrors. It involves drawing a set of principal rays that follow specific predictable paths when they strike a lens. In the case of a diverging lens, the principal rays include:

• A ray parallel to the principal axis, which will diverge as if it came from the focal point on the same side of the lens after passing through the lens.
• A ray passing through the center of the lens, which will continue straight without bending.
• A ray aiming towards the focal point on the far side of the lens, which will emerge parallel to the principal axis.

By extending these rays backward, they will appear to come from a single point, locating the virtual image. The intersection of the rays gives you both the position and height of the image. Using a ruler or grid paper helps in making accurate ray tracing diagrams, which is essential for visualizing the process of image formation.

Image magnification is a measure of how a lens enlarges or reduces the size of an image compared to the object. It's defined by the formula:
\[ m = \frac{-v}{u} = \frac{h'}{h} \]
where \(m\) is the magnification, \(v\) is the image distance, \(u\) is the object distance, \(h'\) is the image height, and \(h\) is the object height. Negative magnification indicates an inverted image, while positive magnification suggests an upright image. For the exercise at hand, the magnification turned out to be 1, meaning the image is the same size as the object. By understanding how to use and interpret the magnification formula, you can not only determine the size of the image but also infer its orientation (upright or inverted).

A virtual image is an image formed by a lens or mirror that appears to be in a location from which light does not actually come. For diverging lenses, the rays diverge after passing through the lens and only appear to originate from a common point when traced back. Unlike a real image, a virtual image cannot be projected onto a screen because the light rays don't actually converge.

In the context of our exercise, the diverging lens produces a virtual image that is the same size as the object and located 90cm in front of the lens, which is also upright. Virtual images produced by diverging lenses are always found on the same side as the object and are always upright. Knowing this characteristic helps in predicting the nature of the image without complex calculations, making it a valuable concept in optics.