The focal points of a thin diverging lens are 25.0 cm from the center of the lens. An object is

step 1 Everyone here it is given a diverging lens of focal length at 25 cm since it is diverging so foc

The focal points of a thin diverging lens are 25.0 cm from...

The focal points of a thin diverging lens are $25.0 \mathrm{~cm}$ from the center of the lens. An object is placed to the left of the lens, and the lens forms an image of the object that is $18.0 \mathrm{~cm}$ from the lens. (a) Is the image to the left or right of the lens? (b) How far is the object from the center of the lens? (c) Is the height of the image less than, greater than, or the same as the height of the object?

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Key Concepts

Diverging Lens

A diverging lens is one that causes light rays to spread out. It is characterized by a negative focal length and always produces virtual, upright, and reduced images. This concept explains why, for a diverging lens, the image is on the same side as the object.

Lens Equation

The lens equation, given by 1/f = 1/s_o + 1/s_i, connects the focal length (f), the object distance (s_o), and the image distance (s_i). For diverging lenses, the appropriate sign conventions must be applied, with the focal length being negative and virtual image distances also typically taken as negative.

Sign Conventions

Sign conventions are critical in optics to determine the correct positions of objects and images relative to the lens. In the context of lens equations, distances measured in the direction of the incoming light are typically considered negative, which is important when dealing with virtual images and diverging lenses.

Magnification

Magnification is defined as -s_i/s_o and describes how the size of an image compares to the size of the object. For diverging lenses, the magnification is less than one, indicating that the image is reduced in size relative to the object, and the positive magnification value confirms that the image is upright.

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