A 1.5-cm-tall object is 90 cm in front of a diverging lens that has a 45 cm focal length. Use ra

step 1 This question is about drawing the ray diagram for diverging lens. So in this situation, we have

A 1.5-cm-tall object is 90 cm in front of a diverging lens...

A 1.5-cm-tall object is 90 $\mathrm{cm}$ in front of a diverging lens that has a $45 \mathrm{cm}$ focal length. Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.

Key Concepts

Ray Tracing

Ray tracing is a graphical method used in geometric optics to determine the path that light rays take through an optical system. It involves drawing key rays from the object as they interact with the lens, and then extending them to locate the image. This method helps in visualizing and measuring the position, size, and orientation of the resulting image.

Thin Lens Equation

The thin lens equation relates the object distance, image distance, and focal length of a lens. It is expressed as 1/f = 1/do + 1/di, where f is the focal length, do is the distance from the lens to the object, and di is the distance from the lens to the image. This fundamental formula is essential for predicting image formation in lenses.

Magnification

Magnification in lens systems is the ratio of the image height to the object height, and it is also related to the distances of the object and image from the lens. It is given by the equation m = hi/ho = -di/do. This concept helps determine how much larger or smaller the image will be compared to the object and provides insight into whether the image is upright or inverted.

Diverging Lens Properties

A diverging lens (also known as a concave lens) causes parallel rays of light to spread out as if they were emanating from a common point (the virtual focus). As a result, the images formed by a diverging lens are typically virtual, reduced in size, and upright relative to the object. Understanding these properties is key when analyzing image formation using ray tracing.

Sign Conventions in Optics

Sign conventions are used to properly apply the thin lens equation and correctly determine the nature of the image. They dictate the positive or negative values for object distances, image distances, and focal lengths. For a diverging lens, the focal length is considered negative, and the resulting image distance is also negative, indicating that the image is virtual and formed on the same side of the lens as the object.

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