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Ch 34: Ray Optics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 34: Ray OpticsProblema 36a
Capitolo 34, Problema 36a

A 1.0-cm-tall object is 60 cm in front of a diverging lens that has a −30 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.

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Start by understanding the problem: A diverging lens has a negative focal length (f = -30 cm). The object is placed 60 cm in front of the lens, and its height is 1.0 cm. We need to determine the image distance and image height using ray tracing.
Draw a scaled diagram: On graph paper, draw the principal axis (a horizontal line). Mark the optical center of the lens at the origin. Place the object 60 cm to the left of the lens on the principal axis, and draw the object as a vertical arrow 1.0 cm tall.
Trace the first ray: Draw a ray from the top of the object parallel to the principal axis. After passing through the lens, this ray will diverge as if it came from the focal point on the same side as the object. Extend the diverging ray backward with a dashed line to locate its virtual origin.
Trace the second ray: Draw a ray from the top of the object heading toward the focal point on the opposite side of the lens. After passing through the lens, this ray will emerge parallel to the principal axis. Extend this ray backward with a dashed line to locate its virtual origin.
Locate the image: The point where the two dashed lines intersect is the location of the virtual image. Measure the distance from the lens to this point to find the image distance (denoted as \(d_i\)). Measure the height of the image on the diagram to determine the image height. Note that the image will be upright and smaller than the object.

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Diverging Lens

A diverging lens, also known as a concave lens, causes parallel rays of light to spread out or diverge. It has a negative focal length, which means that the focal point is virtual and located on the same side as the incoming light. This type of lens always produces virtual images that are upright and smaller than the object.
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Ray Tracing

Ray tracing is a graphical method used to determine the position and characteristics of an image formed by a lens. By drawing specific rays from the object through the lens, one can locate the image's position. The principal rays typically used include the parallel ray, which passes through the focal point after refraction, and the focal ray, which travels through the center of the lens without bending.
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Image Distance and Height

Image distance refers to the distance from the lens to the image formed, while image height is the size of the image compared to the object. For a diverging lens, the image distance is negative, indicating that the image is virtual and located on the same side as the object. The magnification, which relates the image height to the object height, can be calculated using the formula: magnification = image height / object height = - image distance / object distance.
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