If F Is the Focal Length of a Convex Lens $\frac{1}{f}=\frac{1}{v}+\frac{8}{u}$

question 107

Multiple Choice

If f is the focal length of a convex lens and an object is placed at a distance v from the lens, then its image will be at a distance u from the lens, where f ,v ,and u are related by the lens equation $\frac{1}{f}=\frac{1}{v}+\frac{8}{u}$ . Find the rate of change of v with respect to u.

• A) \(\frac{d v}{d u}=\frac{f^{2}}{(u-f)^{2}}\)
• B) \(\frac{d v}{d u}=-\frac{8 f^{2}}{(u-8 f)^{2}}\)
• C) \(\frac{d v}{d u}=\frac{2 f^{2}}{(u-f)^{2}}\)
• D) \(\frac{d v}{d u}=-\frac{f}{(u-f)^{2}}\)
• E) \(\frac{d v}{d u}=-\frac{f^{2}}{u-f}\)

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Definitions:

Annelids

A phylum of invertebrate worms known as segmented worms, which includes earthworms, leeches, and polychaetes.

Segmented Body

The body plan characteristic of certain organisms, including arthropods and annelids, where the body is divided into segments.

Visceral Mass

The concentration of body organs (viscera) located above the foot in mollusks.

Digestive Tract

The series of organs in the human body where food is ingested, digested, absorbed, and waste is expelled.