If $f$ Is the Focal Length of a Convex Lens and an and an Object

question 52

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 $\frac { 1 } { f } = \frac { 1 } { v } + \frac { 1 } { u } .$
Find the rate of change of $v$ with respect to $u$ .

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

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