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Ch 34: Ray Optics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 34: Ray OpticsProblem 69
Chapter 34, Problem 69

CALC A converging lens with focal length f creates a real image of an object. What is the minimum possible distance between the object and its image? Your answer will be a multiple of f.

Verified step by step guidance
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Start by recalling the lens equation: 1f = 1do + 1di, where f is the focal length, do is the object distance, and di is the image distance.
To find the minimum possible distance between the object and its image, define the total distance as D = do + di. Substitute di from the lens equation into this expression.
Rearrange the lens equation to express di in terms of do: di = dof / (do - f). Substitute this into D.
Simplify the expression for D to find a single equation in terms of do and f. Then, differentiate D with respect to do to find the critical points.
Solve the derivative equation to find the value of do that minimizes D. Use this value to calculate the minimum distance D in terms of f.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Converging Lens

A converging lens, or convex lens, is a transparent optical device that bends light rays inward to a focal point. It has a positive focal length and is used to form real images when the object is placed outside its focal length. The behavior of light through a converging lens is governed by the lens formula, which relates the object distance, image distance, and focal length.
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Lens Formula

The lens formula is a mathematical relationship that describes the relationship between the object distance (u), image distance (v), and focal length (f) of a lens. It is expressed as 1/f = 1/v + 1/u. This formula is essential for determining the positions of the object and image in relation to the lens, particularly when calculating distances in optical systems.
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Real Image

A real image is formed when light rays converge and can be projected onto a screen. In the case of a converging lens, a real image occurs when the object is placed outside the focal length. The characteristics of a real image include being inverted and having a distance from the lens that can be calculated using the lens formula, which is crucial for determining the minimum distance between the object and its image.
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Related Practice
Textbook Question

A 25-cm-long rod lies along the optical axis of a converging lens, perpendicular to the lens plane. The lens has a 30 cm focal length. The rod's real , along the optical axis on the other side of the lens, is also 25 cm long. What is the distance from the lens to the nearest end of the rod?

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Textbook Question

An old-fashioned slide projector needs to create a 98-cm-high of a 2.0-cm-tall slide. The screen is 300 cm from the slide. What focal length does the lens need? Assume that it is a thin lens.

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Textbook Question

A plano-concave glass lens (flat on one side, concave on the other) creates an with magnification +0.40 of an object 75 cm from the lens. What is the radius of curvature of the lens's curved surface?

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Textbook Question

An object is 60 cm from a screen. What are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object?

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Textbook Question

A lightbulb is 3.0 m from a wall. What are the focal length and the position (measured from the bulb) of a lens that will form an on the wall that is twice the size of the lightbulb?

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Textbook Question

CALC A wildlife photographer with a 200-mm-focal-length telephoto lens on his camera is taking a picture of a rhinoceros that is 100 m away. Suddenly, the rhino starts charging straight toward the photographer at a speed of 5.0 m/s. What is the speed, in μm/s, image of the of the rhinoceros? Is the image moving toward or away from the lens?

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