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Ch 34: Geometric Optics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 34: Geometric OpticsProblema 49a
Capitolo 34, Problema 49a

A camera lens has a focal length of 180.0 mm and an aperture diameter of 16.36 mm. What is the ƒ-number of the lens?

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1
Step 1: Understand the concept of the ƒ-number. The ƒ-number (or focal ratio) is a dimensionless quantity that describes the light-gathering ability of a lens. It is defined as the ratio of the focal length (f) to the aperture diameter (D). The formula is ƒ-number = f / D.
Step 2: Identify the given values from the problem. The focal length of the lens is f = 180.0 mm, and the aperture diameter is D = 16.36 mm.
Step 3: Substitute the given values into the formula for the ƒ-number. Using MathML, the formula can be expressed as: fD. Replace f with 180.0 mm and D with 16.36 mm.
Step 4: Perform the division to calculate the ƒ-number. Divide the focal length (180.0 mm) by the aperture diameter (16.36 mm). This will yield the ƒ-number.
Step 5: Interpret the result. The ƒ-number is a measure of how much light the lens can gather. A smaller ƒ-number indicates a larger aperture and more light-gathering ability, while a larger ƒ-number indicates a smaller aperture and less light-gathering ability.

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Focal Length

Focal length is the distance from the lens to the point where light rays converge to form a sharp image. It is a critical parameter that determines the lens's magnification and field of view. A longer focal length results in higher magnification, while a shorter focal length provides a wider field of view.
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Aperture Diameter

The aperture diameter refers to the size of the opening in the lens through which light passes. It affects the amount of light entering the camera and influences the depth of field in an image. A larger aperture allows more light, resulting in a shallower depth of field, while a smaller aperture reduces light and increases depth of field.
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ƒ-number (f-stop)

The ƒ-number, or f-stop, is a dimensionless number that represents the ratio of the lens's focal length to the diameter of the aperture. It indicates the lens's light-gathering ability; a lower ƒ-number means a larger aperture and more light, while a higher ƒ-number indicates a smaller aperture and less light. The ƒ-number is crucial for controlling exposure and depth of field in photography.
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Zoom Lens. Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. (a) For a distant object, where is the of the converging lens? (c) Where is the final image? Compare your answer to Fig. 34.43a.

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