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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 40b
Capitolo 34, Problema 40b

An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. If the object is 8.00 mm tall, how tall is the image? Is it erect or inverted?

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Identify the given values: The object distance \( d_o \) is \( 16.0 \; \text{cm} \), the image distance \( d_i \) is \( 36.0 \; \text{cm} \), and the object height \( h_o \) is \( 8.00 \; \text{mm} \) (convert to cm: \( h_o = 0.800 \; \text{cm} \)).
Recall the magnification formula: \( M = -\frac{d_i}{d_o} \), where \( M \) is the magnification, \( d_i \) is the image distance, and \( d_o \) is the object distance. Substitute the given values to calculate \( M \).
Use the relationship between magnification and height: \( M = \frac{h_i}{h_o} \), where \( h_i \) is the image height and \( h_o \) is the object height. Rearrange the formula to solve for \( h_i \): \( h_i = M \cdot h_o \). Substitute the calculated \( M \) and the given \( h_o \) to find \( h_i \).
Determine whether the image is erect or inverted: The sign of \( M \) indicates the orientation of the image. If \( M \) is negative, the image is inverted. If \( M \) is positive, the image is erect.
Summarize the results: Report the calculated image height \( h_i \) and state whether the image is erect or inverted based on the sign of \( M \).

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Lens Formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens. It is given by the equation 1/f = 1/v - 1/u. Understanding this formula is crucial for determining the characteristics of the image formed by the lens, including its position and size.
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Lens Maker Equation

Magnification

Magnification (M) is the ratio of the height of the image (h') to the height of the object (h), expressed as M = h'/h. It also relates to the object and image distances by the formula M = -v/u. This concept helps determine whether the image is erect or inverted based on the sign of the magnification value.
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Mirror Equation

Sign Convention for Lenses

The sign convention for lenses dictates how distances are measured in optics. For a converging lens, distances measured in the direction of the incoming light (toward the lens) are negative, while distances measured in the direction of the outgoing light (away from the lens) are positive. This convention is essential for correctly applying the lens formula and determining the nature of the image.
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Ray Diagrams for Converging Lenses
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