Skip to main content
Ch 34: Geometric Optics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 34: Geometric OpticsProblema 43a
Capitolo 33, Problema 43a

A 1.20 cm tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm.

Guida verificata passo dopo passo
1
Step 1: Use the lens formula to find the image distance (\(d_i\)) for the first lens. The lens formula is \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\), where \(f\) is the focal length of the lens, \(d_o\) is the object distance, and \(d_i\) is the image distance. Substitute \(f = 40.0\ \text{cm}\) and \(d_o = 50.0\ \text{cm}\) into the formula.
Step 2: Rearrange the lens formula to solve for \(d_i\): \(\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}\). Perform the subtraction of the reciprocals of \(f\) and \(d_o\) to find \(\frac{1}{d_i}\), then take the reciprocal to find \(d_i\).
Step 3: Determine the magnification (\(M\)) of the first lens using the formula \(M = -\frac{d_i}{d_o}\). Substitute the values of \(d_i\) and \(d_o\) to calculate \(M\).
Step 4: Calculate the height of the image (\(h_i\)) formed by the first lens using the magnification formula \(h_i = M \cdot h_o\), where \(h_o = 1.20\ \text{cm}\) is the height of the object. Substitute the values of \(M\) and \(h_o\) to find \(h_i\).
Step 5: Summarize the results for the first image (\(I_1\)): its location (\(d_i\)) relative to the first lens and its height (\(h_i\)). These values will be used as inputs for further calculations involving the second lens in subsequent parts of the problem.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Lens Formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens, expressed as 1/f = 1/v - 1/u. This formula is essential for determining the position of the image formed by a lens. In this scenario, it will help calculate the image location (I1) created by the first converging lens.
Video consigliato:
Percorso guidato
05:38
Lens Maker Equation

Magnification

Magnification (M) is the ratio of the height of the image (h') to the height of the object (h), given by M = h'/h = -v/u. This concept is crucial for understanding how the size of the image relates to the size of the object. In this problem, it will be used to find the height of the image formed by the first lens.
Video consigliato:
Percorso guidato
09:03
Mirror Equation

Converging Lens

A converging lens, or convex lens, is thicker at the center than at the edges and causes parallel rays of light to converge at a focal point. The focal length is the distance from the lens to this point. Understanding the behavior of converging lenses is vital for analyzing how they form images, especially in multi-lens systems like the one described in the question.
Video consigliato:
Percorso guidato
07:58
Thin Lens Equation
Pratica correlata
Domanda del libro di testo

Repeat Exercise 34.41 using the same lenses except for the following changes: The second lens is a diverging lens having a focal length of magnitude 60.0 cm.

237
views
Domanda del libro di testo

A lensmaker wants to make a magnifying glass from glass that has an index of refraction n = 1.55 and a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?

1989
views
Domanda del libro di testo

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. Draw a principal-ray diagram.

1575
views
Domanda del libro di testo

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.

1684
views
Domanda del libro di testo

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?

2170
views
Domanda del libro di testo

You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. If the dimensions of the picture on a 35 mm color slide are 24 mm ✖ 36 mm, what is the minimum size of the projector screen required to accommodate the image?

1832
views