Skip to main content
Ch. 32 - Light: Reflection and Refraction
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 32 - Light: Reflection and RefractionProblema 16
Capitolo 31, Problema 16

A dentist wants a small mirror that, when 2.00 cm from a tooth, will produce a 3.0 x upright image. What kind of mirror must be used and what must its radius of curvature be?

Guida verificata passo dopo passo
1
Determine the type of mirror: Since the image is upright and magnified, the mirror must be a concave mirror. Concave mirrors can produce upright, magnified images when the object is within the focal length of the mirror.
Use the magnification formula to relate the image distance \(d_i\) and object distance \(d_o\): \(M = \frac{d_i}{d_o}\), where \(M\) is the magnification. Substitute \(M = 3.0\) and \(d_o = 2.00\,\text{cm}\) to solve for \(d_i\).
Apply the mirror equation to find the focal length \(f\): \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\). Use the values of \(d_o\) and \(d_i\) from the previous step to calculate \(f\).
Relate the focal length \(f\) to the radius of curvature \(R\): \(R = 2f\). Use the focal length obtained in the previous step to find the radius of curvature.
Summarize the results: The mirror is a concave mirror, and its radius of curvature can be determined using the steps above.

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:
5m

Concetti chiave

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

Types of Mirrors

There are two main types of mirrors: concave and convex. Concave mirrors can produce real and inverted images or virtual and upright images, depending on the object's distance from the mirror. In contrast, convex mirrors always produce virtual, upright images. For the scenario described, a concave mirror is required to achieve the specified upright image at a given distance.
Video consigliato:
Percorso guidato
09:03
Mirror Equation

Mirror Formula

The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a mirror: 1/f = 1/v + 1/u. This formula is essential for determining the characteristics of the image produced by the mirror. In this case, knowing the object distance and the magnification allows us to find the image distance and subsequently the focal length.
Video consigliato:
Percorso guidato
09:03
Mirror Equation

Magnification

Magnification (M) is the ratio of the height of the image (h') to the height of the object (h), and it can also be expressed in terms of distances: M = -v/u. A positive magnification indicates an upright image, while a negative value indicates an inverted image. In this problem, the magnification of 3.0 signifies that the image is upright and larger than the object, which is a key factor in determining the type of mirror and its properties.
Video consigliato:
Percorso guidato
09:03
Mirror Equation
Pratica correlata
Domanda del libro di testo

Suppose you are 96 cm from a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 4.5 mm?

1386
views
Domanda del libro di testo

The lateral magnification of a convex mirror is +0.75 for objects 3.2 m from the mirror. What is the focal length of this mirror?

1575
views
Domanda del libro di testo

An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Compute the image size, using Eq. 32–3.

85
views
Domanda del libro di testo

An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Show that the (negative) image distance can be computed from Eq. 32–2 using a focal length of -9.0 cm.

1403
views
Domanda del libro di testo

You look at yourself in a shiny 8.4-cm-diameter Christmas tree ball. If your face is 25.0 cm away from the ball’s front surface, where is your image? Is it real or virtual? Is it upright or inverted?

1492
views
Domanda del libro di testo

An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Show by ray tracing that the image is virtual, and estimate the image distance.

987
views