Question

A small object is placed in front of a converging mirror with radius $R=7.50 \mathrm{~cm}$ so that the image distance equals the object distance. How far is this object from the mirror? a) $2.50 \mathrm{~cm}$ b) $5.00 \mathrm{~cm}$ c) $7.50 \mathrm{~cm}$ d) $10.0 \mathrm{~cm}$ e) $15.0 \mathrm{~cm}$

Name: Problem 7, Chapter 32: University Physics with Modern Physics
Uploaded: 2021-05-20T09:06:27-08:00
Duration: 1 min 8 s
Channel: Narayan Hari
Description: A small object is placed in front of a converging mirror with radius R=7.50 cm so that the image distance equals the object distance. How far is this object from the mirror? a) 2.50 cm b) 5.00 cm c) 7.50 cm d) 10.0 cm e) 15.0 cm

   A small object is placed in front of a converging mirror with radius $R=7.50 \mathrm{~cm}$ so that the image distance equals the object distance. How far is this object from the mirror?
a) $2.50 \mathrm{~cm}$
b) $5.00 \mathrm{~cm}$
c) $7.50 \mathrm{~cm}$
d) $10.0 \mathrm{~cm}$
e) $15.0 \mathrm{~cm}$

University Physics with Modern Physics

Wolfgang Bauer, Gary… 2nd Edition

Chapter 32, Problem 7

Instant Answer

Solved by Expert Narayan Hari

05/20/2021

Step 1

Step 1: The mirror formula for converging mirrors is given by $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance. Show more…

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A small object is placed in front of a converging mirror with radius $R=7.50 \mathrm{~cm}$ so that the image distance equals the object distance. How far is this object from the mirror? a) $2.50 \mathrm{~cm}$ b) $5.00 \mathrm{~cm}$ c) $7.50 \mathrm{~cm}$ d) $10.0 \mathrm{~cm}$ e) $15.0 \mathrm{~cm}$

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Key Concepts

Symmetric Object-Image Configuration

When the object distance equals the image distance in a mirror, the condition leads to a simplified form of the mirror equation. This situation indicates that the object is located at a distance equal to twice the focal length (or at the center of curvature), which is a key concept in analyzing image positions in curved mirror systems.

Relationship between Focal Length and Radius of Curvature

For spherical mirrors, there is a direct relationship between the focal length and the radius of curvature, with the focal length being half the radius (f = R/2). This relationship is crucial in understanding how the curvature of a mirror affects image formation.

Mirror Equation

The mirror equation, given by 1/f = 1/d_o + 1/d_i, relates the focal length of a mirror (f) to the object distance (d_o) and the image distance (d_i). It is a fundamental formula in geometrical optics used for determining image characteristics for mirrors and lenses.

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