College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Applications Of Reflection Of Light
When a light ray (termed as the incident ray) hits a surface and bounces back (forms a reflected ray), the process of reflection of light has taken place.
Sign Convention for Mirrors
A mirror is made of glass that is coated with a metal amalgam on one side due to which the light ray incident on the surface undergoes reflection and not refraction.
Question
![**Problem 2: Calculating Image Height in a Concave Mirror**
An object that is 3.00 cm tall is positioned 12.0 cm away from a concave mirror. The mirror has a radius of curvature of 41.0 cm. Determine the height of the image produced.
[Input Field for Answer] cm
**Explanation:**
To find the height of the image, the mirror formula and magnification formula can be used:
1. **Mirror Formula:**
\[
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
\]
where:
- \( f \) is the focal length of the mirror,
- \( d_o \) is the object distance (12.0 cm),
- \( d_i \) is the image distance.
Given that the radius of curvature \( R \) is 41.0 cm, the focal length \( f \) is:
\[
f = \frac{R}{2} = \frac{41.0}{2} = 20.5 \text{ cm}
\]
2. **Magnification Formula:**
\[
m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}
\]
where:
- \( m \) is the magnification,
- \( h_i \) is the height of the image,
- \( h_o \) is the height of the object (3.00 cm).
Use these formulas to calculate the image distance \( d_i \) and the height of the image \( h_i \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88cd9656-9419-481b-bc0b-e9aadd0312cb%2Fb6f2b5dc-7929-44bf-85cd-9c6093cb751f%2Fkxx2ycf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2: Calculating Image Height in a Concave Mirror**
An object that is 3.00 cm tall is positioned 12.0 cm away from a concave mirror. The mirror has a radius of curvature of 41.0 cm. Determine the height of the image produced.
[Input Field for Answer] cm
**Explanation:**
To find the height of the image, the mirror formula and magnification formula can be used:
1. **Mirror Formula:**
\[
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
\]
where:
- \( f \) is the focal length of the mirror,
- \( d_o \) is the object distance (12.0 cm),
- \( d_i \) is the image distance.
Given that the radius of curvature \( R \) is 41.0 cm, the focal length \( f \) is:
\[
f = \frac{R}{2} = \frac{41.0}{2} = 20.5 \text{ cm}
\]
2. **Magnification Formula:**
\[
m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}
\]
where:
- \( m \) is the magnification,
- \( h_i \) is the height of the image,
- \( h_o \) is the height of the object (3.00 cm).
Use these formulas to calculate the image distance \( d_i \) and the height of the image \( h_i \).
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