Science
Grade 10 • Unit 6: Mirrors
LESSON 6.3
Mirror Equation
Table of Contents
Introduction 1
Learning Competency 2
Learning Objectives 2
Warm-Up 2
Learn about It 3
Mirror Equation 3
Worked Examples 6
Magnification of Image 10
Worked Examples 11
Key Points 14
Check Your Understanding 15
Bibliography 17
Answer to Let’s Practice 18
Science
Grade 10 • Unit 6: Mirrors
Lesson 6.3
Mirror Equation
You already knew what mirrors are and how to use ray diagram techniques to predict the
characteristics of the image that will form. Did you know that you can acquire these same
characteristics by just using an equation?
Introduction
Ray diagramming only presents the image qualitatively. Manufacturing mirrors, especially
those which have critical uses such as side mirrors in automobiles, require accurate
measurement of a part of a mirror such as the focus. So, it is important to know the precise
characteristics of the images formed. How can we predict the characteristics of the image
formed by mirrors without ray diagrams?
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Science
Grade 10 • Unit 6: Mirrors
Learning Competency
At the end of this lesson, the given DepEd learning competency should be met
by the students.
Predict the qualitative characteristics (orientation, type, and
magnification) of images formed by plane and curved mirrors and lenses
(S10FE-IIg-50).
Learning Objectives
In this lesson, you should be able to do the following:
● Predict the type, orientation, and position of an image formed by
different kinds of mirrors using the mirror equation and the ray diagram
method.
● Compute for the magnification of an image.
Warm-Up
Would You Like It Plane or Curved?
Materials
● plane mirror
● spoon
● two identical small toys or colored push pins
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Grade 10 • Unit 6: Mirrors
Procedure
1. Position a toy in front of the plane mirror and another toy in front of the back of
the spoon. Make sure that the toys are equidistant from the mirrors.
2. Observe the images formed from the two mirrors.
Guide Questions
1. In which mirror is the image formed larger?
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2. What causes this difference in the size of images formed?
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3. What would be the size of the image if the other side of the spoon was used?
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Learn about It
Mirror Equation
It is possible to not have all the rays meet when using ray diagrams. Ideally, all three rays
should meet but most of the time, only two rays would. This is mostly due to human error
when doing ray diagrams. There is only one condition when an image will not be formed
when placed in front of a mirror.
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Science
Grade 10 • Unit 6: Mirrors
Essential Question
How can one predict the type, orientation, and position of an image
formed from different types of mirrors using the mirror equation?
Fig. 1. All rays produced from any reference point of an object will converge if they should
converge.
It is possible to mathematically calculate where an image will show up if the distance of the
object is known. It is also possible to know the radius of curvature of a mirror given the
location of the object and the image.
The object distance, image distance, and radius of curvature are interdependent. The
equation that relates the three is called the mirror equation. A set of sign conventions for
the three variables must be established for use with the mirror equation.
In the equation above, p is the object distance, q is the image distance, and f is the focal
length of the image. Units for distances and focal length should be consistent. Take note of
the sign conventions shown in Table 1 for the mirror equation.
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Science
Grade 10 • Unit 6: Mirrors
Table 6.3.1. Sign conventions for the mirror equation
Symbol Situation Sign Illustration
p the object is in front of the +
mirror
q image is in front of the +
mirror (real image)
q image is behind the -
mirror (virtual image)
R, f radius of curvature is in +
front of the mirror
(concave mirror)
R, f radius of curvature is -
behind the mirror (convex
mirror)
R, f mirror has no curvature ∞
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Grade 10 • Unit 6: Mirrors
Remember
In solving the unknown quantities, remember to do the following:
● Check for the consistency of units.
● Isolate the unknown quantity on one side of the equation before
substituting the given values.
Worked Examples
Example 1
What is the focal point distance of a convex mirror if the object located 10 cm away from the
mirror forms a virtual image which is 30 cm away from the mirror?
Solution
Step 1: Identify what is required in the problem.
You are asked to calculate the focal point distance (f).
Step 2: Identify the given in the problem.
The object distance (p) and image distance (q) are given.
Step 3: Write the working equation.
Therefore,
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Science
Grade 10 • Unit 6: Mirrors
Step 4: Substitute the given values.
Step 5: Find the answer.
Therefore, the focal point distance is 15 cm.
Let’s Practice
An image was formed 0.5 m away from the mirror, which is unclassified. The object was
placed 0.5 m away from the mirror. What is the focal distance of the mirror? What type of
mirror is it?
Example 2
An object was placed 1m away from the mirror. If it has a focal length of 1.2 m, how far will
the image formed be from the convex mirror? Where will the image form?
Solution
Step 1: Identify what is required in the problem.
You are asked to calculate the image distance (q).
Step 2: Identify the given in the problem.
The object distance (p) and the focal length (f) are given.
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Grade 10 • Unit 6: Mirrors
Step 3: Write the working equation.
Therefore,
Step 4: Substitute the given values.
Step 5: Find the answer.
Therefore, the image distance is 0.55 m away from the mirror. The image is formed behind
the mirror because of the negative sign.
Let’s Practice
Where will the image of an object 5 meters away from the convex mirror with 2.5 m focal
length form? How far is it from the mirror?
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Grade 10 • Unit 6: Mirrors
Example 3
A concave mirror is a curved mirror wherein the reflecting surface is on the inner surface of
the sphere so that the center of the mirror sinks away from the viewer. A concave mirror
with a radius of curvature of 40 cm, produced an image that is 35 cm in front of a mirror.
How far is the object placed?
Solution
Step 1: Identify what is required in the problem.
You are asked to calculate the object distance (p).
Step 2: Identify the given in the problem.
The radius of curvature (R) and image distance (q) are given. (The focal length (f) is
also implicitly given by dividing the radius of curvature by 2.)
Step 3: Write the working equation.
Therefore,
Step 4: Substitute the given values.
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Science
Grade 10 • Unit 6: Mirrors
Step 5: Find the answer.
Therefore, the object was placed 46.67 cm away from the front of the mirror.
Let’s Practice
A convex mirror has a center of curvature of 2 m. An object was placed 1.25 m away from
this mirror. How far and where will the image appear?
Magnification of Image
The magnification of an image formed by mirrors can be computed either by using the
height of the image and the object or their distances. A positive M means that the image is
upright and a negative value means it is inverted.
The image height is denoted by h’, while the object height is h. For distances, the denotation
is similar to that of the mirror equation: q for the image distance and p for the object
distance. Units of the height and distances should be consistent.
Remember
In solving the unknown quantities, remember to do the following:
● Check for the consistency of units.
● Isolate the unknown quantity on one side of the equation before
substituting the given values.
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Science
Grade 10 • Unit 6: Mirrors
Worked Examples
Example 1
What is the magnification of a convex mirror if it produces a 43 cm high image from a 55 cm
high object?
Solution
Step 1: Identify what is required in the problem.
You are asked to calculate the magnification (M).
Step 2: Identify the given in the problem.
The image height (h’) and object height (h) are given.
Step 3: Write the working equation.
Step 4: Substitute the given values.
Step 5: Find the answer.
Therefore, the magnification of the convex mirror is 0.78.
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Grade 10 • Unit 6: Mirrors
Let’s Practice
What is the magnification of a mirror which produces an image which has the same height
as the object at any distance? What type of mirror is it?
Example 2
A mirror has a magnification of 2.5 times. How far will the image be formed from the
concave mirror if the object is placed 0.5 m away from the mirror?
Solution
Step 1: Identify what is required in the problem.
You are asked to find the image distance (q).
Step 2: Identify the given in the problem.
The magnification (M) and object distance (p) are given.
Step 3: Write the working equation.
Therefore,
.
Step 4: Substitute the given values.
Step 5: Find the answer.
𝑞 =− 1. 25 𝑚
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Grade 10 • Unit 6: Mirrors
Therefore, the image distance is -1.25 m. This means that the image will form behind the
mirror (thus, the image is a virtual image).
Let’s Practice
How far is the object placed in front of a 2.0 times magnifying mirror when the image was
shown 30 cm in front of the mirror?
Example 3
A 70 mm wide Rubix cube was magnified to a 92 mm wide cube (image). How far is the
object when the image was formed 30 cm behind the concave mirror?
Solution
Step 1: Identify what is required in the problem.
You are asked to calculate the object distance (p).
Step 2: Identify the given in the problem.
The object (h) and image height (h’, the width of a cube is equal to its height), and
image distance (q) are given.
Step 3: Write the working equation.
Therefore,
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Science
Grade 10 • Unit 6: Mirrors
Step 4: Substitute the given values.
Step 5: Find the answer.
Therefore, the object distance is 22.83 cm.
Let’s Practice
Dave has a height of 175 cm. If he is 0.5 m away from the front of a magnifying mirror, his
height is increased by 10 cm. How far from the mirror is his image?
Key Points
● The mirror equation relates the object distance, image distance, and focal length. It
is given by the formula:
● Magnification can be computed either by using the height of the image and the
object or their distances. It is given by the formula:
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Science
Grade 10 • Unit 6: Mirrors
Check Your Understanding
A. Identify the relationship of the following. Indicate it as directly proportional if one of
the quantities increases or decreases after the other increases or decreases at the
same time; otherwise, indicate it as inversely proportional.
______________________ 1. magnification and image height
______________________ 2. magnification and image distance
______________________ 3. magnification and object distance
______________________ 4. image height and image distance
______________________ 5. object height and image distance
B. Identify whether the image will be magnified, diminished, or undiminished (same size
as the object). Write M, D, or U, respectively.
_________ 1. A mirror has a magnification power of 0.75.
_________ 2. A mirror has a magnification power of 1.
_________ 3. A mirror has a magnification power of 2.25.
_________ 4. An object which is 35 cm high appears to be 20 cm in front of a
mirror.
_________ 5. A toy car in front of a plane mirror.
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Science
Grade 10 • Unit 6: Mirrors
C. Solve the following problems.
1. What is the magnification power of a mirror which increases a ballpens’ height
(9 cm) by 2 cm?
Solution and answer:
2. How far will an object appear (image distance) if it is placed 1 meter away
from a convex mirror with focal length of 40 cm?
Solution and answer:
3. How far will an object appear (image distance) if it is placed 1 meter away
from a concave mirror with focal length of 40 cm?
Solution and answer:
4. How far will an object appear (image distance) if it is placed 1 meter away
from a plane mirror?
Solution and answer:
5. What should be the object’s distance if its image should appear 30 cm behind
a convex mirror with a focal length of 45 cm?
Solution and answer:
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Science
Grade 10 • Unit 6: Mirrors
Bibliography
Giancoli, Douglas C. 2013. Physics: Principles with Applications 7th Edition. New Jersey:
Pearson
Hugh D. Young, et al. 2012. Sears and Zemansky’s University Physics with Modern Physics 13th
Edition. California: Pearson Education Inc.
The Physics Classroom. “Reflection and the Ray Model of Light.” Accessed May 1, 2017 at
http://www.physicsclassroom.com/class/refln.
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Science
Grade 10 • Unit 6: Mirrors
Answer to Let’s Practice
1. An image was formed 0.5 m away from the mirror, which is unclassified. The object
was placed 0.5 m away from the mirror. What is the focal distance of the mirror?
What type of mirror is it?
Answer: The mirror is a plane mirror. It has no focal point.
2. Where will the image of an object 5 meters away from the convex mirror with 2.5 m
focal length form? How far is it from the mirror?
Answer: The image will form behind the mirror at a distance of 1.67 meters.
3. A convex mirror has a center of curvature of 2 m. An object was placed 1.25 m away
from this mirror. How far and where will the image appear?
Answer: The image will form behind the mirror at a distance of 0.55 m.
4. What is the magnification of a mirror which produces an image which has the same
height as the object at any distance? What type of mirror is it?
Answer: The magnification is 1. It is a plane mirror.
5. How far is the object placed in front of a 2.0 times magnifying mirror when the image
was shown 30 cm in front of the mirror?
Answer: The object was placed 60 cm behind the mirror.
6. Dave has a height of 175 cm. If he is 0.5 m away from the front of a magnifying
mirror, his height is increased by 10 cm. How far from the mirror is his image?
Answer: Dave’s image is 0.52 m behind the mirror.
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