Grade 10 • Unit 6: Mirrors

LESSON 6.2
Convex Mirrors
Table of Contents

Learning Competency 1

Learning Objectives 1

Suggested Time Frame 1

Essential Questions 1

Prerequisite Topic 2

Lesson Proper 2
A. Introduction to the Lesson 2
B. Discussion 7
C. Practice & Feedback 21

Performance Assessment 22

Synthesis 24

Bibliography 26
 Grade 10 • Unit 6: Mirrors

Unit 6 | Mirrors
Lesson 2: Convex 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:
● Identify the parts of a curved mirror.
● Explain the characteristics of a convex mirror.
● Use ray diagramming to determine the characteristics of images formed
by convex mirrors.

Suggested Time Frame

1 session (or approximately 50 minutes)

Essential Questions
At the end of this lesson, the student should be able to answer the following questions.
● How do convex mirrors create images?
● What are the uses of convex mirrors?
● How can one predict the type and orientation of the image formed by a convex
mirror using ray diagramming?

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 Grade 10 • Unit 6: Mirrors

Prerequisite Topic
The students should know the following prerequisite topic before proceeding with the
lesson.
● Images Formed by a Plane Mirror

Lesson Proper

A. Introduction to the Lesson

Start the lesson by asking the students what phenomenon governs the behavior of light.
The suggested activities after the questions may also be done in class. You may use any of
the suggested activities below:

Link to the downloadable presentation slides: 6.2. Convex Mirror

1. Recall Fermat’s principle of least time and the behavior of light. How does light
behave?
a. Light ordinarily travels in a straight-line path called ray. A ray is a line with an
arrowhead at the end of it.
b. The idea that the path which light travels is the one that uses the shortest
time is called Fermat’s principle of least time.
c. This means that for the light to go from one point to another, it takes the
shortest and most efficient path available to it.

Fig. 1. Light takes the shortest path possible.

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2. Recall that images are formed as light reflects on a plane mirror. How is light being
reflected on surfaces? What does the law of reflection state?
a. Light reflection is seen as light rays bouncing off an object.
b. The angle of incidence, θi, is the angle which an incident ray makes with an
imaginary line perpendicular to the surface, referred to as the normal. The
angle of reflection, θr, is the angle in which the reflected ray makes with the
normal.
c. The law of reflection states that the incident and reflected rays lie in the
same plane with the normal and that the angle of reflection equals the angle
of incidence, θi = θr.

Option A: The Truth Within: Finding Sense in Reflections

In this activity, students will recall the previously discussed concepts about
reflection.

Duration: approximately 5 minutes

Materials:
● material 1
● material 2

Teacher’s Preparation:
● The teacher will prepare conceptual questions about reflection and plane
mirrors.

Procedure:
1. Divide the classroom into two sides.
2. One side will be the ‘true’ side and the other one will be the ‘false’ side. 3.
You will ask several questions about plane mirrors and reflection. Some
examples are listed below:

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 Grade 10 • Unit 6: Mirrors

a. The law of reflection states that the angle of incidence is equal to

the angle of reflection.
Answer: true
b. The law of reflection only applies to specular reflection.
Answer: false
c. Fermat’s principle of least time governs the light ray tracing of
reflection of light.
Answer: true
d. Plane mirrors produce enlarged images of objects.
Answer: false
e. Plane mirrors do not follow the law of reflection.
Answer: false
3. The students should identify whether the statements are true or false by
going to the side that corresponds to their answer.

Teacher’s Notes
Tell the students to take note of the concepts stated above since the discussion
is also about reflection but with convex mirrors instead.

3. Introduce convex and concave mirrors. Convex and concave mirrors are mirrors
with curvatures.
a. Emphasize that images are also formed in mirrors with curvatures. Ask: Are
the images formed in mirrors with curvatures the same as the images formed in
plane mirrors?
b. You may use Option B to answer the question and facilitate the discussion.

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Option B: Spoon-tastic mirror!

In this activity, students will observe the image formed by a convex mirror.

Duration: approximately 5 minutes

Materials:
● spoon
● a small toy or a colored push pin

Quipper Reference: Unit 6: Mirrors, Lesson 2: Convex Mirrors

Procedure:
Ask the students to follow the instructions provided below.
1. Observe the toy in terms of its height, width, and other physical
characteristics. You may use a ruler to measure it accurately or use it for
reference.
2. Place the toy in front of the back of the spoon as a mirror.
3. Observe the image (shown in the mirror) formed from the actual toy.

Guide Questions
1. What are the similarities and differences between the toy and its formed
image?
Answer: The image is upright but appears smaller than the toy. It is also
reversed laterally.
2. Are the height and width of the toy and its image the same?
Answer: No, the toy’s size has been diminished.
3. Is the image vertically inverted or upright relative to the object?
Answer: The image is upright.

c. Alternatively, you can use Option C to further stimulate the discussion on

formed images.

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Option C: Electronic Mirror

In this activity, students will compare the image formed by a spoon to an electronic
mirror simulator.

Duration: approximately 10 minutes

Teacher’s Preparation:
● The teacher may project the website to the class if no computers are
available to use.

Materials:
● computer
● spoon
● a small toy or a colored push pin

Procedure:
1. Observe the toy in terms of its height, width, and other physical
characteristics. You may use a ruler to measure or as a reference.
2. Place the toy in front of the back of the spoon as a mirror.
3. Observe the image (shown in the mirror) formed from the actual toy.
4. Using the link below, try to differentiate the image produced by the spoon
and the electronic mirror.

Electronic Mirror
Nerd Island Studios. 2014. “Lenses and Mirrors”.
https://www.physicsclassroom.com/Physics-Interactives/Refractio
n-and-Lenses/Optics-Bench/Optics-Bench-Refraction-Interactive.

5. Remember to place the object at the opposite part of the curvature of the
mirror.

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Guide Questions:
1. What similarities and differences did you notice between the object (actual
toy) and the image (shown in the mirror)?
Answer: The image is smaller and it is laterally reversed.
2. Are the height and width of the image and object the same? Why or why
not?
Answer: They are not the same. This can be attributed to the shape of the
mirror.
3. Is the image vertically upright or not relative to the object? Why or why not?
Answer: The image is upright relative to the object.
4. Are your answers in numbers 1 to 4 supported by the electronic mirror?
Answer: Yes, they are supported by the electronic mirror.
5. How did the electronic mirror predict the location and the characteristics of
the image?
Answer: It uses different rays.

Teacher’s Notes
This activity is an extended activity of Option A. The electronic mirror will help
the students confirm whether their observations are correct or incorrect.

B. Discussion
Using any of the activities from the introduction, you can use the options below and follow
the suggested flow.
1. Identify and define the different parts of a convex mirror.
a. The principal axis is an imaginary line passing through the center of the
sphere at the exact center of the mirror.
b. The point on the mirror’s surface where the principal axis meets the mirror is
known as the vertex.

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c. The point in the center of the sphere from which the mirror was sliced is
known as the center of curvature, C.
d. Halfway between the center of curvature and vertex is the focal point, F.
e. The distance between the vertex and the focal point is the focal length, f.
f. You can define the different necessary parts and ask the students to label the
diagram in Option A.

Option A: Label Me!

In this activity, the students will label the different parts of a curved mirror.

Duration: approximately 5 minutes

Materials:
● chalk/whiteboard marker

Teacher’s Preparation:
● printing of black curved mirror

Procedure:
1. Show the class the following diagram:

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2. Ask 1 student to label a part in the diagram.

3. Call another student until the diagram is fully labeled.
4. You can ask the students to explain each part after they have labeled it.

Answer:

Teacher’s Notes
After the activity, you can already highlight the parts by repeating the
explanations of the students in a clearer manner.

2. After discussing the parts of a curved mirror, focus on convex mirrors. You can use
the presentation to supplement the discussion. What is a convex mirror?
a. There are two types of curved mirrors—convex and concave mirrors.
b. A convex mirror is a curved mirror wherein the reflecting surface is on the
outer surface of the sphere so that the center of the mirror bulges towards
the viewer.
c. This mirror focuses light away from the focal point, which is why it is called a
diverging mirror.
3. Emphasize that every type of mirror has different types of images formed. In this
discussion, you will only focus on the image formed by a convex mirror. How can

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convex mirrors produce an image? What are the characteristics of the image formed by
convex mirrors?
a. In order to find where an image will be located when an object is placed in
front of a mirror, a technique called ray diagramming is used.
b. The following steps are used in order to locate and describe the image
produced by the curved mirror.
i. First, a reference ray starting from the object going parallel to the
principal axis is drawn. It reflects through the focal point, F after it hits
the mirror. This is called the principal ray.

ii. The second reference ray goes through F and then goes parallel to the
principal axis after hitting the mirror. This is called the focal ray.

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iii. The third reference ray goes through C then goes back along with
itself through C. This is called the central ray.

c. Take note that the principal rays are coded as red rays, focal rays are coded
as blue, and the central rays as green.
d. Since the F and C of a convex mirror are situated behind the mirror’s surface,
dotted lines are extended along with the reflected rays to points behind the
mirror. The intersection of two or more rays locates the image.
e. You can refer to the following examples and use them as a practice exercise
in class.

Example 1:
Determine the location and characteristics of the image of the arrow using
ray diagramming techniques in the given illustration below.

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Solution:
Step 1: Draw the principal ray.

Step 2: Draw the focal ray.

Step 3: Draw the central ray.

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Step 4: Draw the image formed on the intersection of lines.

Therefore, the image which is upright, virtual, and reduced is

formed at the back of the mirror.

Example 2
What is the orientation, size, and type of image formed from the object
positioned in front of a convex mirror below?

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 Grade 10 • Unit 6: Mirrors

Solution:
Step 1: Draw the principal ray.

Step 2: Draw the focal ray.

Step 3: Draw the central ray.

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Step 4: Draw the image at the intersection of lines.

The image is formed at the back of the mirror. It appears

upright, diminished (smaller) and it is a virtual image.

Example 3:
What is the orientation, size, and type of image formed from the object
positioned in front of a convex mirror if the object’s distance from the mirror
is 40 cm?

Solution:
Step 1: Draw the diagram for the situation.

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Step 2: Draw the principal ray.

Step 3: Draw the focal ray.

Step 4: Draw the central ray.

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Step 5: Draw the image at the intersection of lines.

The image is formed at the back of the mirror. It appears

upright, diminished (smaller) and it is a virtual image.

f. You can use Option B as a practice set for your students.

Option B: Ray It!

In this activity, the students will show the image formed by a convex mirror using
ray diagrams.

Duration: approximately 20 minutes

Teacher’s preparation:
● The teacher will prepare blank convex mirror diagrams.

Materials:
● chalk or pen (three different colors, preferably red, green, and blue)
● ruler

Procedure:
1. For each problem, ask 3 students to draw the principal ray, focal ray, and
central ray.

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2. For each ray, make sure to use different colors of chalk.

a. red chalk for principal rays
b. blue chalk for focal rays
c. green chalk for central rays
3. Give the following problems to your students.

a. Given the illustration below, determine the location and

characteristics of the image of the arrow using ray diagramming
techniques.

b. What is the orientation, size, and type of image formed from the
diagram below?

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c. What is the orientation, size, and type of image formed from the
diagram below?

Answer:
The image is always upright, virtual, and reduced and is always formed at the back
of the mirror.

Teacher’s Notes
You can ask a student if there is any pattern that he can see with the image
produced by a convex mirror.

4. Mirrors are objects that are good at reflecting light. However, the type of image they
produce is different depending on which type of mirror it is.
a. You can use the acronym LOST to describe the image formed by a plane
mirror and a convex mirror.
i. location
ii. orientation
iii. size
iv. type
b. The image formed by a convex mirror can be summarized as:
i. location: the distance of the image is nearer to the mirror compared
to the distance of the object. It is always at the back of the mirror.
ii. orientation: image is upright relative to the object

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iii. size: reduced or smaller than the object

iv. type: virtual
c. You can use Option C to compare the image formed by convex mirrors and
plane mirrors.

Option C: With Curves and Without Curves: Beautiful Images!

In this activity, students will differentiate the image formed by a plane mirror and a
convex mirror.

Duration: approximately 10 minutes

Materials:
● plane mirror
● curved mirror (convex)
● a pencil

Procedure:
1. Place a pencil in front of a plane mirror and a curved mirror. Observe the
formed images on the mirrors.
2. Draw ray diagrams on how these images of the pencil are formed in a plane
and curved mirror. Based on the ray diagrams, use the following table to
differentiate the image formed by a plane mirror and a convex mirror.

Plane Convex (Curved)

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Teacher’s Notes
You can show actual images formed by a plane mirror and a convex mirror at
this point. Also, an example of a ray diagram by a plane mirror can help.

C. Practice & Feedback

Use the following strategies to assess student understanding.
1. The teacher will post a blank diagram of a convex mirror. You can refer to the image
below to use. The teacher will call different students to answer the following
problems. If a student was not able to answer correctly, call another student to help
them:

a. Label the blank diagram with the parts of a curved mirror discussed in this
section.
b. Show the image formed when the object is at:
i. 5 centimeters
ii. 10 centimeters
iii. 15 centimeters
Use arrows as objects.
c. Ask one student to summarize the images formed by a convex mirror using
LOST.

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Performance Assessment
Use the following strategies to assess student understanding.

I. Create a convex mirror diagram with a focal length of 5 cm. Show the
image formed when the object is at the following distances from the vertex.
Write the image description using LOST.
a. 5 centimeters
b. 10 centimeters
c. 15 centimeters

II. Use the Check Your Understanding section in the study guide. Students may
answer it in their notebooks and will be checked and graded afterward.
Choose only selected items if not possible due to time.

A. Read and analyze the following statements given. Write T if the statement is
correct and F if it is false.
1. There are usually three rays in ray diagramming for convex mirrors.
Answer: T
2. Ray diagramming techniques follow the law of reflection.
Answer: T
3. In the ray diagramming of mirrors, it is assumed that no refraction will occur.
Answer: T
4. Curved mirrors are mirrors that form a section of a sphere.
Answer: F
5. Convex and concave mirrors form the same characteristics of images.
Answer: F

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B. Match column B with its definition in column A. Write the letter of your answer
on the space before each number.

Column A Column B

1. It is the point that is halfway between the a. diminished

center of curvature and the vertex. b. magnified
Answer: j c. virtual
2. It refers to a point in the center of the d. upright
sphere from which the mirror was sliced. e. vertex
Answer: f f. center of
3. This is also known as a diverging mirror. curvature
Answer: g g. convex mirror
4. It is an imaginary line passing through the h. concave mirror
center of the sphere at the exact center of i. principal axis
the mirror. j. focal point
Answer: i k. ray diagramming
5. It is a point on the mirror’s surface where
the principal axis meets the mirror.
Answer: e
6. A type of curved mirror wherein the
reflecting surface is on the outer surface of
the sphere so that the center of the mirror
bulges towards the viewer.
Answer: g
7. It is a technique that uses three reference
rays in order to locate the image.
Answer: k
8. It also means that the image is smaller than
the object.
Answer: a
9. It is used to describe an image formed

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behind the mirror.

Answer: c
10. A type of mirror that focuses light away
from the focal point.
Answer: g

III. If time permits, you can use the following additional assessments.

Recall Worksheet (Level 1) 10-item recall quiz

Appendix A1. Assess-Recall Worksheet

Comprehension Worksheet 10-points guided assessment

(Level 2) Appendix A2. Assess-Comprehension Worksheet

Application Worksheet (Level 10-points Essay

3) Appendix A3. Assess-Application Worksheet

Synthesis
Use the following strategies to end the session.
1. The teacher will ask several students to summarize the whole lesson by answering
the questions:
a. How can convex mirrors form an image?
Answer: A convex mirror is a curved mirror wherein the reflecting surface is
on the outer surface of the sphere so that the center of the mirror bulges
towards the viewer. Ray diagramming is used to check the images formed by
the convex mirror. The created images in convex mirrors are always located
behind the mirror—virtual, upright, and diminished (smaller than the object).
b. Do the convex mirrors follow the law of reflection? Why or why not?
Answer: Convex mirrors still follow the law of reflection. The plane is assumed
to reflect the light where the incident and reflected angles are equal.
2. To further deepen understanding, you may also ask the following.
a. Is there any possibility that a convex mirror will produce a magnified image?

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Why?
Answer: No. A convex mirror diverges light that is reflected on it. These
reflected rays will never meet at a point in front of a mirror, so it is
impossible to actually form a real image, what more of a magnified image.
b. What are the other uses of the convex mirror?
Answer: Convex mirrors could be used for surveillance purposes in
convenience stores.
c. In which region will the image appear using the following diagram below?
Answer: The image will appear in the III region or behind the mirror. The
image will be upright, diminished, and virtual.

3. As an assignment, present several applications of convex mirrors and ask them to

research about these at home:
a. buildings such as large offices, stores, and hospitals use convex mirrors as
internal mirrors located in corners
b. convex side mirrors in vehicles
c. convex mirrors used for security purposes

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Bibliography

Giancoli, Douglas C. Physics: Principles with Applications, 7th Edition. New Jersey: Pearson,
2013.

Hugh D. Young, et al. Sears and Zemansky’s University Physics with Modern Physics, 13th
Edition. California: Pearson Education Inc., 2012.

“Reflection and the Ray Model of Light.” The Physics Classroom. Accessed April 12, 2022.
http://www.physicsclassroom.com/class/refln.

Serway, Raymond A. and Jerry S. Faughn. Physics. USA: Holt, 2012.

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Appendix A1. Recall Worksheet

(with Answer Key)
Instructions: Choose the best answer. (10 points)

Question 1 The point on the mirror’s surface

What do you call the point on the mirror’s surface where the principal axis meets the
where the principal axis meets the mirror? mirror is known as the vertex.

vertex
focal point
center of curvature
focal Length

Question 2 The line passing through the center

What do you call the line passing through the of the sphere and through the
center of the sphere and through the centers of centers of curvature of all the
curvature of all segments of the lens? segments of the lens or mirror is
called the principal axis.
principal axis
vertex
center of curvature
focal point

Question 3 A curved mirror with the center

What do you call mirrors that seem to form a bulging towards the viewer and a
section of a sphere? curved mirror that focuses light
away from the focal point are
curved mirror considered diverging mirrors.
diverging mirror
converging mirror
plane mirror

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Question 4 Convex mirrors are curved mirrors

Which of the following statements best describes that form a section of a sphere. A
a convex mirror? curved mirror with the center
bulging towards the viewer
Convex mirrors are curved mirrors that form a
section of a sphere.
Convex mirrors are segments of a huge plane
mirror.
Convex mirrors focus the light away from the
viewer.
A convex mirror is a circular mirror.

Question 5 A convex mirror is a curved mirror

Which of the following is another name for a wherein the reflecting surface is on
convex mirror? the outer surface of the sphere so
that the center of the mirror bulges
diverging mirror towards the viewer. This mirror
converging mirror focuses light away from the focal
focusing mirror point which is why it is called a
concave mirror diverging mirror.

Question 6 In order to find where an image will

Which of the following is used in order to be located if an object is placed in
determine the image formed by a curved mirror? front of a mirror, a technique called
ray diagramming is used.
ray diagramming
light diagramming
light tracing
ray tracing

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Question 7 A reference ray starting from the

What do you call the ray which is parallel to the object going parallel to the
principal axis? principal axis is drawn. It reflects
through the focal point, F, after it
principal ray hits the mirror. This is called the
reference ray principal ray.
central ray
focal ray

Question 8 The second reference ray for ray

Which of the following rays is drawn when it diagramming goes through F and
follows the track below? then goes parallel to the principal
object ⟶ focal point ⟶ reflected parallel to the axis after hitting the mirror. This is
principal axis called the focal ray.

focal ray
central ray
reference ray
principal ray

Question 9 The third reference ray for ray

Which of the following ray is drawn through the diagramming goes through C then
following? goes back along itself through C.
object ⟶ through central point ⟶ reflected This is called the central ray.
along itself

central ray
focal ray
reference ray
principal ray

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Question 10 The created images in convex

Which of the following does not describe the mirrors are always located behind
image formed by a convex mirror? the mirror—virtual, upright, and
diminished (smaller than the
enlarged object).
diminished
virtual
upright

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Appendix A2. Comprehension Worksheet

(with Answer Key)
Instructions: Answer the problem by following the instructions below. Use red, blue, and
green crayons as instructed in each step. (10 points)

What is the orientation, size, and type of image formed from the object positioned in front
of a convex mirror if the object’s distance from the mirror is 20 cm?

Step 1: Draw a diagram for the

situation.

Step 2: Draw the principal ray

using a red crayon.

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Step 3: Draw the focal ray using a

blue crayon.

Step 4: Draw the central ray using

a green crayon.

Step 5: Draw the image on the

intersection.

Step 6: Describe the image The image is formed at the back of the mirror. It
formed. appears upright, diminished (smaller) and it is a
virtual image.

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Appendix A3. Application Worksheet

(with Answer Key)
Instructions: Draw the image which will form when your initials are viewed on a convex
mirror. Show your answer by doing the ray diagram. (10 points)
Answers may vary: All principles should be followed when doing this activity.

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