Objectives (5 - 10 minutes)

1. Understand the Lens Makers' Equation: The main objective of this lesson is for students to understand the concept of the lens makers' equation and how it is applied. They should be able to identify and interpret the terms of the equation, as well as use the equation correctly to solve related problems.

2. Apply the Equation in Practical Problems: In addition to understanding the theory, students should be able to apply the lens makers' equation in practical situations. This involves the ability to identify the given quantities and those that are requested, as well as knowing how to manipulate the equation to obtain the correct answer.

3. Develop Critical Thinking and Problem-Solving Skills: Through the study of the lens makers' equation and its application in problems, students should also develop their critical thinking and problem-solving skills. They should be able to analyze a problem, identify which information is relevant, and apply the equation appropriately to reach a solution.

Secondary Objectives:

• Promote Autonomous Learning: By adopting the inverted classroom methodology, the lesson also aims to promote students' autonomous learning. They will have the opportunity to study the content in advance and arrive at the lesson prepared to discuss and solve problems together.

• Stimulate Participation and Collaboration: The inverted classroom methodology also promotes students' participation and collaboration. They will be encouraged to share their doubts, ideas, and solutions during the lesson, fostering an active and engaging learning environment.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher starts the lesson by briefly reviewing the basic concepts of geometric optics necessary for understanding the topic, such as the definition of lenses, types of lenses (convex and concave), and their characteristics. Additionally, the teacher reviews how light behaves when passing through a lens, emphasizing the formation of images.

2. Initial Problem Situations: Next, the teacher presents two initial problem situations to the students that will be the starting point for exploring the topic. For example: "Imagine you are wearing glasses and need to know the focal length of the lenses to correct your vision. How could you find that out?" and "Suppose you are designing a camera and need to determine the focal length of the lens you will use. How could you do that?".

3. Contextualization: The teacher then contextualizes the importance of the topic, explaining how the lens makers' equation is used in practice, whether in the manufacturing of lenses for glasses or in the engineering of cameras and microscopes. For instance, the teacher may mention how the correct choice of the focal length of a lens can affect the image quality in a camera or the effectiveness of a corrective lens in a pair of glasses.

4. Topic Introduction: To spark students' interest, the teacher can introduce the topic with two curiosities. First, they can mention that the lens makers' equation, despite its apparent complexity, is actually a simplification of a more general equation known as the Gullstrand equation. Next, they can talk about how the discovery of the lens makers' equation was an important milestone in the history of optics, allowing significant advances in areas such as astronomy and medicine.

5. Lesson Objectives: Finally, the teacher presents the lesson Objectives, explaining that the main objective is for students to understand the lens makers' equation and know how to apply it. They also highlight the secondary objectives of promoting autonomous learning and active student participation in the lesson.

Development (20 - 25 minutes)

1. Virtual Laboratory Activity (10 - 15 minutes):

   • Scenario: The teacher presents students with a scenario in which they are engineers at a lens factory. They receive orders from customers who need lenses with specific characteristics, such as a certain focal length or a certain refractive power. The students' task is to use the lens makers' equation to design and manufacture the requested lenses.
   • Tool: The teacher uses an optics simulation software that allows students to adjust the parameters of a virtual lens (such as the curvature of the lens faces, the refractive index of the lens material, etc.) and instantly see how these adjustments affect the focal length and refractive power of the lens.
   • Activity: In groups, students receive a set of lens orders and are challenged to design and manufacture the corresponding lenses. They must use the lens makers' equation to determine the necessary parameters for each lens and then adjust the virtual lens in the simulation software to meet these parameters. They should record their calculations and adjustments in a report that will be presented at the end of the activity.

2. Debate (5 - 10 minutes):

   • Scenario: After the laboratory activity, the teacher proposes a debate on the importance of the lens makers' equation in industry and science.
   • Preparation: Students are divided into two groups, one group defending the idea that the lens makers' equation is essential and another group arguing that it is dispensable. Each group has a few minutes to discuss and prepare their arguments.
   • Debate: Students present their arguments, and the teacher acts as a moderator, ensuring that everyone has the opportunity to speak and that the debate remains respectful and focused on the topic.

3. Application in Everyday Situations (5 - 10 minutes):

   • Scenario: The teacher asks students to imagine everyday situations where knowledge of the lens makers' equation would be useful.
   • Discussion: In groups, students discuss and list possible situations. Some suggestions may include: choosing sunglasses with the correct protection for a specific light environment, selecting a camera lens to capture a specific image, understanding how the human eye lens works, among others.
   • Presentation: Each group presents their situations and explains how the lens makers' equation could be used to solve the problem.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • The teacher invites all groups to share their solutions or conclusions from the activities. Each group will have a maximum of 3 minutes to present their ideas.
   • During the presentations, the teacher should encourage students to ask questions, provide constructive feedback, and express their opinions. This promotes the exchange of ideas and collaborative learning.

2. Connection with Theory (3 - 5 minutes):

   • After the presentations, the teacher reviews the theoretical concepts covered in the lesson and how they connect with the practical activities carried out.
   • For example, the teacher can explain how the lens makers' equation, which was studied theoretically, was applied in the virtual laboratory activity and in the debates. They can also reinforce the importance of critical thinking and problem-solving in applying the theory.

3. Individual Reflection (2 - 3 minutes):

   • The teacher suggests that students silently reflect for a minute on what they learned in the lesson.
   • After this minute, the teacher asks some questions to guide the students' reflection. For example: "What was the most important concept you learned today?" and "What questions have not been answered yet?".
   • Students are encouraged to write down their answers, which can be shared later in a future lesson, if appropriate.

4. Feedback and Closure (1 - 2 minutes):

   • To conclude the lesson, the teacher requests quick feedback from students on the inverted classroom and the activities carried out. They may ask, for example, if students found the methodology effective, if they had difficulties at any point, or if they have suggestions to improve the dynamics of future lessons.
   • The teacher thanks everyone for their participation and effort, and reinforces the importance of continuous study and practice in consolidating learning. They may also give a preview of what will be covered in the next lesson.

Conclusion (5 - 10 minutes)

1. Summary of Contents (2 - 3 minutes):

   • The teacher should start the Conclusion of the lesson by revisiting the main points discussed and learned. They should recall the lens makers' equation, its relevance, and how it is applied in practice.
   • Additionally, they should emphasize the concepts of focal length and refractive power, showing how they are used in the equation and in problem-solving.
   • The teacher can use diagrams on the board or slides to visually reinforce the concepts and facilitate students' understanding.

2. Linking Theory with Practice (1 - 2 minutes):

   • Next, the teacher should explain how the lesson connected theory with practice. They can mention the activities carried out, such as the simulation in the virtual laboratory and the debate, and how they allowed students to apply the lens makers' equation in a concrete and contextualized way.
   • The teacher should highlight how the theoretical understanding of the concepts was fundamental for the completion of the activities and how the practical application of these concepts helped solidify learning.

3. Additional Materials (1 - 2 minutes):

   • The teacher should suggest additional study materials for students who wish to deepen their knowledge on the topic. These may include Physics books, educational websites, explanatory videos, among others.
   • For example, the teacher may recommend a video showing the application of the lens makers' equation in the manufacturing of glasses, or an interactive website that allows students to explore different lens configurations and see how they affect image formation.
   • The additional materials should be chosen to complement and reinforce what was learned in the lesson, without overwhelming students with excessive or unnecessary information.

4. Importance of the Subject (1 - 2 minutes):

   • Finally, the teacher should summarize the importance of the topic addressed for daily life. They can reinforce how the lens makers' equation is used in practice, in various areas such as the optics industry, camera and microscope engineering, medicine, among others.
   • The teacher can also highlight how understanding and mastering this topic can be useful for students in their personal lives, for example, in choosing glasses or camera lenses, or to better understand how the human eye works.
   • The idea is to show students that what they learned in the lesson is not just abstract theory, but has concrete and relevant practical applications.