Physics · Grade 12

Active learning ideas

Mirror and Lens Equations

This topic requires students to move beyond memorizing equations to applying sign conventions and interpreting physical outcomes. Active labs and group work let students test predictions, confront misconceptions with real measurements, and see how optics behave differently for mirrors versus lenses.

• Ontario Curriculum Expectations
• HS.PS4.B.1

• 25–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 35 min · Pairs

Pairs Lab: Concave Mirror Verification

Provide each pair with a concave mirror, illuminated pin object, and screen. Students measure object distance d_o, adjust screen for sharp image, record d_i, and determine f from multiple trials. Calculate predicted d_i for new d_o using the mirror equation, then test and compare results. Discuss sign conventions based on findings.

Explain the relationship between object distance, image distance, and focal length.

Facilitation Tip

During Pairs Lab: Concave Mirror Verification, circulate to ensure students align the object, mirror, and screen along the same axis before collecting data.

What to look for

Provide students with a diagram of a converging lens and an object placed at twice the focal length. Ask them to use the thin lens equation to calculate the image distance and magnification, then sketch the resulting image. Check their calculations and sketches for accuracy.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 45 min · Small Groups

Small Groups: Converging Lens Circuit

Groups receive a converging lens, light source, object arrow, and screen. They position the object at various distances beyond 2f, f, and between f and 2f. Record measurements, apply lens equation to predict image position and magnification, form the image, and sketch ray diagrams to confirm.

Analyze how magnification is calculated and interpreted for mirrors and lenses.

Facilitation Tip

In Small Groups: Converging Lens Circuit, assign each group a different object distance to compare results and build collective understanding.

What to look for

Present students with a scenario: 'A concave mirror has a focal length of 10 cm. An object is placed 5 cm in front of it.' Ask them to calculate the image distance and state whether the image is real or virtual, and upright or inverted, justifying their answer using sign conventions.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 25 min · Whole Class

Whole Class Demo: Diverging Lens Images

Use an optical bench with diverging lens and object. Project image formation on screen while class notes positions. Teacher inputs class-suggested d_o into equation live, predicts virtual image location. Students replicate calculations individually then share parallax method to locate virtual images.

Calculate image characteristics for complex optical systems using relevant equations.

Facilitation Tip

For Whole Class Demo: Diverging Lens Images, pause after each setup to have students sketch predicted images before revealing the actual outcome.

What to look for

Pose the question: 'How does changing the object distance affect the image formed by a diverging lens?' Have students work in pairs to use the mirror and lens equations to predict and explain the changes in image distance and magnification as the object moves closer to the lens.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 50 min · Small Groups

Stations Rotation: Mixed Optics Challenges

Set up stations with mirrors, lenses, and combo systems. At each, students solve for image properties given two variables, predict with equation, then verify using apparatus. Rotate every 10 minutes, compiling results to analyze complex systems like lens-mirror pairs.

Explain the relationship between object distance, image distance, and focal length.

Facilitation Tip

At Station Rotation: Mixed Optics Challenges, place a ruler or grid paper behind each station so students measure heights directly on the image plane.

What to look for

Provide students with a diagram of a converging lens and an object placed at twice the focal length. Ask them to use the thin lens equation to calculate the image distance and magnification, then sketch the resulting image. Check their calculations and sketches for accuracy.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start with clear sign convention anchors, then let students explore through guided inquiry. Research shows students grasp optics best when they combine algebraic calculation with physical measurement and iterative testing. Avoid rushing to the equations; instead, build intuition with quick trials before formalizing the model.

Students will correctly use mirror and lens equations with proper sign conventions to predict image position, size, and orientation. They will justify their answers with sketches, calculations, and peer discussions, showing confidence in distinguishing real from virtual images.

---

Watch Out for These Misconceptions

• During Pairs Lab: Concave Mirror Verification, watch for students ignoring sign conventions when they see a real image on the screen.

  Prompt students to measure distances from the mirror and record signs based on the standard convention: positive for real images formed in front of the mirror, negative for virtual ones behind it. Have them plot d_o vs d_i on graph paper to reveal the expected hyperbolic relationship and sign patterns.

• During Small Groups: Converging Lens Circuit, watch for students interpreting magnification greater than 1 as always upright.

  Ask groups to measure both object and image heights directly on their benches. When they see inverted enlarged images, have them recalculate magnification and discuss how the negative sign indicates inversion. Compare their results to predictions before moving to the next station.

• During Station Rotation: Mixed Optics Challenges, watch for students applying mirror conventions to lenses without adjustment.

  Circulate and ask each group to explain their sign choices for the diverging lens station. When a group’s image fails to form, guide them to review the lens equation and sign table together, emphasizing that diverging lenses always produce virtual images regardless of object position.

---

Methods used in this brief

• Problem-Based Learning
• Stations Rotation