Physics · 9th Grade · Electromagnetic Radiation and Optics · Weeks 28-36

Curved Mirrors: Concave and Convex

Analyzing image formation in spherical concave and convex mirrors.

• Common Core State Standards
• HS-PS4-1
• CCSS.MATH.CONTENT.HSG.CO.A.2

About This Topic

Curved mirrors come in two main types: concave (curving inward, like the inside of a bowl) and convex (curving outward, like the back of a spoon). Both are analyzed using the same ray diagram rules and the mirror equation, but they produce very different image types depending on where the object is placed relative to the focal point.

Concave mirrors converge reflected light rays. When an object is placed beyond the focal point, reflected rays converge to form a real, inverted image that can be projected onto a screen. The closer the object is to the focal point (from outside), the farther away the real image forms, and the larger it is. When the object is inside the focal point, reflected rays diverge and a virtual, upright, magnified image appears behind the mirror. This is the geometry behind shaving mirrors and makeup mirrors: the face is inside the focal point. Concave mirrors also focus parallel light rays to a single focal point, which is the principle behind satellite dishes, solar cookers, and reflecting telescopes.

Convex mirrors always produce virtual, upright, and diminished images, regardless of object position. Because they diverge incoming light, they provide a wider field of view than a flat mirror of the same size. This is why convex mirrors are used as car side mirrors (with the warning 'Objects in mirror are closer than they appear'), security mirrors in stores, and road safety mirrors at blind intersections. Active learning through ray diagram construction and mirror exploration helps students connect abstract geometry to these practical everyday applications.

Key Questions

1. How do convex mirrors provide a wider field of view for drivers?
2. How can a concave mirror be used to start a fire or cook food?
3. Differentiate between real and virtual images formed by curved mirrors.

Learning Objectives

• Calculate the image distance and magnification for objects placed at various positions relative to a concave mirror using the mirror equation.
• Compare and contrast the characteristics of images formed by concave and convex mirrors, identifying whether they are real or virtual, upright or inverted, and magnified or diminished.
• Explain the optical principles that allow convex mirrors to provide a wider field of view in specific applications.
• Design a ray diagram to predict the location and nature of the image formed by a concave mirror when the object is placed inside its focal point.

Before You Start

Reflection and the Law of Reflection

Why: Students need to understand the fundamental principles of light reflection, including the angle of incidence equaling the angle of reflection, before analyzing curved mirrors.

Ray Diagrams for Plane Mirrors

Why: Familiarity with drawing ray diagrams to locate images formed by flat mirrors provides a foundation for the more complex ray tracing involved with curved mirrors.

Key Vocabulary

Concave Mirror	A mirror with a reflecting surface that curves inward, like the inside of a bowl. It converges parallel light rays to a focal point.
Convex Mirror	A mirror with a reflecting surface that curves outward, like the back of a spoon. It diverges parallel light rays.
Focal Point (F)	The point on the principal axis of a curved mirror where parallel light rays converge (concave) or appear to diverge from (convex) after reflection.
Real Image	An image formed by the actual convergence of light rays, which can be projected onto a screen.
Virtual Image	An image formed where light rays appear to diverge from, but do not actually converge; it cannot be projected onto a screen.
Magnification	The ratio of the image height to the object height, indicating whether the image is enlarged, reduced, or the same size.

Watch Out for These Misconceptions

Common Misconception

Concave mirrors always produce magnified images.

What to Teach Instead

Concave mirrors produce different image types depending on object position. Objects beyond the center of curvature produce real, inverted, diminished images. Objects between the focal point and the center produce real, inverted, magnified images. Objects inside the focal point produce virtual, upright, magnified images. Object position relative to the focal point determines everything.

Common Misconception

Real images can be seen by the eye but virtual images cannot.

What to Teach Instead

Both real and virtual images can be seen. Real images, where light actually converges, can also be projected onto a screen. Virtual images, where light only appears to diverge from a location with no actual light present, can be seen by the eye looking into the mirror but cannot be projected. Visibility is not what distinguishes real from virtual.

Common Misconception

Convex mirrors make objects appear closer than they are.

What to Teach Instead

Convex mirrors make objects appear farther away than they actually are, which is why car side mirrors carry the warning 'Objects in mirror are closer than they appear.' The diminished image size the convex mirror produces is what the brain interprets as greater distance, even though the object is actually nearer than the image suggests.

Active Learning Ideas

Curved Mirror Ray Diagram Workshop

Students receive a printed sheet with three concave mirror problems (object outside focal point, at focal point, inside focal point) and two convex mirror problems. Using the three standard ray rules (parallel ray reflects through focus, focal ray reflects parallel, center ray reflects back), they construct diagrams for each case, then describe image type, orientation, and relative size. They highlight which cases produce real vs. virtual images.

35 min·Individual

Spoon Mirror Exploration

Each student gets a metal spoon. They hold the concave (inner) side toward them at arm's length and note the image, then slowly bring the spoon toward their face, observing the changes. They repeat with the convex (outer) side. Students record observations for at least five positions and sketch what they see, then match each observation to a ray diagram case they studied.

20 min·Individual

Think-Pair-Share: Why Convex Mirrors Are Used in Cars

Show a side-by-side comparison of a flat mirror and a convex mirror showing the same scene. Ask: what advantages does the convex mirror provide, and what is the tradeoff? Students think individually, pair for discussion focusing on field of view vs. apparent distance, then share. The class articulates why both properties (wider view AND appearing farther away) arise from the same physics.

15 min·Pairs

Solar Cooker Design Analysis

Groups receive a diagram of a parabolic solar cooker and its geometric cross-section. They identify the focal point, trace three parallel sun rays to confirm they converge, calculate the approximate focal length from the dish dimensions, and estimate how much sunlight area is focused to a single point. They then compare this to a flat mirror of the same size and calculate the theoretical temperature gain factor.

30 min·Small Groups

Real-World Connections

• Astronomers use large concave mirrors in reflecting telescopes, such as the Hubble Space Telescope, to gather faint light from distant stars and galaxies, forming magnified real images for observation.
• Security personnel in retail stores and traffic engineers at blind intersections utilize convex mirrors to monitor wide areas, providing a broad, albeit diminished, virtual image that enhances situational awareness.

Assessment Ideas

Quick Check

Provide students with a diagram of a concave mirror and an object placed beyond the focal point. Ask them to draw the principal ray, the focal ray, and the parallel ray, then identify the location and characteristics (real/virtual, inverted/upright, magnified/diminished) of the image formed.

Discussion Prompt

Pose the question: 'Why does your car's side mirror have the warning 'Objects in mirror are closer than they appear'?' Facilitate a discussion where students explain the properties of convex mirrors and how they affect perceived distances.

Exit Ticket

Ask students to write down one application of a concave mirror and one application of a convex mirror. For each, they should briefly explain why that specific mirror type is suited for the application, referencing image characteristics.

Frequently Asked Questions

How do convex mirrors provide a wider field of view for drivers?

Convex mirrors have a curved surface that diverges incoming light from a wide range of directions, allowing the mirror to reflect light from a much broader angular range than a flat mirror of the same size. This wider field of view comes at the cost of apparent distance accuracy: objects appear smaller and therefore seem farther away than they actually are.

How can a concave mirror be used to start a fire or cook food?

A concave parabolic mirror reflects parallel incoming rays and converges them at the focal point. By orienting the mirror toward the sun, sunlight from a large mirror area is concentrated to a single small spot, concentrating a large amount of light energy into a very small area. The resulting temperature at the focal point can reach hundreds of degrees, enough to ignite tinder or cook food.

What is the difference between real and virtual images formed by curved mirrors?

A real image forms where reflected light rays physically converge. Real images are always inverted, can be projected onto a screen, and form in front of the mirror. A virtual image forms where reflected rays appear to diverge from behind the mirror, but no light actually exists there. Virtual images are always upright, cannot be projected, and appear behind the mirror.

How does active learning improve student understanding of curved mirror images?

Spoon exploration activities, where students observe image changes as they move the spoon toward their face, connect abstract ray diagram cases to direct sensory experience. Solar cooker geometric analysis and convex mirror field-of-view comparisons show engineering relevance. Ray diagram construction workshops then formalize what students have already observed, making the mathematics meaningful rather than arbitrary.