Year 11 Physics Module 3: Waves 40 min Lesson 14 of 18

Reflection of Light and Mirrors

The law of reflection still applies to light, but mirrors let us go further. Plane mirrors create upright virtual images, concave mirrors can focus light and form real images, and convex mirrors trade magnification for a wider field of view.

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Think First

Why does a car's rear-view mirror warn that objects may be closer than they appear, even though the mirror is still reflecting light according to the usual reflection law?

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Key Relationships — This Lesson

$i = r$  |  $\dfrac{1}{f} = \dfrac{1}{d_o} + \dfrac{1}{d_i}$  |  $m = -\dfrac{d_i}{d_o}$
f = focal length do = object distance di = image distance m = magnification
Plane mirror: image distance = object distance   |   Concave: can form real or virtual images   |   Convex: virtual, upright, reduced

M
Formula Reference — Mirrors

$i = r$
Law of Reflection
Angles are measured from the normal.
Use when: tracing reflected rays from plane or curved mirrors.
Common trap: measuring from the mirror surface instead of the normal.
$1/f = 1/d_o + 1/d_i$
Mirror Equation
Relates focal length, object distance, and image distance.
Use when: solving mirror image-position problems.
Common trap: ray-diagram reasoning should still make sense qualitatively before you trust the numbers.

Know

  • The law of reflection for light
  • How plane mirrors form images
  • The difference between concave and convex mirrors
  • The key rays used in mirror diagrams

Understand

  • Why a plane-mirror image appears behind the mirror
  • Why concave mirrors can focus or magnify
  • Why convex mirrors give a wider field of view
  • How image characteristics depend on ray intersections

Can Do

  • Apply the law of reflection in ray diagrams
  • Construct simple plane, concave, and convex mirror diagrams
  • Describe image position, orientation, magnification, and type
  • Use the mirror equation and magnification relation

Misconceptions to Fix

Wrong: A machine can produce more work output than work input.

Right: Energy is conserved; machines can only transform energy, never create it (efficiency ≤ 100%).

📚 Core Content

Key Terms
even though the mirrorstill reflecting light according to the usual reflection law?
Anglesmeasured from the normal
Energyconserved; machines can only transform energy, never create it (efficiency ≤ 100%)
rate at which workdone or energy is transferred; P = W/t
mirror as the objectin front — a result that follows directly from the law of reflection applied to a flat surface
The imagevirtual because the reflected rays do not actually meet there
01Plane Mirrors

Plane Mirrors

A plane mirror forms an upright virtual image that appears the same distance behind the mirror as the object is in front — a result that follows directly from the law of reflection applied to a flat surface.

The reflected rays diverge after leaving the mirror, but the eye traces them backward in straight lines. That backward extension gives the apparent image location. The image is virtual because the reflected rays do not actually meet there. This means a plane-mirror image cannot be projected onto a screen placed at the image location — there is no real light energy arriving at that point.

Another important property is lateral inversion: the image appears reversed left-to-right. This is why the word "AMBULANCE" is painted in reverse on the front of emergency vehicles — so drivers looking in their rear-view mirrors can read it correctly. The image is also the same size as the object, giving a magnification of exactly 1. These predictable, symmetric properties make plane mirrors the simplest case in geometrical optics and the foundation for understanding more complex curved mirrors.

Australian Context The Sydney Harbour Bridge uses plane mirrors in some of its maintenance inspection systems to allow engineers to view hard-to-see structural elements. The predictable virtual image position means technicians can accurately judge distances and alignment without needing direct line of sight.
02Concave and Convex Mirrors

Concave and Convex Mirrors

Curved mirrors modify the way reflected rays travel, which in turn changes the position, size, and nature of the image formed.

Concave Mirror

  • Curves inward
  • Can converge rays
  • Can produce real or virtual images
  • Used in headlights and telescopes

Convex Mirror

  • Curves outward
  • Causes rays to diverge
  • Produces virtual, upright, reduced images
  • Used in rear-view and security mirrors

A concave mirror brings parallel rays together at the focal point, which makes it a converging mirror. This focusing ability is useful whenever light needs to be concentrated — in solar furnaces, satellite dishes, and car headlights. A convex mirror, by contrast, makes parallel rays spread out as if they came from a focal point behind the mirror. It is a diverging mirror. Because the rays always diverge after reflection, a convex mirror can never form a real image.

The sign convention for mirrors is important: for concave mirrors, the focal length is positive; for convex mirrors, it is negative. Object distances are always positive for real objects. Image distances are positive for real images (formed in front of the mirror) and negative for virtual images (formed behind the mirror).

03Key Rays for Mirror Diagrams

Key Rays for Mirror Diagrams

Ray diagrams work because a few reliable rays are enough to locate the image — but only if each ray is drawn with care and understanding.

For concave mirrors, a ray parallel to the principal axis reflects through the focal point, a ray through the focal point reflects parallel to the axis, and a ray through the centre of curvature reflects back on itself. For convex mirrors, the reflected rays diverge as if they came from points behind the mirror. The same three rays can be used for convex mirrors if you extend them backward through the mirror to find the virtual image location.

Drawing accurate ray diagrams is not just a graphical exercise — it builds physical intuition. Before using the mirror equation, you should be able to predict qualitatively whether the image will be real or virtual, enlarged or reduced. If your calculated answer contradicts your ray diagram, one of them is wrong.

Diagram habit after drawing rays, always describe the image as real or virtual, upright or inverted, and enlarged, reduced, or same size. In HSC exams, image description questions are common and each characteristic carries marks.
Ray Diagram Protocol — every mirror diagram
Step 1 — Draw principal axis, mirror, focal point (F), and centre of curvature (C)
Step 2 — Draw the object as an upright arrow on the principal axis
Step 3 — Trace at least two key rays from the top of the object and apply reflection rules
Step 4 — Locate the image where reflected rays intersect (real) or where their backward extensions intersect (virtual)
04Describing the Image

Describing the Image

Image characteristics come from where reflected rays meet, or appear to meet — and these four descriptors should be stated for every image.

If reflected rays really meet in space, the image is real and can be projected onto a screen. If they only appear to come from a point when traced backward, the image is virtual. Concave mirrors can do both; convex mirrors produce virtual images only. The magnification tells us the size ratio: |m| > 1 means enlarged, |m| < 1 means reduced, and |m| = 1 means same size. A negative magnification indicates an inverted image.

The mirror equation and magnification formula allow us to calculate these characteristics quantitatively. However, the sign conventions must be applied consistently. A common mistake is to treat all image distances as positive. Remember: real images are in front of the mirror (positive di for mirrors), virtual images are behind (negative di).

Mirror typeObject positionImage typeOrientationSize
PlaneAnyVirtualUprightSame size
ConcaveBeyond CRealInvertedReduced
ConcaveAt CRealInvertedSame size
ConcaveBetween C and FRealInvertedEnlarged
ConcaveInside FVirtualUprightEnlarged
ConvexAnyVirtualUprightReduced

Common Misconceptions

Virtual images are not "real" so they cannot be seen.
Virtual images cannot be projected onto a screen, but they are definitely seen. Your reflection in a bathroom mirror is a virtual image, and you see it clearly. The eye's lens focuses the diverging reflected rays onto the retina.
A concave mirror always forms a real image.
A concave mirror only forms real images when the object is outside the focal length. When the object is placed inside the focal length, the reflected rays diverge and the image is virtual, upright, and enlarged — this is how a shaving mirror works.
Magnification is always positive.
Magnification can be negative. A negative m means the image is inverted. The magnitude |m| tells you the size factor. For example, m = −2 means the image is real, inverted, and twice as large as the object.
05The Mirror Equation and Magnification

The Mirror Equation and Magnification

The mirror equation provides a quantitative relationship between object position, image position, and focal length — but it only works when the sign convention is applied correctly.

The equation $1/f = 1/d_o + 1/d_i$ is derived from the geometry of reflected rays and is valid for both concave and convex mirrors, provided the sign convention is followed. For concave mirrors, f is positive; for convex mirrors, f is negative. Object distances for real objects are always positive. Image distances are positive for real images (in front of the mirror) and negative for virtual images (behind the mirror).

The magnification formula $m = -d_i/d_o$ connects image size to position. If $d_i$ is negative (virtual image), then m is positive, confirming that virtual images are upright. If $d_i$ is positive (real image), then m is negative, confirming that real images are inverted. Using these equations together allows you to predict all four image characteristics from a single calculation.

Real-World Anchor Dentists use small concave mirrors placed inside the patient's mouth. Because the tooth is placed inside the focal length, the mirror produces an enlarged, upright, virtual image that makes cavities and surface details much easier to see. The magnification comes directly from the mirror equation with $d_o < f$.
06Why These Mirrors Are Useful

Why These Mirrors Are Useful

Mirror design is chosen to match the job — each mirror type solves a specific optical problem by exploiting the geometry of reflected rays.

Concave mirrors can focus light into a beam or magnify an object depending on placement, which is useful in headlights and shaving mirrors. In car headlights, the bulb is placed at the focal point of a concave reflector, so the reflected rays emerge parallel and produce a strong, directed beam. Convex mirrors sacrifice magnification to widen the field of view, which is why they are used in rear-view and security settings. A driver can see a much larger area behind the vehicle in a convex mirror than in a plane mirror of the same size.

The trade-off is distance perception: because convex mirrors produce reduced images, objects appear smaller and therefore farther away than they actually are. This explains the safety warning on car side mirrors: "Objects in mirror are closer than they appear." The mirror is still obeying the law of reflection at every point — the warning exists because of the geometry of the curved surface, not because the laws of physics have changed.

Australian Context The "Big Pineapple" tourist attraction on the Sunshine Coast and many other large roadside icons are designed to be visible from a distance. Large convex security mirrors at road intersections across rural Australia help drivers see around blind corners — the wide field of view provided by convex curvature saves lives by revealing oncoming traffic that would otherwise be hidden.
Mirror Selection Protocol — choosing the right mirror
Step 1 — Is a wide field of view needed? If yes, choose convex
Step 2 — Is focusing or magnification needed? If yes, choose concave
Step 3 — Is an undistorted same-size image needed? If yes, choose plane

✏️ Worked Examples

Worked Example 1 Type 14 — Plane Mirror

Problem Setup

Scenario: An object is 2.0 m in front of a plane mirror. State the image position and image type.

Solution

1
Image distance equals object distance
For a plane mirror, the image appears the same distance behind the mirror as the object is in front. This follows from the law of reflection and the flat geometry of the mirror surface.
2
Image position = 2.0 m behind the mirror
This follows from the symmetry of the reflected rays. If the object is 2.0 m in front, the virtual image is 2.0 m behind.
3
Image type = virtual and upright
The rays do not actually meet behind the mirror; they only appear to when traced backward. The image has the same orientation as the object.

What would change if...

If the object moved closer to the mirror, the image would move closer by the same amount on the other side. The total distance from object to image would be twice the object distance. For example, at 0.5 m from the mirror, the image is 0.5 m behind, so object-to-image separation is 1.0 m.

Worked Example 2 Type 14 — Mirror Equation

Problem Setup

Scenario: A concave mirror has focal length 10 cm and an object is placed 30 cm in front of it. Find the image distance and magnification, then describe the image characteristics.

Solution

1
$1/f = 1/d_o + 1/d_i$
Use the mirror equation. For a concave mirror, $f = +10$ cm. The object is real, so $d_o = +30$ cm.
2
$1/10 = 1/30 + 1/d_i$
Substitute $f = 10$ cm and $d_o = 30$ cm.
3
$1/d_i = 1/10 - 1/30 = 2/30 = 1/15$, so $d_i = 15$ cm
The image forms in front of the mirror ($d_i$ positive), so it is a real image.
4
$m = -d_i/d_o = -15/30 = -0.5$
The negative sign confirms the image is inverted. The magnitude 0.5 means it is half the size of the object — reduced.

What would change if...

If the object were placed inside the focal length (e.g. at 5 cm), the concave mirror would produce a virtual upright image instead. Using the same equation: $1/d_i = 1/10 - 1/5 = -1/10$, giving $d_i = -10$ cm (virtual) and $m = -(-10)/5 = +2$ (upright and enlarged).

Visual Break

Which Mirror?

Mirror application Is a wide field of view needed? Security, rear-view, corner mirrors Yes No Convex mirror Continue below Is focusing or magnification needed? Headlights, telescopes, shaving mirrors Yes No Concave mirror Plane mirror

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Law of Reflection

  • Angle of incidence = angle of reflection ($i = r$)
  • Both angles measured from the normal, not the surface
  • Applies to both plane and curved mirrors at every point
  • The incident ray, reflected ray, and normal all lie in the same plane

Plane Mirrors

  • Image distance = object distance
  • Virtual, upright, same size as object
  • Lateral inversion (left-right reversal)
  • Magnification m = +1

Concave Mirrors

  • Converging mirror — f is positive
  • Object outside F → real, inverted image
  • Object inside F → virtual, upright, enlarged image
  • Used in headlights, shaving mirrors, telescopes

Convex Mirrors

  • Diverging mirror — f is negative
  • Always forms virtual, upright, reduced images
  • Wider field of view than plane mirrors
  • Used in rear-view mirrors and security mirrors

🏃 Activities

Activity 01 — Pattern A

Mirror Sort

Match each application to the mirror type that makes the most sense.

For each application, state the mirror type and explain in one sentence why that mirror is the best choice.

  1. Shaving mirror
  2. Car rear-view side mirror
  3. Shop security mirror
  4. Car headlight reflector
  5. Dentist's mouth mirror
  6. Bathroom mirror

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Activity 02 — Pattern A

Image Description

Describe the image formed by a convex mirror using the four standard descriptors.

Write one sentence for each characteristic: (1) real or virtual, (2) upright or inverted, (3) enlarged or reduced, (4) explain why this combination makes convex mirrors useful for rear-view mirrors.

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Activity 03 — Pattern B

Ray Rule Recall

List the three key rays commonly used for concave mirror diagrams and say what each one does after reflection.

For each ray, also state where on the diagram the ray must originate (e.g. from the top of the object) and what special point it must pass through or be parallel to.

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Activity 04 — Pattern C

Magnification Calculation

Calculate and interpret magnification for two mirror scenarios.

For each scenario, find the magnification and describe what it tells you about the image.

  1. A concave mirror forms a real image with $d_o = 20$ cm and $d_i = 60$ cm.
  2. A convex mirror forms a virtual image with $d_o = 30$ cm and $d_i = -10$ cm.

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Interactive: Mirror Image Locator
Interactive: Mirror Law Calculator
Revisit Your Thinking

Earlier you were asked why a rear-view mirror can make objects seem farther away even though it still obeys the reflection law.

The full answer: a convex mirror still reflects rays with angle of incidence equal to angle of reflection, but its curved shape makes the reflected rays diverge. That produces a reduced virtual image and a wider field of view, which is useful for driving but makes objects seem farther away than they really are.

Now revisit your prediction. How does mirror shape change the image without breaking the reflection law?

Annotate your prediction in your book with what you now understand differently.

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Revisit Your Initial Thinking

Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?

✅ Check Your Understanding

Multiple Choice

6 MARKS

1. In mirror problems, reflection angles are measured from:

A
The mirror surface
B
The principal axis only
C
The normal
D
The focal point

2. A plane mirror forms an image that is:

A
Real and inverted
B
Virtual and upright
C
Always enlarged
D
Always in front of the mirror

3. A convex mirror is especially useful in rear-view mirrors because it:

A
Provides a wider field of view
B
Always magnifies the image
C
Forms real inverted images only
D
Eliminates the law of reflection

4. For a concave mirror, a ray parallel to the principal axis reflects:

A
Parallel to the axis again
B
Straight through the mirror
C
Away from the focal point randomly
D
Through the focal point

5. If reflected rays actually meet in front of a mirror, the image is:

A
Virtual
B
Always upright
C
Real
D
Impossible

6. A concave mirror with focal length 8 cm and object distance 24 cm forms an image at:

A
8 cm
B
12 cm
C
24 cm
D
32 cm

Short Answer

10 MARKS

7. Explain why a plane-mirror image is described as virtual. 3 MARKS

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8. State two image characteristics of a convex mirror and explain why this mirror is used in rear-view mirrors. 3 MARKS

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9. A concave mirror has focal length 12 cm and object distance 18 cm. Find the image distance using the mirror equation and describe the image type. 4 MARKS

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Comprehensive Answers

Activity 01 — Mirror Sort

  1. Shaving mirror → Concave: Placed inside the focal length, it produces an enlarged, upright, virtual image that makes facial details easier to see.
  2. Rear-view side mirror → Convex: The diverging surface gives a wider field of view, allowing the driver to see more traffic behind the vehicle.
  3. Security mirror → Convex: Same principle — the wide field of view lets shopkeepers monitor large areas with a single mirror.
  4. Headlight reflector → Concave: The bulb is placed at the focal point so reflected rays emerge parallel, producing a strong, directed beam.
  5. Dentist's mouth mirror → Concave: Placed close to the tooth (inside F), it provides an enlarged, upright virtual image for better visibility.
  6. Bathroom mirror → Plane: Produces an undistorted, same-size virtual image with predictable left-right reversal.

Multiple Choice

1. C — reflection angles are measured from the normal.

2. B — plane mirrors form upright virtual images.

3. A — convex mirrors widen the field of view.

4. D — a parallel ray reflects through the focal point in a concave mirror.

5. C — actual intersection of reflected rays gives a real image.

6. B — $1/8 = 1/24 + 1/d_i$, so $1/d_i = 1/12$ and $d_i = 12$ cm.

Short Answer — Model Answers

Q7 (3 marks): A plane-mirror image is virtual because the reflected rays do not actually meet behind the mirror. Instead, the eye traces the reflected rays backward and interprets them as coming from a point behind the mirror. The image is therefore apparent rather than formed by real ray intersection.

Q8 (3 marks): A convex mirror forms a virtual, upright, reduced image. It is used in rear-view mirrors because the reduced image gives a wider field of view, allowing the driver to see more of the area behind the vehicle.

Q9 (4 marks): Use $1/f = 1/d_o + 1/d_i$. So $1/12 = 1/18 + 1/d_i$, which gives $1/d_i = 1/12 - 1/18 = 1/36$. Therefore $d_i = 36$ cm. The image forms in front of the mirror, so it is a real image.

Mark lesson as complete

Tick when you have finished the activities and checked the answers.