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.
Use the PDF for classwork, homework or revision. It includes key ideas, activities, questions, an extend task and success-criteria proof.
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?
Type your prediction below. You will revisit it at the end.
Write your prediction in your book. You will revisit it at the end.
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
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.
Curved mirrors modify the way reflected rays travel, which in turn changes the position, size, and nature of the image formed.
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).
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.
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 type | Object position | Image type | Orientation | Size |
|---|---|---|---|---|
| Plane | Any | Virtual | Upright | Same size |
| Concave | Beyond C | Real | Inverted | Reduced |
| Concave | At C | Real | Inverted | Same size |
| Concave | Between C and F | Real | Inverted | Enlarged |
| Concave | Inside F | Virtual | Upright | Enlarged |
| Convex | Any | Virtual | Upright | Reduced |
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.
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.
✏️ Worked Examples
Scenario: An object is 2.0 m in front of a plane mirror. State the image position and image type.
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.
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.
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
🏃 Activities
For each application, state the mirror type and explain in one sentence why that mirror is the best choice.
Type your matched explanations below.
Write your matched explanations in your book.
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.
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.
Type your three key rays below.
Write your three key rays in your book.
For each scenario, find the magnification and describe what it tells you about the image.
Type your calculations and interpretations below.
Write your calculations and interpretations in your book.
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.
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
1. In mirror problems, reflection angles are measured from:
2. A plane mirror forms an image that is:
3. A convex mirror is especially useful in rear-view mirrors because it:
4. For a concave mirror, a ray parallel to the principal axis reflects:
5. If reflected rays actually meet in front of a mirror, the image is:
6. A concave mirror with focal length 8 cm and object distance 24 cm forms an image at:
7. Explain why a plane-mirror image is described as virtual. 3 MARKS
8. State two image characteristics of a convex mirror and explain why this mirror is used in rear-view mirrors. 3 MARKS
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
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.
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.
Tick when you have finished the activities and checked the answers.