Light – Reflection and Refraction · Lesson 6 of 15
Image Formation by a Convex Mirror
“Everything looks smaller, but at least the mirror sees more traffic.”
• Predict images formed by a convex mirror for distant and finite objects. • Explain why convex-mirror images are always virtual, erect and diminished. • Describe how the image moves as the object moves. • Compare the fields of view of plane, concave and convex mirrors. • Justify the use of convex mirrors in vehicles.
A vehicle mirror must show a large region behind the driver without turning every passing vehicle upside down. A convex mirror achieves this by spreading reflected rays and fitting a wide scene into a smaller, erect image.
Image Positions
| Object position | Image position | Size | Nature |
|---|---|---|---|
| At infinity | At F behind the mirror | Highly diminished, point-sized | Virtual and erect |
| Between infinity and P | Between P and F behind the mirror | Diminished | Virtual and erect |
Detailed Ray Diagrams for the Two Cases
The table above summarises the two possible object-position cases for a convex mirror. In the diagrams below, blue lines show incident rays, red lines show reflected rays, the orange arrow is the object and the purple arrow or point is the image. Dashed purple lines are backward extensions used to locate a virtual image; they do not represent actual light travelling behind the mirror.
Object at Infinity
An object at a very large distance sends rays that reach the convex mirror almost parallel to the principal axis. After reflection, the rays spread apart in front of the mirror. Each reflected ray travels as though it came from the principal focus behind the mirror. When the reflected rays are extended backward, their extensions meet at the principal focus. Since the actual reflected rays never meet, the image is virtual. In the limiting case of an infinitely distant object, its angular extent becomes extremely small, so the image is highly diminished and is represented by a point. The point lies on the principal axis, and the image is described as erect.
• Object position: At infinity. • Image position: At the principal focus behind the mirror. • Relative size: Highly diminished or point-sized. • Orientation: Erect. • Nature: Virtual. • Screen test: The image cannot be received on a screen.
Object at Any Finite Distance
Place the object at any finite distance in front of the convex mirror. From the top of the object, draw one ray parallel to the principal axis. It reflects outward and appears to come from the principal focus. Draw a second ray directed toward the principal focus behind the mirror; after reflection, it travels parallel to the principal axis. The reflected rays diverge, so extend them backward behind the mirror. Their backward extensions intersect between the pole and principal focus, locating a virtual image. The image arrow is above the principal axis, so it is erect, and it is shorter than the object arrow, so it is diminished. A ray directed toward the centre of curvature may be used instead of the second ray; it retraces its path and gives the same image position.
• Object position: Anywhere between infinity and the pole in front of the mirror. • Image position: Between the pole and principal focus behind the mirror. • Relative size: Diminished. • Orientation: Erect. • Nature: Virtual. • Screen test: The image cannot be received on a screen. • Motion: As the object moves away, the image moves toward the principal focus and becomes smaller; as the object approaches the mirror, the image moves toward the pole and becomes larger but remains diminished.
A parallel ray reflects as though it came from F behind the mirror. A second ray directed toward C returns along its path. The actual reflected rays diverge, but their backward extensions meet between P and F. Because the meeting is only apparent, the image is virtual. It remains above the axis and is therefore erect. Its height is smaller than the object's height, so it is diminished.
Movement of the Image
When a finite object moves away from a convex mirror, its image moves from a position near P toward F and becomes smaller. It never crosses F. When the object is extremely far away, the incoming rays are nearly parallel and the image approaches a point at F.
Problem
A pencil is moved away from a convex mirror. Predict the changes in its image.
- 1.For every finite position, the image lies between P and F behind the mirror.
- 2.As the object distance increases, rays arrive more nearly parallel.
- 3.The apparent intersection therefore moves toward F.
- 4.The image becomes smaller but remains virtual and erect.
Field of View
The extent of the surrounding region visible through an optical device from a particular viewing position.
Because a convex mirror bulges outward, rays from a wider range of directions can be reflected toward the observer. The price of this wider field is a diminished image: objects appear smaller and may seem farther away than they are. This trade-off is valuable for observing traffic or large objects.
Uses of Convex Mirrors
Convex mirrors are fitted as rear-view or wing mirrors because they always provide an erect image and show a larger area than a comparable plane mirror. A small convex mirror can also show the full image of a tall building or tree, whereas a small plane mirror may not capture the same field from the same position.
Observing a Convex-Mirror Image
Hold a convex mirror and an upright pencil. Observe the image, then move the pencil gradually away. Record its orientation, size and position relative to P and F. Repeat by viewing a distant object with plane, concave and convex mirrors of comparable sizes. The convex mirror should reveal the widest region.
A convex mirror makes objects appear smaller, so their apparent distance can be misleading. Its main advantage is awareness of a wider region, not exact distance estimation.
Quiz
Where does a finite object's image lie in a convex mirror?
Which set always describes a convex-mirror image?
As an object moves away, its convex-mirror image moves toward which point?
Why is a convex mirror preferred for rear viewing?
What happens for an object at infinity?
Practice Problems
- Describe the image of a distant tree in a convex mirror. Solution: It is highly diminished, virtual and erect, and forms at F behind the mirror.
- A convex-mirror image is observed near P. What can be inferred about the object? Solution: The object is at a finite and relatively nearer distance; as an object approaches the mirror, its image moves toward P and grows, while remaining diminished.
- Why does a convex mirror show more area than a plane mirror? Solution: Its outward curvature redirects rays from a wider range of directions toward the observer.
- Can a convex mirror project a candle image on a screen? Explain. Solution: No. Reflected rays diverge and only their backward extensions meet behind the mirror, so the image is virtual.
- Compare rear viewing with a plane and convex mirror of equal size. Solution: The plane mirror gives a same-sized image but a narrower field. The convex mirror gives smaller erect images and a wider field, so more traffic is visible.
Key Takeaways
• A convex mirror always forms a virtual, erect and diminished image. • A finite object's image lies between P and F behind the mirror. • A distant object's image approaches a point at F. • Moving the object away moves the image toward F and reduces it. • Outward curvature gives a convex mirror a wide field of view. • Vehicle mirrors use the wide field while accepting reduced image size.