How Does a Convex Mirror Form Images? Ray Diagrams & Key Properties
A convex mirror is a type of spherical mirror with an outward-curved reflecting surface. Unlike a concave mirror that curves inward, the convex mirror’s bulging surface faces the incoming light.
This unique shape causes parallel rays of light to diverge after reflection. As a result, convex mirrors are also called diverging mirrors. These mirrors are commonly used where a wide field of view is needed, such as in vehicle side mirrors, security mirrors, and certain optical devices.
Convex Mirror: Main Features
- Shape: Outward-curved, part of a spherical surface.
- Focal Point: The focal point is virtual and appears behind the mirror.
- Image Formation: Always forms a diminished (smaller), upright, and virtual image.
- Field of View: Offers a wide perspective because reflected rays spread outward.
- Uses: Widely found in vehicle mirrors, security setups, and optical instruments.
Understanding Image Formation with Convex Mirrors
When an object is placed in front of a convex mirror, the reflected rays diverge, but their extensions appear to meet at a point behind the mirror. The image formed is always virtual (cannot be projected on a screen), upright, and smaller than the actual object. This holds true regardless of the distance of the object from the mirror.
| Object Position | Nature of Image | Image Location |
|---|---|---|
| At infinity | Highly diminished, virtual, erect | At the principal focus, behind the mirror |
| Anywhere between infinity & pole | Diminished, virtual, erect | Between the pole and the focus, behind the mirror |
Key Formulas for Convex Mirrors
| Formula | Description |
|---|---|
| 1/f = 1/v + 1/u | Mirror formula for all spherical mirrors (u: object distance, v: image distance, f: focal length; for convex mirrors, f is positive) |
| Magnification (m) = h'/h = v/u | Ratio of image height (h') to object height (h), or image distance (v) to object distance (u) |
Step-by-Step Approach to Solving Convex Mirror Numericals
| Step | Procedure |
|---|---|
| 1 | Identify values for u (object distance), f (focal length), and h (height), applying sign conventions. |
| 2 | Use the mirror formula to find v (image distance). |
| 3 | Calculate magnification using m = v/u. |
| 4 | Determine image height with h' = m × h. |
Solved Example: Convex Mirror
Suppose an object is placed 30 cm in front of a convex mirror with a focal length of 15 cm. Find the image position and its height if the object height is 20 cm.
- Given: u = -30 cm (object distance), f = +15 cm (positive for convex), h = 20 cm.
- Mirror formula: 1/f = 1/v + 1/u ⇒ 1/15 = 1/v + 1/(-30).
- 1/v = 1/15 + 1/30 = (2+1)/30 = 3/30 ⇒ 1/v = 1/10 ⇒ v = +10 cm (behind mirror).
- Magnification m = v/u = 10/(-30) = -1/3.
- Image height h' = m × h = -1/3 × 20 = -6.67 cm (negative sign denotes erect image for a convex mirror).
Therefore, the image is virtual, upright, and diminished, located 10 cm behind the mirror, and its height is 6.67 cm.
Common Applications of Convex Mirrors
- Vehicle side/rear-view mirrors: Wide-angle view for better road safety.
- Security and surveillance: Used in stores, ATMs, and buildings to monitor large areas.
- Optical devices: Helps in instruments that require broad image capture.
- Street light reflectors: Spreads light over a larger region.
Convex vs Concave Mirrors: Comparison Table
| Property | Convex Mirror | Concave Mirror |
|---|---|---|
| Shape | Curved outward | Curved inward |
| Focal length | Positive | Negative |
| Type of image | Always virtual, upright, diminished | Can be real/inverted or virtual/erect |
| Applications | Vehicles, security, ATMs | Shaving mirrors, headlights, reflectors |
Related Learning Resources and Next Steps
- Uses of Convex Mirror
- Concave and Convex Mirrors
- Magnification Formula for Mirror
- Mirror Equation
- Difference Between Concave and Convex Mirror
Mastering the properties and formulas of convex mirrors is essential for understanding image formation and practical applications in Physics. Regular practice with formula-based problems and conceptual questions helps build confidence in this fundamental topic.
FAQs on Convex Mirror – Ray Diagram, Formula, Image Properties & Uses
1. What is a convex mirror?
A convex mirror is a curved mirror with its reflecting surface bulging outward. It reflects light rays outward and is also called a diverging mirror. Convex mirrors always form virtual, erect, and diminished images regardless of object position.
2. What image is formed by a convex mirror?
A convex mirror always forms a virtual, erect, and diminished image. The image appears behind the mirror between its pole and principal focus, and it is upright and smaller than the actual object.
3. Why are convex mirrors used in vehicles?
Convex mirrors are used in vehicle side mirrors because they provide a wider field of view. This helps drivers see more area behind and to the side of their vehicle, improving safety. Images appear reduced in size but show a larger area.
4. What is the mirror formula for a convex mirror?
The mirror formula for a convex mirror is: 1/f = 1/v + 1/u
- Here, f is the focal length (positive for convex mirrors),
- v is the image distance (measured from the mirror),
- u is the object distance (always negative according to sign convention).
5. Write two uses of convex mirrors with examples.
Common uses of convex mirrors include:
- Vehicle rear-view mirrors: Give a wide view, help drivers observe traffic behind.
- Security and surveillance mirrors: Used in shops, ATMs, and corridors to monitor wide areas.
6. How is the image formed by a convex mirror different from that by a concave mirror?
Convex mirrors always form virtual, erect, and diminished images. In contrast, concave mirrors can form real or virtual images, which may be magnified or diminished, depending on object distance. Real images by concave mirrors are inverted, while virtual images are erect.
7. What are the properties of image formed by a convex mirror?
Properties of images by a convex mirror:
- Always virtual and behind the mirror
- Erect (upright) orientation
- Diminished in size (smaller than the object)
- Located between the mirror’s pole and principal focus
8. How do you draw the ray diagram for image formation in a convex mirror?
Ray diagram steps for a convex mirror:
1. Draw the mirror with outward bulge and principal axis.
2. Place the object in front of the mirror.
3. Draw one ray parallel to the principal axis; after reflection, it appears to diverge from the focus behind the mirror.
4. Draw another ray directed at the pole; it reflects symmetrically.
5. Extended reflected rays meet at a point behind the mirror, showing image location.
9. Why do images in convex mirrors appear smaller?
Images in convex mirrors appear smaller because these mirrors diverge incoming rays. The extensions of the reflected rays meet at a point behind the mirror, forming a diminished (reduced) image compared to the object's actual size.
10. What is the magnification formula for a convex mirror?
The magnification (m) by a convex mirror is given by:
m = (image height) / (object height) = v / u
Here, the magnification is always less than 1 for a convex mirror, indicating the image is smaller than the object. The value is positive, showing the image is erect.
11. Give two real-life examples of convex mirrors (other than in vehicles).
Examples of convex mirrors in daily life:
- Security mirrors in shops and malls
- Safety mirrors at ATM counters and blind curves/turnings on roads
12. What is the sign convention for the focal length of a convex mirror?
The focal length of a convex mirror is always taken as positive according to the New Cartesian sign convention. The reflecting surface bulges toward the object, and the focus lies behind the mirror.
