Image Formation by Concave Mirror at Different Positions of the Object
Complete NCERT Guide for CBSE, NEET, JEE and Competitive Exams
Key Takeaways
- Understand how a concave mirror forms real and virtual images.
- Learn all six standard object positions with image characteristics.
- Master Pole (P), Focus (F), Principal Axis and Centre of Curvature (C).
- Useful for NCERT, CBSE, NEET, JEE and other competitive examinations.
- Includes summary table, applications and frequently asked questions.
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| Image formation by a concave mirror |
Introduction
A concave mirror is a spherical mirror whose reflecting surface curves inward toward the centre of the sphere. Since it converges parallel rays of light to a single point known as the principal focus, it is also called a converging mirror. Unlike a plane mirror, a concave mirror can produce both real and virtual images depending on the position of the object.
The image formed by a concave mirror changes as the object moves from infinity to the pole of the mirror. The image may be enlarged, diminished or the same size as the object, and it may appear inverted or erect. Understanding these image characteristics is essential for drawing ray diagrams and solving numerical as well as conceptual questions in optics.
This article explains the image formation by a concave mirror at different object positions using simple language, making it suitable for school students and competitive exam aspirants. By the end of this guide, you will understand the six standard image formation cases, their practical applications and the key concepts required for examinations.
Basic Principles of Concave Mirrors
The image formation by a concave mirror depends entirely on the position of the object with respect to the Pole (P), Principal Focus (F), and Centre of Curvature (C). A concave mirror reflects light according to the Laws of Reflection, where the angle of incidence is always equal to the angle of reflection.
Since a concave mirror is a converging mirror, parallel rays of light incident on its reflecting surface meet at a common point called the principal focus. As the object moves closer to or farther from the mirror, the position, size, and nature of the image also change.
Key Principles
- Light always obeys the laws of reflection.
- Parallel rays incident on the mirror converge at the principal focus.
- The image characteristics depend on the object's position relative to F and C.
- A concave mirror can produce both real and virtual images.
- Real images can be obtained on a screen, whereas virtual images cannot.
Rules for Drawing Ray Diagrams
To determine the position of an image formed by a concave mirror, four standard rays are commonly used in ray diagrams. These rays make image construction simple and are frequently used in NCERT and competitive examinations.
Rule 1
A ray of light travelling parallel to the principal axis is reflected through the principal focus (F).
Rule 2
A ray passing through the principal focus (F) is reflected parallel to the principal axis.
Rule 3
A ray passing through the centre of curvature (C) retraces its original path after reflection because it strikes the mirror normally.
Rule 4
A ray striking the pole (P) of the mirror is reflected such that the angle of incidence equals the angle of reflection.
Important Terms Related to Concave Mirror
Before studying image formation, it is important to understand the basic parts of a concave mirror. These terms are frequently used in ray diagrams, mirror formula problems, and board examinations.
Pole (P)
The Pole is the geometric centre of the reflecting surface of the mirror. It serves as the reference point for measuring object distance and image distance.
Principal Axis
The Principal Axis is an imaginary straight line passing through the Pole (P) and the Centre of Curvature (C). Most ray diagrams are drawn with respect to this axis.
Principal Focus (F)
The Principal Focus is the point where parallel rays of light meet after reflection from the concave mirror. The distance between the Pole and the Focus is called the Focal Length (f).
Centre of Curvature (C)
The Centre of Curvature is the centre of the sphere from which the concave mirror is formed. It is represented by the letter C.
Radius of Curvature (R)
The distance between the Pole (P) and the Centre of Curvature (C) is known as the Radius of Curvature. It is related to focal length by the formula:
R = 2f
Focal Length (f)
The distance between the Pole (P) and the Principal Focus (F) is called the Focal Length. It is equal to half of the radius of curvature.
f = R/2
Exam Tip
Remember the relation R = 2f. Questions based on the relationship between the radius of curvature and focal length are very common in NCERT, CBSE, NEET, and JEE examinations.
Image Formation by Concave Mirror at Different Positions of the Object
The image formation by a concave mirror depends entirely on the position of the object with respect to the Principal Focus (F) and the Centre of Curvature (C). As the object moves along the principal axis, the image changes in position, size, and nature. Understanding these six standard cases is essential for solving ray diagram questions in NCERT, CBSE, NEET, JEE, and other competitive examinations.
A concave mirror can produce both real and virtual images. Real images are formed in front of the mirror and can be obtained on a screen, whereas virtual images are formed behind the mirror and cannot be projected onto a screen.
1. Object at Infinity
When the object is located at a very large distance, such as the Sun or distant stars, the light rays reaching the mirror are almost parallel to each other. After reflection, these rays converge at the principal focus.
At the Principal Focus (F)
Real and Inverted
Highly Diminished (Point-sized)
Reflecting telescopes used in astronomy.
2. Object Beyond the Centre of Curvature (C)
When the object is placed beyond the centre of curvature, the reflected rays converge between the focus and the centre of curvature.
Between F and C
Real and Inverted
Diminished
Object placed far away from a concave mirror.
3. Object at the Centre of Curvature (C)
When the object is placed exactly at the centre of curvature, the reflected rays meet again at the same point after reflection.
At C
Real and Inverted
Same as the Object
The image and object are at equal distances from the mirror.
4. Object Between the Centre of Curvature (C) and the Focus (F)
When the object is moved between the centre of curvature and the principal focus, the reflected rays meet beyond the centre of curvature. The image becomes magnified.
Beyond C
Real and Inverted
Enlarged (Magnified)
Image projection experiments in laboratories.
5. Object at the Principal Focus (F)
When the object is placed exactly at the principal focus, the reflected rays become parallel after reflection. Therefore, they meet only at infinity.
At Infinity
Real and Inverted
Highly Enlarged
The image cannot be obtained on a nearby screen.
6. Object Between the Pole (P) and the Focus (F)
When the object is placed between the pole and the focus, the reflected rays diverge after reflection. Their backward extensions appear to meet behind the mirror, producing a virtual image.
Behind the Mirror
Virtual and Erect
Enlarged (Magnified)
Shaving mirrors, makeup mirrors, and dental mirrors.
Memory Trick
Far → Small → Same → Large → Infinite → Virtual
- Infinity → Focus → Point Image
- Beyond C → Between F & C → Small
- At C → Same Size
- Between C & F → Large
- At F → Infinity
- Between P & F → Virtual & Enlarged
Common Mistakes
- Confusing the Focus (F) with the Centre of Curvature (C).
- Forgetting that only one image is virtual in a concave mirror—the case when the object lies between the Pole and the Focus.
- Assuming every enlarged image is virtual. An enlarged image can also be real when the object is placed between C and F.
- Drawing incorrect ray diagrams by not following the four standard ray rules.
Summary Table of Image Formation by Concave Mirror
The table below provides a quick comparison of the image formed by a concave mirror at different object positions. It is useful for quick revision before school examinations and competitive exams such as CBSE, NEET, and JEE.
| Object Position | Image Position | Nature of Image | Image Size |
|---|---|---|---|
| At Infinity | At Focus (F) | Real, Inverted | Highly Diminished |
| Beyond Centre of Curvature (C) | Between F and C | Real, Inverted | Diminished |
| At Centre of Curvature (C) | At Centre of Curvature (C) | Real, Inverted | Same Size |
| Between C and F | Beyond Centre of Curvature (C) | Real, Inverted | Enlarged |
| At Focus (F) | At Infinity | Real, Inverted | Highly Enlarged |
| Between Pole (P) and Focus (F) | Behind the Mirror | Virtual, Erect | Enlarged |
Quick Revision Notes
Real Image
- Can be obtained on a screen.
- Always inverted.
- Formed in front of the mirror.
Virtual Image
- Cannot be obtained on a screen.
- Always erect.
- Appears behind the mirror.
Magnified Image
- Object between C and F → Real
- Object between P and F → Virtual
Diminished Image
- Object at Infinity
- Object Beyond C
Mirror Formula
1/f = 1/v + 1/u
Where:
- f = Focal Length
- u = Object Distance
- v = Image Distance
Magnification Formula
m = -v/u
Where:
- m = Magnification
- v = Image Distance
- u = Object Distance
Sign Convention for Concave Mirror
According to the New Cartesian Sign Convention:
- All distances are measured from the Pole (P).
- Distances measured in the direction of incident light are positive.
- Distances measured opposite to the direction of incident light are negative.
- Object distance (u) is always negative.
- Focal length (f) of a concave mirror is negative.
- Radius of curvature (R) is also negative.
Most Common Examination Questions
Very Important Questions
- Why is a concave mirror called a converging mirror?
- When does a concave mirror produce a virtual image?
- Where is the image formed when the object is placed at the centre of curvature?
- Write the mirror formula.
- State the relationship between focal length and radius of curvature.
- Why is a concave mirror used as a shaving mirror?
- Draw the ray diagram when the object is placed between C and F.
- Draw the ray diagram when the object is between P and F.
Exam Tips
- Remember only one virtual image is formed by a concave mirror.
- All real images formed by a concave mirror are inverted.
- The image is same size only when the object is at the centre of curvature.
- Use two principal rays while drawing ray diagrams.
- Learn the mirror formula and sign convention together.
- Memorize the order: Infinity → Beyond C → C → Between C & F → F → Between P & F.
Common Mistakes Students Make
Mistake 1
Confusing Focus (F) with Centre of Curvature (C).
Mistake 2
Using the wrong sign convention while solving numerical problems.
Mistake 3
Drawing incorrect reflected rays in ray diagrams.
Mistake 4
Thinking every enlarged image is virtual.
Applications of Concave Mirrors
Concave mirrors are widely used in science, medicine, transportation, and everyday life because they can converge light rays and produce enlarged images. Their ability to form both real and virtual images makes them one of the most useful optical devices.
🔭 Reflecting Telescopes
Large concave mirrors collect light from distant stars and galaxies, producing bright and clear astronomical images.
🦷 Dental Mirrors
Dentists use concave mirrors to obtain enlarged, upright images of teeth for detailed examination and treatment.
🪒 Shaving & Makeup Mirrors
When the face is placed between the pole and focus, the mirror forms a magnified virtual image, making grooming easier.
🚗 Vehicle Headlights
A bulb placed at the principal focus produces a powerful parallel beam of light, improving visibility at night.
☀ Solar Furnaces
Large concave mirrors concentrate sunlight at a single point to generate extremely high temperatures.
🔬 Scientific Instruments
Concave mirrors are used in optical laboratories, microscopes, projectors, and other precision instruments.
Real-Life Examples of Concave Mirrors
You interact with concave mirrors more often than you may realize. Some common examples include:
- Shaving mirrors
- Makeup mirrors
- Dental examination mirrors
- Reflecting telescopes
- Vehicle headlights
- Searchlights
- Solar cookers and solar furnaces
- Scientific optical instruments
Frequently Asked Questions (FAQs)
1. What is a concave mirror?
A concave mirror is a spherical mirror whose reflecting surface curves inward. It converges parallel rays of light toward the principal focus.
2. Why is a concave mirror called a converging mirror?
Because it brings parallel rays of light together at a single point called the principal focus after reflection.
3. When does a concave mirror form a virtual image?
A virtual, erect, and magnified image is formed when the object is placed between the Pole (P) and the Focus (F).
4. Can a concave mirror produce both real and virtual images?
Yes. A concave mirror forms real images when the object is placed beyond the focus, and a virtual image when the object is between the pole and the focus.
5. Which image formed by a concave mirror can be obtained on a screen?
Only real images can be projected onto a screen because the reflected rays actually meet.
6. Why are concave mirrors used in headlights?
Placing the light source at the principal focus produces a parallel beam of light that travels a long distance.
7. Why are concave mirrors used by dentists?
They provide an enlarged and upright image of teeth, allowing better examination and treatment.
8. What is the relationship between focal length and radius of curvature?
The radius of curvature is twice the focal length. R = 2f
Conclusion
Understanding the image formation by a concave mirror at different positions of the object is one of the most important topics in geometrical optics. The position of the object determines whether the image will be real or virtual, erect or inverted, enlarged or diminished.
By learning the six standard object positions, remembering the ray diagram rules, and practicing the summary table, students can confidently solve examination questions and understand the practical use of concave mirrors in daily life.
Quick Revision
- ✔ Concave mirror is a converging mirror.
- ✔ Real images are always inverted.
- ✔ Virtual image is formed only when the object lies between P and F.
- ✔ At C → Same Size.
- ✔ Between C & F → Enlarged.
- ✔ Beyond C → Diminished.
- ✔ At Infinity → Point-sized image at Focus.
- ✔ Remember: R = 2f
References
- NCERT Science – Class 10
- NCERT Exemplar Problems
- CBSE Physics Curriculum
- Standard School Physics Textbooks