Ray Diagrams and Real-World Applications of Concave and Convex Mirrors
Concave mirrors form both real and virtual images of objects, while convex mirrors form a virtual and erect image.
We find mirrors at our home, in our cars, beauty salons, etc. The list is endless! However, mirrors are called mirrors in a common language, while scientifically, each one of these is categorized into concave and convex mirrors.
Concave and convex mirrors are spherical mirrors. Now, if I ask you what a concave mirror is and how you differentiate it from a convex mirror, you say that it is possible by looking at the images of these two drawn below:
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Concave and Convex Mirror Images
In the above introduction, you understood the basic diagram of concave and convex mirrors. A ray diagram for a concave mirror varies with the object placed at varying positions.
Before starting with the ray diagram of each case, we need to know the following terms:
Principal Axis
The line passing through the centre of the sphere is called the principal axis.
Pole
The centre of the reflecting surface is called the pole (P).
Centre of Curvature
A concave mirror is carved out of a sphere, and its centre is called the centre of curvature (C).
The Radius of Curvature
Radius of the sphere (R)
Focus
The midpoint between C and P.
Sign Conventions:
When the object is placed in front of the mirror, the object is taken as negative.
Signs of the radius of curvature and focal length are also taken negatively.
Ray Diagram of Concave
Now, to understand it in detail, we will first look at the ray diagram concave mirror:
The Image Formed by a Concave Mirror
A concave mirror forms different images for the objects lying at different positions; let’s look at various cases one-by-one:
1. An Object Placed at Infinity
When an object is placed at infinity, the images coming from the distant object parallel to the principal axis converge at the focus ‘F’, as shown in the ray diagram below:
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2. An Object is Placed at C
When an object is placed at C, the real and inverted image is formed at C itself, as you can see in the ray diagram below:
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3. An Object Placed Beyond C
When an object is placed beyond C, the real and inverted image is formed between C and F, as you can see in the image below:
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4. An Object Placed Between C and F
When the object is placed between C and F, the real and inverted image is formed beyond C, as you can see in the ray diagram below:
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5. An Object is Placed at F
When an object is placed at F, the image coming from the distant object pass through C, strike the surface of the mirror, and hence, the reflected ray comes out parallel to the incident ray, as shown below:
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In all the above cases, the image is formed in front of the mirror. Now, we will look at the case of virtual images formed by the concave mirror.
6. An Object Placed Between P and F
This is a special case for the ray diagram of the concave mirror. When an object is placed between P and F, an image is formed behind the mirror. The rays appear to meet each other, so we represent these rays by a dotted line, as shown in the ray diagram below:
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So, the ray diagram for the image formed for the objects placed at different positions is:
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Image Formation by a Convex Mirror
We know that the convex mirrors form a virtual and erect image, and now we will look at the ray diagrams of the convex mirror:
1. An Object Placed at Infinity
When an object is placed at infinity, the incident rays passing parallel to the principal axis converge at F. The image formed is virtual and the zero-sized image is formed as you can see in the ray diagram below:
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2. An Object Placed Between Infinity and P
When an object is placed between infinity and P, the virtual and diminished image is formed between F and P, as you can see in the ray diagram below:
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3. An Object Placed at P
When an object is placed at P, the image will form at the pole itself.
The nature of the image is virtual, upright, and of the same size as that of the object.
Now, let’s look at the convex mirror image formation table:
FAQs on Concave Mirrors vs Convex Mirrors Explained
1. What are the essential terms used to describe spherical mirrors like concave and convex mirrors?
Understanding spherical mirrors requires knowing these key terms as per the CBSE 2025-26 syllabus:
- Pole (P): The geometric centre of the spherical mirror's reflecting surface.
- Centre of Curvature (C): The centre of the sphere of which the mirror is a part.
- Radius of Curvature (R): The distance between the pole and the centre of curvature.
- Principal Axis: The imaginary straight line passing through the pole and the centre of curvature.
- Principal Focus (F): The point on the principal axis where rays parallel to the axis converge (concave) or appear to diverge from (convex) after reflection.
- Focal Length (f): The distance between the pole and the principal focus. It is half the radius of curvature (f = R/2).
2. What is the main difference between a concave mirror and a convex mirror?
The main difference lies in their shape and how they affect light. A concave mirror has a reflecting surface that curves inwards, causing it to converge light rays. It can form both real and virtual images. In contrast, a convex mirror has a reflecting surface that bulges outwards, causing it to diverge light rays and always form a virtual, erect, and diminished image.
3. How does the image formed by a concave mirror change as an object moves closer to it?
The nature, position, and size of the image formed by a concave mirror depend entirely on the object's position:
- At infinity: Image is at the focus (F), highly diminished, real, and inverted.
- Beyond the centre of curvature (C): Image is between F and C, diminished, real, and inverted.
- At C: Image is also at C, same size as the object, real, and inverted.
- Between C and F: Image is beyond C, magnified, real, and inverted.
- At F: Image is formed at infinity, highly magnified, real, and inverted.
- Between the pole (P) and F: Image is behind the mirror, magnified, virtual, and erect.
4. Why are convex mirrors the standard choice for rear-view mirrors in vehicles?
Convex mirrors are used as rear-view mirrors for two critical safety reasons. Firstly, they provide a much wider field of view than a plane mirror of the same size, allowing the driver to see more of the traffic behind them. Secondly, they always form an erect (upright) and diminished image, ensuring that the driver's view is not inverted and that objects appear manageable within the mirror's frame.
5. What are some common real-world examples of concave and convex mirrors?
Both types of mirrors have distinct applications based on their properties:
- Concave mirrors are used for focusing light or magnification. Examples include shaving mirrors, dentists' mirrors, reflectors in car headlights and torches, and in solar furnaces to concentrate sunlight.
- Convex mirrors are used for a wide view. Examples include rear-view mirrors in vehicles, security mirrors in shops and ATMs, and on sharp curves on roads.
6. What are the standard rules for drawing ray diagrams for spherical mirrors?
To determine the position and nature of an image, we typically use two of these four rules:
- A ray of light parallel to the principal axis will pass through the principal focus (F) after reflection from a concave mirror, or appear to diverge from F for a convex mirror.
- A ray passing through the principal focus (F) will emerge parallel to the principal axis after reflection.
- A ray passing through the centre of curvature (C) will reflect back along the same path, as it strikes the mirror normally (at 90°).
- A ray incident obliquely at the pole (P) is reflected obliquely, making the angle of incidence equal to the angle of reflection with the principal axis.
7. What is the Cartesian Sign Convention used for calculations involving spherical mirrors?
As per CBSE guidelines, the New Cartesian Sign Convention is used for consistency in mirror formula calculations:
- The pole (P) of the mirror is taken as the origin.
- The principal axis is the x-axis.
- The object is always placed to the left of the mirror.
- All distances measured to the left of the pole (against the direction of incident light) are negative.
- All distances measured to the right of the pole are positive.
- Heights measured upwards and perpendicular to the principal axis are positive.
- Heights measured downwards are negative.
8. What is the mirror formula and what does magnification signify?
The relationship between the object distance (u), image distance (v), and focal length (f) of a spherical mirror is given by the mirror formula: 1/v + 1/u = 1/f. Magnification (m) describes the relative size and orientation of the image. It is given by m = h'/h = -v/u, where h' is the image height and h is the object height. A negative magnification indicates a real and inverted image, while a positive magnification indicates a virtual and erect image.
9. What happens to the image if the lower half of a concave mirror's reflecting surface is covered with black paper?
If the lower half of a concave mirror is covered, a complete image of the object is still formed. The position and size of the image remain unchanged. This is because light rays from all points on the object can still strike the upper half of the mirror and reflect to form the image. However, the brightness or intensity of the image will be reduced, as the number of reflected rays contributing to the image formation is halved.
10. Why can a concave mirror form a real image, but a convex mirror cannot?
The ability to form a real image depends on whether the reflected light rays actually converge. A concave mirror is a converging mirror; it can bend parallel light rays to meet at a single, real point in front of the mirror. This physical intersection of rays is what forms a real image that can be projected on a screen. In contrast, a convex mirror is a diverging mirror. It spreads out all reflected rays, which only appear to meet at a virtual point behind the mirror. Since the rays never actually meet, a real image cannot be formed.
11. Under what specific condition does a concave mirror act as a magnifying glass, like in a shaving mirror?
A concave mirror functions as a magnifier, producing a virtual, erect, and enlarged image, only when the object is placed between its pole (P) and its principal focus (F). In this specific region, the reflected rays diverge and appear to come from a point behind the mirror, creating the magnified virtual image needed to see a clear, enlarged view for tasks like shaving or applying makeup.
12. How would immersing a spherical mirror in water affect its focal length?
The focal length of a spherical mirror would not change at all if it were immersed in water or any other transparent medium. The focal length (f) is an intrinsic property of the mirror's physical structure, determined solely by its radius of curvature (f = R/2). Unlike a lens, whose focal length depends on the refractive index of the surrounding medium, a mirror's reflective properties are independent of the medium in front of it.
