Image Formation By Spherical Mirrors

Edited By Vishal kumar | Updated on Jul 02, 2025 06:10 PM IST

Spherical mirrors, including concave and convex mirrors, play a crucial role in the formation of images in various optical devices. Understanding how these mirrors form images helps us grasp the fundamental principles of reflection and optics. In everyday life, concave mirrors are used in shaving mirrors to provide a magnified view of the face, while convex mirrors serve as essential safety tools in vehicle rearview mirrors by offering a wider field of view.

This Story also Contains

Image formation by spherical mirrors
Rules For Ray Diagrams
Image Formation by Concave Mirror
Image Formation by Convex Mirror:
Solved Examples Based on Image Formation by Spherical Mirrors
Summary

Image Formation By Spherical Mirrors

In this article, we are going to study image formation by spherical mirrors in which we will cover sign conversion, rules for ray diagrams and some of the solved examples.

Image formation by spherical mirrors

Image formation by spherical mirrors depends on the position of the object relative to the mirror's surface and principal axis. Both concave and convex mirrors have unique properties that influence the characteristics of the images they produce, including their nature, size, and orientation.

Sign conventions

In the cartesian sign convention direction of the incident, the ray is taken as +ve.
All the measurements are measured from the pole.
If the incident ray is travelling from left to right the distance, measurement along the right direction will be taken as positive.
We can treat this direction as +ve x-axis direction and the rest can be decided on the basis of the graph that we use in mathematics. Like upward direction will be taken as +ve as it is +ve y-axis. And downward as -ve
Height above the principle axis is taken as positive and below it is taken as negative.
Angles measured from the normal in an anti-clockwise sense are positive, while those in a clockwise sense are negative.

Rules For Ray Diagrams

The position of the image formed by spherical mirrors can be found by taking two rays of light coming from a point on the object which intersect each other to form an image. The following are the rules which are used for obtaining images formed by spherical mirrors.

Rule 1: A ray of light that runs parallel to the principal axis, after reflection, passes through the principal focus F of a concave mirror or appears to pass through the principal focus of a convex mirror.

Rule 2: A ray of light passing through the centre of curvature in a concave mirror or a ray of light going towards the centre of curvature of a convex mirror is reflected back along the same path.

Rule 3: A ray of light passing through the principal focus of a concave mirror or appearing to pass through the principal focus of a convex mirror becomes parallel to the principal axis after reflection.

Rule 4: A ray incident at the pole is reflected back making the same angle as the principal axis.

Image Formation by Concave Mirror

1: For a real object very far away from the mirror, the real image is formed at the focus.

2: For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

3: For a real object at C, the real image is formed at C. The image is inverted and the same size as the object.

4: For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object.

5: For a real object at f, no image is formed. The reflected rays are parallel and never converge.

6: For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object.

Image Formation by Convex Mirror:

1. When the object is at infinity, a point-sized image is formed at the principal focus behind the convex mirror.

Properties of image: The image is highly diminished, virtual and erect.

2. When the object is between infinity and the pole of a convex mirror, a diminished, virtual and erect image is formed between the pole and focus behind the mirror.

Properties of image: The image is diminished, virtual and erect.

Solved Examples Based on Image Formation by Spherical Mirrors

Example 1: An object is at a distance of 10 cm from a mirror and the image of the object is at a distance of 30 cm from the mirror on the same side as the object. The nature of the mirror and its focal length are:

1) Convex, 15cm

2) Concave, 1.5cm

3) Convex, 7.5cm

4) Concave, 7.5cm

Solution:

Sign Convention

1) All distances are measured from the pole.

2) Distance measured in the direction of incident rays is taken as positive.

3) Distance measured in the direction opposite to that of incident rays is taken as negative.

4) Distance above the principal axis as positive and below the principal axis as negative.

u = -10 cm

v = - 30cm from sign convention

from mirror formula

$\begin{aligned} & \frac{1}{f}=\frac{1}{v}+\frac{1}{u}=-\frac{1}{30}-\frac{1}{10}=\frac{-4}{30} \\ & \mathrm{f}=-7.5 \mathrm{~cm}\end{aligned}$

since focal length is negative hence its mirror concave.

Hence, The answer is the option (4).

Example 2: What type of image will form when the object is between infinity and the pole of a convex mirror?

1) A diminished, Real and erect image is formed between the pole and the focus behind the mirror.

2) A diminished, virtual and erect image is formed between the pole and the focus behind the mirror.

3) A diminished, virtual and inverted image is formed between the pole and the focus behind the mirror.

4) an enlarged, virtual and erect image is formed between the pole and the focus behind the mirror.

Solution:

When the object is between infinity and the pole of a convex mirror, a diminished, virtual and erect image is formed between the pole and focus behind the mirror.

Properties of image: The image is diminished, virtual and erect.

Example 3: What type of image will form for a real object between the Center of curvature(C) and focus(f) in the concave mirror?

1) For a real object between C and f, a real image is at C. The image is inverted and larger than the object.

2) For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object.

3) For a real object between C and f, a real image is formed outside of C. The image is erect and larger than the object.

4) For a real object between C and f, a real image is formed outside of C. The image is inverted and diminished than the object.

Solution:

For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object.

Example 4: A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value $|f|=40$ cm. The image of an object produced by the mirror is of height 25 cm and has the same orientation as the object. One may conclude from the information :

1) The image is virtual, opposite side of a convex mirror.

2) The image is real, same side as a concave mirror

3) The image is real, same side as the convex mirror.

4) The image is virtual, opposite side of the concave mirror.

Solution

Since the orientation is the same image is virtual. Since the image is smaller the mirror has to be convex.

Hence, the answer is option (1).

Example 5: The direction of a ray of light incident on a concave mirror is shown by PQ while directions in which the ray would travel after reflection is shown by four rays marked $1,2,3$ and 4 (figure). Which of the four rays correctly shows the direction of the reflected ray?

1) 1
2) 2
3) 3
4) 4

Solution:

The PQ ray of light passes through focus F and incident on the concave mirror, after reflection the ray, should become parallel to the principal axis as shown by the ray - 2 in the figure.

Hence, the answer is option (2).

Summary

Depending on its position in relation to the mirror, a spherical mirror which is like the concave and convex mirrors, creates an image. When the object is placed beyond the focal point, real and inverted images are formed by the concave mirror while virtual and upright images are formed when the object lies between the mirror and the focal point. In relation to the object’s distance, size, and character vary with distance.

Frequently Asked Questions (FAQs)

1. Why do concave mirrors sometimes form upright images and other times inverted images?

The orientation of the image formed by a concave mirror depends on the object's position relative to the focal point. When the object is placed between the focal point and the mirror, the image is upright and virtual. When the object is beyond the focal point, the image is inverted and real.

2. What happens to the image when an object is placed at the center of curvature of a concave mirror?

When an object is placed at the center of curvature of a concave mirror, the image formed is real, inverted, and the same size as the object. It appears at the same location as the object, i.e., at the center of curvature.

3. How does the size of an image change as an object moves closer to a concave mirror?

As an object moves closer to a concave mirror, the size of the image generally increases. When the object is beyond the center of curvature, the image is smaller than the object. As it moves closer, the image size increases, becoming equal to the object at the center of curvature, and larger than the object between the center of curvature and the focal point.

4. How does the image change when an object crosses the focal point of a concave mirror?

When an object crosses the focal point of a concave mirror (moving from beyond the focal point to between the focal point and the mirror), the image undergoes a dramatic change. It transitions from being real and inverted to virtual and upright. The image size also changes from being finite to becoming larger and eventually infinite as the object passes through the focal point.

5. Why does a concave mirror form a magnified image when used as a shaving or makeup mirror?

When used as a shaving or makeup mirror, a concave mirror forms a magnified image because the face is typically placed between the focal point and the mirror. In this position, the mirror forms a virtual, upright image that is larger than the object, providing a magnified view.

6. What's the difference between real and virtual images formed by spherical mirrors?

Real images are formed when light rays actually converge at a point after reflection. They can be projected on a screen and are always inverted. Virtual images, on the other hand, are formed when light rays appear to diverge from a point after reflection. They cannot be projected on a screen and are always upright.

7. Can a convex mirror ever form a real image?

No, a convex mirror always forms virtual images. This is because the reflected rays from a convex mirror always diverge, never converging to form a real image. The virtual image formed is always upright and smaller than the object.

8. Why do side-view mirrors on cars often say "Objects in mirror are closer than they appear"?

Side-view mirrors on cars are typically convex mirrors. Convex mirrors always form virtual images that are smaller than the actual objects. This property allows for a wider field of view but makes objects appear farther away than they actually are, hence the warning.

9. What is the significance of the focal point in image formation by spherical mirrors?

The focal point is crucial in determining the nature and position of the image formed. For concave mirrors, objects beyond the focal point form real, inverted images, while objects between the focal point and the mirror form virtual, upright images. For convex mirrors, the focal point (which is behind the mirror) helps determine the position and size of the virtual image formed.

10. How does the radius of curvature affect the focusing power of a spherical mirror?

The focusing power of a spherical mirror is inversely proportional to its radius of curvature. A smaller radius of curvature results in a more sharply curved mirror, which has a shorter focal length and thus a higher focusing power. Conversely, a larger radius of curvature leads to a flatter mirror with a longer focal length and lower focusing power.

11. What is a spherical mirror?

A spherical mirror is a curved reflective surface that forms part of a sphere. It can be either concave (curves inward) or convex (curves outward). These mirrors reflect light in specific ways, forming images that can be real or virtual, depending on the mirror type and object position.

12. How does the focal point of a spherical mirror relate to its radius of curvature?

The focal point of a spherical mirror is located halfway between the mirror's center of curvature and its vertex. Mathematically, the focal length (f) is equal to half the radius of curvature (R). This relationship is expressed as f = R/2.

13. What is spherical aberration and how does it affect image formation?

Spherical aberration is an optical effect where light rays reflecting from different parts of a spherical mirror don't converge at a single focal point. This occurs because the outer edges of the mirror have a different focal length than the center. As a result, the image formed can be blurred or distorted, especially for objects far from the mirror's axis.

14. How does the mirror equation relate object distance, image distance, and focal length?

The mirror equation relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror. It is expressed as 1/f = 1/u + 1/v. This equation allows us to calculate any one of these quantities if the other two are known, making it a fundamental tool in understanding image formation by spherical mirrors.

15. How does the magnification of an image relate to the object and image distances in spherical mirrors?

The magnification (m) of an image in spherical mirrors is defined as the ratio of the image height to the object height. It can be calculated using the formula m = -v/u, where v is the image distance and u is the object distance. The negative sign indicates that if the image is inverted, the magnification will be negative. For enlarged images, |m| > 1, and for diminished images, |m| < 1.

16. What is the difference between the center of curvature and the focal point of a spherical mirror?

The center of curvature is the center of the sphere of which the mirror forms a part. It's located at a distance equal to the radius of curvature from the mirror's vertex. The focal point, on the other hand, is the point where parallel rays converge after reflection (for concave mirrors) or appear to diverge from (for convex mirrors). It's located halfway between the center of curvature and the mirror's vertex.

17. How does the sign convention work for spherical mirrors?

In the sign convention for spherical mirrors, distances measured in the direction of incident light are considered positive, while those measured opposite to the direction of incident light are negative. For concave mirrors, the focal length is positive, while for convex mirrors, it's negative. Object distances are always positive, while image distances are positive for real images and negative for virtual images.

18. What happens to the image when an object is placed at infinity in front of a concave mirror?

When an object is placed at infinity in front of a concave mirror, the incoming light rays are essentially parallel. These parallel rays converge at the focal point after reflection. As a result, a real, inverted, and highly diminished (point-sized) image is formed at the focal point of the mirror.

19. Why are concave mirrors used in telescopes and satellite dishes?

Concave mirrors are used in telescopes and satellite dishes because of their ability to concentrate incoming parallel rays to a single focal point. This property allows them to gather and focus light from distant stars (in telescopes) or radio waves (in satellite dishes) effectively. The concentrated signals at the focal point can then be detected or further processed.

20. Why is the image formed by a convex mirror always behind the mirror?

The image formed by a convex mirror is always behind the mirror because the reflected rays diverge after hitting the mirror surface. When these diverging rays are traced backwards, they appear to originate from a point behind the mirror. This point is where the virtual image appears to be located, and it's always behind the mirror surface regardless of the object's position.

21. How does the concept of infinite focal points apply to plane mirrors?

Plane mirrors can be thought of as having an infinite focal length, or focal points at infinity. This is because:

22. How does the position of an object affect the nature of the image formed by a convex mirror?

For a convex mirror, the nature of the image remains consistent regardless of the object's position. The image is always virtual, upright, and smaller than the object. However, as the object moves closer to the mirror, the image size increases slightly and appears closer to the mirror surface, though it always remains behind the mirror and smaller than the object.

23. Why do convex mirrors always form diminished images?

Convex mirrors always form diminished (smaller) images because they cause incident parallel rays to diverge upon reflection. This divergence creates a virtual image that appears to be behind the mirror and is always smaller than the object, regardless of the object's position. The curvature of the mirror spreads out the reflected light, resulting in a smaller image.

24. How do spherical mirrors differ from parabolic mirrors in terms of image formation?

Spherical mirrors suffer from spherical aberration, where light rays from the edges of the mirror don't converge at the same point as rays from near the center. This can lead to slightly blurred images, especially for objects far from the mirror's axis. Parabolic mirrors, on the other hand, are designed to eliminate spherical aberration. They can focus all parallel incoming rays to a single point, producing sharper images, which is why they're often used in high-quality optical instruments.

25. How does the focal length of a spherical mirror change if it's immersed in water?

When a spherical mirror is immersed in water, its focal length remains unchanged. This is because the focal length depends on the mirror's radius of curvature, which is a physical property of the mirror and doesn't change when submerged. However, the apparent depth of the image might change due to the refraction of light in water, but this doesn't affect the mirror's focal length itself.

26. What is the relationship between the focal length and the power of a spherical mirror?

The power of a spherical mirror is defined as the reciprocal of its focal length, expressed in meters. Mathematically, Power (P) = 1/f, where f is the focal length in meters. The unit of power is diopter (D). A mirror with a shorter focal length has a higher power, meaning it has a stronger ability to converge or diverge light rays.

27. How does the image formation in a concave mirror change as an object moves from infinity towards the mirror?

As an object moves from infinity towards a concave mirror:

28. Why do dentists use concave mirrors?

Dentists use concave mirrors because when held close to the teeth (within the focal length), they produce an enlarged, upright, virtual image. This magnification allows dentists to see small details in the mouth more clearly. Additionally, concave mirrors can focus light onto the area being examined, providing better illumination in the confined space of the mouth.

29. How does the image change in a convex mirror as an object moves closer to it?

As an object moves closer to a convex mirror:

30. What is the difference between longitudinal and lateral magnification in spherical mirrors?

Longitudinal magnification refers to the ratio of the image depth to the object depth along the mirror's axis. Lateral magnification is the ratio of the image height to the object height perpendicular to the mirror's axis. In spherical mirrors, these magnifications are not always equal, especially for objects with significant depth. This can lead to distortion in the image, particularly for objects far from the mirror's axis.

31. How does the radius of curvature of a spherical mirror affect its field of view?

The radius of curvature of a spherical mirror affects its field of view inversely. Mirrors with a smaller radius of curvature (more curved) have a wider field of view, while those with a larger radius (flatter) have a narrower field of view. This is why convex mirrors, which have a small radius of curvature, are often used as security mirrors or car side-view mirrors to provide a wider view of the surroundings.

32. What is the significance of the principal axis in image formation by spherical mirrors?

The principal axis is an imaginary line passing through the center of curvature and the pole (vertex) of the mirror. It's significant because:

33. How does the image formation in a spherical mirror differ from that in a plane mirror?

Key differences in image formation between spherical and plane mirrors include:

34. Why do concave mirrors form real images in some cases and virtual images in others?

Concave mirrors form real images when the object is beyond the focal point because the reflected rays actually converge to a point in front of the mirror. They form virtual images when the object is between the focal point and the mirror because the reflected rays diverge and only appear to come from a point behind the mirror when extended backwards. The transition occurs at the focal point, where parallel rays are reflected parallel to the principal axis.

35. What is the relationship between the angle of incidence and the angle of reflection in spherical mirrors?

In spherical mirrors, as in all mirrors, the angle of incidence is equal to the angle of reflection. However, it's important to note that:

36. How does the position of the center of curvature affect image formation in concave mirrors?

The center of curvature (C) plays a crucial role in image formation for concave mirrors:

37. Why do convex mirrors always form images that are upright and smaller than the object?

Convex mirrors always form upright, smaller images because: