Concave Mirror Image Formation Table: Position, Nature, and Size of Image Explained
The Concave Mirror Image Formation concept is central to mastering JEE Main optics. A concave mirror is a spherical mirror with its reflecting surface curved inward, converging incoming parallel rays to a focal point. Understanding which image forms—real or virtual, magnified or diminished—depends on the object’s position relative to the mirror’s focal length and center of curvature. This page explains image prediction, drawing ray diagrams, and solving related problems, aligned strictly to JEE syllabi.
In optics, key terms include the focal length (f), principal axis, pole (P), center of curvature (C), and principal focus (F). These concepts are repeatedly tested in JEE. Concave mirrors are used in devices like telescopes, shaving mirrors, and headlights. Accurate understanding aids in both theoretical and numerical questions.
Concave Mirror Image Formation: Definition and Working Principle
A concave mirror, also known as a converging mirror, reflects light from its inward curved surface. The rules of reflection of light govern concave mirror image formation. When a parallel beam strikes such a mirror, rays reflect through the principal focus. This property makes concave mirrors essential in focusing applications.
For JEE Main, you should recall that the nature, size, and position of images depend on the location of the object relative to the focal point and the center of curvature. The mirror’s curvature is defined by its radius (R), with focal length f = R/2.
The mirror formula and magnification provide mathematical methods to calculate image position and properties, vital for numericals.
Ray Diagrams for Concave Mirror Image Formation
The process of image formation by concave mirror follows two main laws: the angle of incidence equals the angle of reflection, and the incident ray, reflected ray, and normal lie in the same plane. Mastering specific ray paths helps in constructing accurate diagrams for JEE problems.
- A ray parallel to the principal axis reflects through the focus (F).
- A ray passing through focus reflects parallel to the axis.
- A ray through the center of curvature (C) reflects back on itself.
- A ray aimed at the pole (P) reflects symmetrically to the axis.
By drawing at least two of these rays from a point on the object, their intersection (real or virtual) gives the location of the image. Practice using the sign conventions in mirrors for consistency.
Concave Mirror Image Formation: Object Position vs. Image Nature
Predicting image formation by concave mirror is simplified with a summary table. This chart is ideal for last-minute JEE revision.
| Object Position | Image Position | Nature | Size | Orientation |
|---|---|---|---|---|
| At infinity | At focus (F) | Real | Highly diminished | Inverted |
| Beyond center (C) | Between F and C | Real | Diminished | Inverted |
| At center (C) | At C | Real | Same size | Inverted |
| Between C and F | Beyond C | Real | Magnified | Inverted |
| At focus (F) | At infinity | Real | Highly magnified | Inverted |
| Between F and P | Behind mirror | Virtual | Magnified | Erect |
Key Properties and Rules in Concave Mirror Image Formation
The image formed by a concave mirror is not always real, nor always inverted. If the object is beyond the focal length, a real and inverted image is produced. If the object is between the focus and pole, the image is virtual, erect, and magnified.
Always apply the mirror equation for precise calculations:
- 1/v + 1/u = 1/f, where v is image distance, u is object distance, f is focal length.
- A virtual image forms only when the object is closer to the mirror than the focal point.
- The sign convention is vital for correct answers in JEE.
- Real versus virtual images can be remembered by their formation sides with respect to the mirror.
Numerical Example: Concave Mirror Image Formation Calculation
Let’s solve a common JEE-style question. Suppose an object is placed 20 cm from a concave mirror with focal length 10 cm. Find the image position and magnification.
Using the mirror formula:
1/v + 1/u = 1/f
1/v + 1/(-20) = 1/(-10)
1/v = 1/(-10) + 1/20 = (-2+1)/20 = -1/20
So v = -20 cm (image is real and on the same side as object) and magnified by
m = -v/u = -(-20)/(-20) = -1 (same size, inverted).
Thus, the image is real, inverted, at 20 cm, and same size as object.
Concave vs Convex Mirror: Quick Comparison
| Feature | Concave Mirror | Convex Mirror |
|---|---|---|
| Image possible | Real or virtual | Always virtual |
| Magnification | Enlarged, reduced, or same size | Diminished only |
| Orientation | Inverted or erect | Always erect |
| Uses | Headlights, shaving mirrors | Rear-view mirrors |
- Compare more details with lens and mirror differences.
- For convex image properties see real vs. virtual image.
Practical Uses and Application of Concave Mirror Image Formation
- Used in reflecting telescopes to focus light.
- Essential in shaving and makeup mirrors for magnified upright images.
- Applied in headlights to direct parallel beams.
- Key for solar furnaces where focused heat is needed.
- Critical in microscopic setups for illumination, discussed in microscope and telescope comparison.
Vedantu Physics experts recommend repeated practice of ray diagram construction and concise image property summaries. For advanced practice, see optics practice papers and mock tests.
In JEE Main, questions on concave mirror image formation test both memory and application of concepts. Be attentive to the specific object position, apply the correct rule, and always double-check sign conventions. For further reading, explore mirror formula calculations and related circuit problems to sharpen analytical skills.
FAQs on How Images Form in Concave Mirrors: Rules, Diagrams & Examples
1. What is the image formation of a concave mirror?
Image formation by a concave mirror depends on the object’s position relative to the mirror’s focal point and center of curvature.
- When the object is beyond the center of curvature, the image forms between the focus and the center, is real, inverted, and diminished.
- If the object is at the center of curvature, the image also forms at the center, is real, inverted, and same size.
- Between center and focus, the image is real, inverted, and magnified.
- At focus, the image forms at infinity.
- Between focus and pole, the image is virtual, erect, and enlarged.
Ray diagrams illustrate these cases clearly.
2. Does a concave mirror form erect or inverted images?
A concave mirror forms both erect and inverted images depending on the object's position:
- Erect and virtual image when the object is placed between focus (F) and pole (P)
- Inverted and real images when the object is beyond the focus (F)
3. What are the properties of the image formed by a concave mirror?
The properties of an image formed by a concave mirror depend on where the object is placed:
- The image can be real or virtual
- It can be inverted or erect
- The size may be magnified, diminished, or the same
- The image may appear in front of or behind the mirror
These properties are best summarized in a concave mirror image formation table.
4. When does a concave mirror form a real or a virtual image?
A concave mirror forms a real image when the object is placed beyond the focus (F), and a virtual image when the object is between the focus and the pole.
- Real, inverted images: object beyond F
- Virtual, erect images: object between F and P
Real images are on the same side as the object, while virtual images appear behind the mirror.
5. How do you draw a ray diagram for image formation by a concave mirror?
To draw a ray diagram for concave mirror image formation:
- Draw the principal axis
- Mark the pole (P), focus (F), and center of curvature (C)
- From the top of the object, draw at least two rays:
- Ray parallel to the principal axis reflects through focus
- Ray through center of curvature reflects back on itself
- Ray passing through focus reflects parallel to principal axis
- Intersection gives the image location and nature
6. Can a concave mirror ever produce an image the same size as the object?
Yes, a concave mirror produces an image of the same size as the object when the object is placed at the center of curvature (C).
- The image forms at C
- It is real and inverted
- Its size equals that of the object
This is a key concept for understanding ray diagrams and numericals.
7. Why does image formation differ at infinity and at the focal point in a concave mirror?
Image formation differs because of the path of reflected rays:
- When object is at infinity, rays are parallel; they converge at the focus forming a point image at F, highly diminished and real.
- When object is at F, reflected rays are parallel after reflection; the image is formed at infinity, highly enlarged and real.
8. Is the image always inverted in a concave mirror?
No, the image formed by a concave mirror is not always inverted.
- The image is inverted and real when the object is placed beyond the focal point.
- It is erect and virtual when the object is placed between the focus and the pole.
Understanding object positions is key for predicting image orientation in exams.
9. Where are concave mirrors used in real life?
Concave mirrors are used in:
- Shaving and make-up mirrors (for enlarged virtual images)
- Dental and ENT reflectors (to focus light inside the mouth/throat)
- Headlights and torches (reflecting parallel beams)
- Telescope and microscope objectives (collecting light)
10. How is a concave mirror different from a convex mirror?
The main differences between a concave and convex mirror are:
- Concave mirrors can form real or virtual images; convex always forms virtual, erect, diminished images
- Concave mirrors converge light; convex diverges it
- Uses differ: concave for focusing (headlights, mirrors); convex for wide views (vehicle mirrors)
