🌈 Reflection of Light at Curved Surfaces
Class 10 Physical Science | Interactive Colourful Mind Maps
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🔵 SPHERICAL MIRRORS: BASIC TERMS
- A mirror whose reflecting surface forms part of a sphere.
- Concave mirror: reflecting surface curves inward.
- Convex mirror: reflecting surface bulges outward.
The geometrical centre of the reflecting surface of a spherical mirror.
The centre of the sphere of which the mirror is a part.
The distance between the pole and the centre of curvature: R = PC.
The point where rays parallel to the principal axis converge, or appear to diverge from, after reflection.
The distance between the pole and principal focus: f = PF. For a spherical mirror of small aperture, the magnitude of the focal length is approximately half the radius of curvature.
The straight line passing through the pole and centre of curvature.
🟢 RULES FOR RAY DIAGRAMS
A ray parallel to the principal axis is reflected through the principal focus in a concave mirror. In a convex mirror, it appears to diverge from the principal focus behind the mirror.
A ray passing through the principal focus of a concave mirror is reflected parallel to the principal axis. For a convex mirror, a ray directed towards its focus is reflected parallel to the axis.
A ray directed through the centre of curvature strikes the mirror normally and retraces its path after reflection.
At the pole, the principal axis acts as the normal. The angle of incidence equals the angle of reflection.
🔴 CONCAVE MIRROR: IMAGE FORMATION
Image at F; real, inverted and highly diminished (point-sized in the ideal case).
Image between C and F; real, inverted and diminished.
Image at C; real, inverted and the same size as the object.
Image beyond C; real, inverted and enlarged.
Reflected rays emerge parallel to one another; the image is formed at infinity in the ideal ray model.
Image behind the mirror; virtual, erect and enlarged.
🟣 CONVEX MIRROR
For a real object placed in front of a convex mirror, the image forms behind the mirror between P and F.
The image is always virtual, erect and diminished for a real object at a finite distance.
Convex mirrors show a larger area behind or around the observer than a comparable plane mirror.
The focus and centre of curvature of a convex mirror are virtual and lie behind the mirror.
🟠 MIRROR FORMULA & MAGNIFICATION
1/f = 1/v + 1/u
f = focal length, v = image distance, u = object distance.
Use the Cartesian sign convention consistently.
m = hᵢ/hₒ = −v/u
hᵢ is image height and hₒ is object height.
Positive magnification indicates an erect image; negative magnification indicates an inverted image under the usual mirror sign convention.
|f| ≈ R/2
For a spherical mirror with small aperture, the magnitude of focal length is approximately half the radius of curvature. With Cartesian signs, the signed relation is f = R/2.
- Measure distances from the pole.
- Distances in the direction of incident light are positive; distances opposite to it are negative.
- Heights above the principal axis are positive; below it are negative.
🟡 APPLICATIONS OF SPHERICAL MIRRORS
A concave mirror can produce an enlarged, erect, virtual image when the face is placed between its pole and focus.
Convex mirrors provide a wider field of view and produce erect, diminished images. Objects may appear farther away than they really are.
A light source placed near the focus of a concave reflector can produce a beam of approximately parallel rays.
A concave mirror can give an enlarged, erect image when the tooth is within its focal length.
Concave mirrors collect and focus light from distant objects.
Convex mirrors are used in shops, corridors and road bends to view a wider area.
⭐ QUICK REVISION
Converging mirror for parallel incident rays. It can form real or virtual images depending on the object's position.
Diverging mirror for parallel incident rays. For a real object, it forms a virtual, erect and diminished image.
Formed where reflected rays actually meet. It can be projected onto a screen and is inverted for the usual concave-mirror real-image cases.
Formed where reflected rays appear to meet. It cannot be projected onto a screen.
1/f = 1/v + 1/u
m = −v/u = hᵢ/hₒ
f = R/2
The last relation uses signed distances under the Cartesian sign convention and is approximate for spherical mirrors of small aperture.
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📝 Notes for Students
1. Types of spherical mirrors
- Concave mirror: reflecting surface curves inward; parallel rays are brought together at the focus after reflection.
- Convex mirror: reflecting surface bulges outward; parallel rays spread out after reflection and appear to come from the focus.
2. Important differences
| Feature | Concave Mirror | Convex Mirror |
|---|---|---|
| Action on parallel rays | Converging | Diverging |
| Focus | Real | Virtual |
| Image for a real object | Real or virtual | Always virtual |
| Common use | Shaving mirror, reflector | Rear-view mirror |
3. Image formation by a concave mirror
- Object beyond C → image between C and F; real, inverted and diminished.
- Object at C → image at C; real, inverted and same size.
- Object between C and F → image beyond C; real, inverted and enlarged.
- Object at F → image at infinity in the ideal ray model.
- Object between F and P → image behind the mirror; virtual, erect and enlarged.
Exam tip: Always draw the principal axis, mark P, F and C, and use at least two standard rays to locate the image. Remember to state the image's position, nature and size.
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