Light reflection from mirrors is a guaranteed scoring area in the CDS / OTA Science paper. Almost every year one or two questions test mirror types, where the image forms, or a quick mirror-formula calculation. This Cavalier note builds the topic from first principles, gives you the ray-tracing rules, and trains you on real exam-style numericals so you never lose these easy marks.
Why Mirrors Matter in the CDS Exam
Optics is one of the most predictable chunks of the CDS General Science paper, and mirrors form its easiest gateway. The Union Public Service Commission likes this topic because a single line of theory or one quick formula can decide a mark — with no diagram even needed.
Questions usually fall into three buckets: (1) conceptual — which mirror is used in a vehicle headlight or a rear-view application; (2) image-nature — real or virtual, erect or inverted, magnified or diminished; and (3) numerical — find v, f or magnification using the mirror formula.
The good news is that the entire topic is built on a tiny core of ideas: two laws of reflection, a handful of ray rules, one formula and a sign convention. Once those are firm, even an unfamiliar-looking question becomes a routine application. Compare this with biology or current affairs, where the syllabus is vast and unpredictable — mirrors are bounded, logical and repetitive across years, which is exactly what you want in a timed objective paper with negative marking.
If you master only the ray rules and the mirror formula, you can attempt nearly every mirror question that has ever appeared. The investment-to-marks ratio here is excellent. Spend twenty focused minutes on this page and you have effectively banked a mark.
Reflection of Light and Its Laws
A mirror works by reflection — light bouncing back into the same medium after striking a smooth, polished surface. The behaviour follows two simple laws that hold for every reflecting surface, flat or curved.
Law 1: The angle of incidence (i) equals the angle of reflection (r), i.e. ∠i = ∠r.
Law 2: The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.
Both angles are measured from the normal (the line perpendicular to the surface), never from the surface itself. This is a favourite trap: a question may give the angle between the incident ray and the mirror, and you must first subtract from 90° before applying the law. A polished surface gives regular reflection and a clear image; a rough surface gives diffused (scattered) reflection and no clear image, although the two laws are still obeyed by each tiny portion of the surface.
Two consequences worth remembering for the exam: a ray striking a mirror at 90° (straight on, along the normal) retraces its own path because i = r = 0°; and if the mirror is rotated by an angle θ while the incident ray is fixed, the reflected ray turns by 2θ. This doubling principle appears in instrument questions and is easy marks once you recall it.
Plane Mirror and Its Image
A plane mirror is a flat reflecting surface. It is the first case you should lock down because its image properties are fixed and frequently tested.
- The image is virtual (cannot be caught on a screen) and erect.
- The image is the same size as the object (magnification = 1).
- Image distance behind the mirror equals object distance in front of it.
- The image shows lateral inversion — left appears as right (why AMBULANCE is written reversed on vehicles).
If you move towards a plane mirror at speed v, your image approaches you at 2v, because both you and the image move. This relative-speed fact is a popular trap.
Two more plane-mirror facts examiners love. First, to see your full image in a plane mirror you need a mirror only half your height, fixed at the right level — the size does not depend on how far you stand. Second, the number of images formed by two plane mirrors inclined at an angle θ is given by n = (360° ÷ θ) − 1. For two mirrors at 60° you get 5 images; at 90° you get 3. A kaleidoscope uses exactly this multiple-reflection idea.
Spherical Mirrors: Concave and Convex
A spherical mirror is part of a hollow sphere. If the inner (caved-in) surface reflects, it is concave (converging); if the outer bulging surface reflects, it is convex (diverging).
Key terms
- Pole (P): the centre of the mirror surface.
- Centre of curvature (C): centre of the sphere of which the mirror is a part.
- Radius of curvature (R): distance PC.
- Principal focus (F): point where rays parallel to the principal axis meet (concave) or appear to diverge from (convex).
- Focal length (f): distance PF.
For a spherical mirror, focal length is half the radius of curvature: f = R ÷ 2. A concave mirror converges light; a convex mirror always diverges it.
The principal axis is the straight line passing through the pole and the centre of curvature. Both F and C lie in front of a concave mirror (on the reflecting side), which is why their distances come out negative in the sign convention. For a convex mirror, F and C lie behind the mirror because the reflected rays only appear to come from there. An easy memory hook: think of a concave mirror as a “cave” that collects and concentrates light, while a convex mirror “sheds” light outwards.
Ray Rules for Drawing Images
To locate an image you need just any two of these standard rays. Their intersection (real or apparent) is where the image forms.
- A ray parallel to the principal axis, after reflection, passes through F (concave) or appears to come from F (convex).
- A ray through F becomes parallel to the principal axis after reflection.
- A ray through the centre of curvature C retraces its path (hits the mirror normally).
- A ray striking the pole P reflects symmetrically about the principal axis (angle i = angle r).
You rarely have to draw in CDS, but knowing rules 1 and 2 lets you instantly reason out where the image sits for any object position — faster than memorising a table blindly.
Concave Mirror: Image for Each Object Position
The concave mirror is the star of the topic because its image changes dramatically with object distance. Learn this sequence cold.
- Object at infinity: image at F, real, inverted, highly diminished (a point).
- Beyond C: image between F and C, real, inverted, diminished.
- At C: image at C, real, inverted, same size.
- Between C and F: image beyond C, real, inverted, magnified.
- At F: image at infinity, real, inverted, highly magnified.
- Between F and P: image behind the mirror, virtual, erect, magnified — the shaving-mirror case.
A concave mirror gives a virtual erect image only when the object lies between the pole and the focus. In every other position the image is real and inverted.
Convex Mirror and Practical Uses
A convex mirror is wonderfully consistent: no matter where the object is, the image is always virtual, erect and diminished, formed between the pole and the focus behind the mirror.
Because it covers a wider field of view, the convex mirror is used as a rear-view (wing) mirror in vehicles and for security mirrors at blind corners. The concave mirror, being converging, is used in vehicle headlights, torches, shaving mirrors, dentists' mirrors and solar concentrators / telescopes.
Students often write that a convex mirror gives a wider view because it magnifies. It is the opposite — it diminishes the image, packing a larger scene into a small field. That is exactly why it widens coverage.
Quick contrast to memorise
- Concave — converging; can give real or virtual images; used where you need to focus or magnify light.
- Convex — diverging; gives only virtual, erect, diminished images; used where you need a wide field of view.
- A plane mirror is the limiting case of a spherical mirror whose radius is infinite, so its focal length is infinite and magnification is exactly one.
If an option says a convex mirror forms a real or magnified image for a real object, eliminate it instantly — that can never happen. This single elimination rule solves many MCQs without any calculation.
Sign Convention, Mirror Formula and Magnification
For numericals, adopt the New Cartesian Sign Convention: the pole is the origin, the principal axis is the x-axis, and distances measured against the incident light (and below the axis) are negative.
Mirror formula: 1/v + 1/u = 1/f, where u = object distance, v = image distance, f = focal length.
Magnification: m = −v ÷ u = h′ ÷ h (image height ÷ object height).
Concave mirror: f is negative. Convex mirror: f is positive. Object distance u is always negative (object is in front).
Reading the answer: if v comes out negative the image is real (in front of the mirror); if positive it is virtual (behind). If m is negative the image is inverted; if positive, erect. A magnitude of m greater than 1 means magnified, less than 1 means diminished.
Worked Example: Using the Mirror Formula
An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find the position, nature and magnification of the image.
v = −60 cm: image is 60 cm in front of the mirror, so it is real and inverted. Since m = −2, the image is magnified twice. This matches our rule — the object (30 cm) lies between C (40 cm) and F (20 cm), so the image is real, inverted and enlarged.
Common Mistakes to Avoid
Forgetting the sign convention. Object distance u is always negative. Plugging u = +30 will flip your whole answer.
Confusing R and f. Always remember f = R/2. If R = 40 cm, then f = 20 cm, not 40.
Other frequent slips: assuming a convex mirror can form a real image (it never does for a real object); thinking a plane mirror magnifies (m = 1 always); and writing that the image in a plane mirror is reversed top-to-bottom — it is reversed only left-to-right (lateral inversion).
Previous-Year Style Question
Q. The mirror used as a rear-view mirror in vehicles and the mirror used in a vehicle's headlight are, respectively:
Answer: Convex and concave. A convex mirror is used as the rear-view mirror because it always gives an erect, diminished image with a wide field of view. A concave (converging) mirror is used in headlights so that a bulb at its focus produces a strong parallel beam of light.
Q. An object placed between the pole and the focus of a concave mirror forms an image that is:
Answer: Virtual, erect and magnified (formed behind the mirror). This is the principle of the shaving / make-up mirror.
Quick Revision
- Laws of reflection: ∠i = ∠r; incident ray, reflected ray and normal are coplanar.
- Plane mirror: virtual, erect, same size, laterally inverted; m = 1.
- Concave (converging): image varies with position; only virtual-erect when object is between P and F.
- Convex (diverging): always virtual, erect, diminished; wide view; used as rear-view mirror.
- f = R ÷ 2. Mirror formula 1/v + 1/u = 1/f; magnification m = −v/u.
- Sign convention: u negative; concave f negative, convex f positive.
Frequently asked questions
What is the difference between a real and a virtual image?
A real image is formed when reflected rays actually meet; it can be caught on a screen and is inverted. A virtual image is formed where rays only appear to meet behind the mirror; it cannot be projected on a screen and is erect.
Why is a convex mirror preferred as a rear-view mirror?
A convex mirror always forms an erect, diminished image and covers a wider field of view, letting the driver see a larger area of traffic behind the vehicle in a small mirror.
What is the relation between focal length and radius of curvature?
For a spherical mirror, the focal length is half the radius of curvature, f = R/2. So a mirror of radius 30 cm has a focal length of 15 cm.
When does a concave mirror form a virtual image?
A concave mirror forms a virtual, erect and magnified image only when the object is placed between its pole and its principal focus, as in a shaving mirror.
What does the sign of magnification tell us?
A negative magnification means the image is real and inverted, while a positive magnification means it is virtual and erect. A magnitude above 1 indicates enlargement and below 1 indicates a diminished image.
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