Light always travels in straight lines until it hits a surface and bounces back — that bounce is reflection. When the surface is curved like a spoon, you get a spherical mirror that can shrink, flip or magnify images. NDA loves this chapter because one formula plus a clean sign convention solves almost every question. Let us build it step by step.
Why This Topic Matters for NDA
Optics is among the most scoring areas of NDA General Science. Out of the optics questions asked each year, a big share comes from mirrors — either a direct formula numerical or a concept question on real vs virtual images.
The good news: this chapter has very few formulas. Once you fix the sign convention in your head, the same mirror formula handles concave mirrors, convex mirrors, and even plane mirrors as a special case. Compare this to a chapter like mechanics, where dozens of formulas compete for memory — here, mastering one relation and one convention covers the whole topic.
Mirrors also link neatly to everyday objects examiners love to reference: torches, headlights, shaving mirrors, dentists' mirrors, solar cookers and vehicle rear-view mirrors. Knowing which mirror sits in each device often answers a question outright, with no calculation at all.
NDA mixes theory and numericals here. Roughly half the questions are pure concept (uses of mirrors, nature of image) and need zero calculation. Do not skip the definitions.
What is Reflection of Light
Reflection is the bouncing back of light into the same medium when it strikes a polished or shiny surface. A smooth, mirror-like surface gives a clear image; this is called regular reflection.
A rough surface like paper or a wall scatters light in all directions — this is diffuse (irregular) reflection. That is why you can see a wall from any angle but it does not act as a mirror. Even in diffuse reflection each individual ray still obeys the laws of reflection — the surface only looks scattered because it is uneven at the microscopic level. Reflection is also the reason we see most objects at all: they bounce light into our eyes.
Two important rays/lines are defined at the point where light hits the surface:
- Incident ray — the ray coming towards the surface.
- Reflected ray — the ray bouncing back.
- Normal — an imaginary line drawn perpendicular (at 90°) to the surface at the point of incidence.
The angle between the incident ray and the normal is the angle of incidence (i), and the angle between the reflected ray and the normal is the angle of reflection (r).
The Two Laws of Reflection
All of reflection rests on just two rules, and they apply to every mirror — plane or curved.
Law 1: The angle of incidence equals the angle of reflection → i = r.
Law 2: The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.
A neat consequence: if a ray hits a mirror head-on (along the normal, i = 0°), it bounces straight back along the same path. Also, if you rotate a mirror by an angle θ while the incident ray stays fixed, the reflected ray rotates by 2θ — a favourite NDA twist. This doubling effect is the working principle of devices like the mirror galvanometer, where a small mirror rotation produces a large, easily measured deflection of a light spot.
Both laws hold for curved mirrors too. The trick is simply that the normal at any point on a spherical mirror passes through the centre of curvature, so the same i = r rule still applies at each point of incidence.
Angles in reflection are always measured from the normal, never from the mirror surface. If a question gives the angle from the surface, subtract it from 90° first.
Images in a Plane Mirror
A flat (plane) mirror is the simplest case. Its image has fixed, exam-ready properties:
- The image is virtual (cannot be caught on a screen) and erect (upright).
- It is the same size as the object — magnification = 1.
- The image distance behind the mirror equals the object distance in front.
- The image is laterally inverted — left and right appear swapped (which is why AMBULANCE is written reversed on vehicles).
To see your full height in a plane mirror, the mirror needs to be only half your height, fixed at the correct level. This is independent of how far you stand.
If two plane mirrors are placed at an angle θ, the number of images formed is (360°/θ) − 1. For example, at 60° you get 360/60 − 1 = 5 images. At 90° you get 3 images, and when the two mirrors are parallel (θ = 0°) the formula gives infinite images — which is why a barber's two facing mirrors seem to repeat your reflection endlessly.
Lateral inversion is purely a left-right swap, not a top-bottom one; your head still stays at the top in the mirror. This is a frequent NDA trap, so remember: a plane mirror flips left and right, never up and down.
Spherical Mirrors: Concave and Convex
A spherical mirror is a part of a hollow sphere with one side silvered. There are two types:
- Concave mirror — the reflecting (silvered) surface curves inward, like the inside of a spoon. It is converging; it brings parallel rays to a point.
- Convex mirror — the reflecting surface bulges outward, like the back of a spoon. It is diverging; it spreads parallel rays apart.
Key terms you must know
- Pole (P): the centre of the mirror surface.
- Centre of curvature (C): the centre of the sphere the mirror is part of.
- Radius of curvature (R): distance from pole to C.
- Principal focus (F): the point where rays parallel to the principal axis meet (concave) or appear to come from (convex) after reflection.
- Focal length (f): distance from pole to focus.
For a spherical mirror, the focal length is half the radius of curvature: f = R / 2.
The Sign Convention (New Cartesian)
This single rule decides whether your answer is right or wrong, so memorise it.
Take the pole as origin and the incident light travelling left to right.
- Distances measured in the direction of incident light are positive; against it are negative.
- So objects in front of the mirror have negative distance (u is −ve).
- Heights above the axis are positive; below are negative.
With this convention, focal length is negative for a concave mirror and positive for a convex mirror. Getting this sign right is half the battle in numericals.
Students plug u = +30 cm instead of u = −30 cm. The object is always in front of the mirror, so u is negative in almost every NDA problem. Forgetting the minus sign flips your whole answer.
The Mirror Formula and Magnification
One equation links the object distance (u), image distance (v) and focal length (f):
Mirror formula: 1/v + 1/u = 1/f
Magnification: m = h′/h = −v/u
Here h is object height and h′ is image height. The sign of m tells you everything about the image:
- m negative → image is real and inverted.
- m positive → image is virtual and erect.
- |m| > 1 → enlarged; |m| < 1 → diminished; |m| = 1 → same size.
If v comes out negative, the image is in front of the mirror → real. If v is positive, the image is behind the mirror → virtual. This lets you state the nature without drawing a ray diagram.
Images Formed by Concave and Convex Mirrors
For a concave mirror, the image changes dramatically with object position:
- Object at infinity → image at F, highly diminished, real, inverted.
- Object beyond C → image between F and C, diminished, real, inverted.
- Object at C → image at C, same size, real, inverted.
- Object between C and F → image beyond C, enlarged, real, inverted.
- Object at F → image at infinity, highly enlarged.
- Object between F and P → image behind mirror, enlarged, virtual, erect (this is the shaving-mirror case).
A convex mirror is simpler. For any object position, the image is always virtual, erect and diminished, located between P and F behind the mirror. That wide, small image is why convex mirrors are used as rear-view and security mirrors — they give a large field of view.
A quick way to remember the concave table: as the object moves from infinity towards the mirror, the image moves outward from the focus, growing larger and crossing from diminished to enlarged exactly at the centre of curvature, where object and image are the same size. The moment the object passes the focus and comes nearer than F, the image jumps behind the mirror and turns virtual and erect. Picture a spoon: hold it far and your face is tiny and upside down; bring it close and your face becomes large and upright.
Concave mirror → used in torches, headlights, shaving mirrors, dentist mirrors, solar cookers. Convex mirror → vehicle rear-view mirrors and shop security mirrors.
Worked Example: Find the Image
An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find the image distance, magnification and the nature of the image.
So v = −60 cm (image is 60 cm in front of the mirror). Since v is negative, the image is real. m = −2 means the image is inverted and twice the object's size (enlarged).
Common Mistakes to Avoid
1. Wrong signs: Concave f is negative, convex f is positive. Object distance u is negative. Mixing these is the number-one error.
2. Confusing R and f: The formula is f = R/2. If a question gives R = 40 cm, then f = 20 cm — do not plug R into the mirror formula directly.
3. Wrong mirror for the use: A convex mirror can never form a real or enlarged image. A "magnified virtual erect" image of a near object comes from a concave mirror.
Always read whether the question asks for nature, position, or size — many marks are lost by answering the wrong part.
Previous-Year Style Question
Q. The image formed by a convex mirror of a real object is always:
Answer: Virtual, erect and diminished. A convex mirror diverges reflected rays, so for every real object position the image lies behind the mirror, between the pole and focus, smaller than the object. This wide field of view is exactly why convex mirrors are used as vehicle rear-view mirrors.
Q. A concave mirror has focal length 15 cm. Where should an object be placed to get a magnified, virtual, erect image?
Answer: Between the focus and the pole (object distance less than 15 cm). Only in this region does a concave mirror form an enlarged, virtual, erect image — the principle of a shaving mirror.
Quick Revision
- Laws of reflection: i = r; incident ray, reflected ray and normal lie in one plane.
- Plane mirror image: virtual, erect, same size, laterally inverted.
- Spherical mirror: f = R/2; concave converges, convex diverges.
- Mirror formula: 1/v + 1/u = 1/f; magnification m = −v/u.
- Sign convention: object distance u is negative; concave f negative, convex f positive.
- Convex mirror image is always virtual, erect, diminished → rear-view mirrors.
- Concave mirror gives enlarged virtual image only when object is between F and P.
Practise five numericals with both mirror types daily for a week. Once signs become automatic, every mirror question in NDA becomes a 20-second solve.
Frequently asked questions
What is the difference between a concave and a convex mirror?
A concave mirror curves inward and converges light, so it can form real, inverted or enlarged virtual images depending on object position. A convex mirror bulges outward, diverges light, and always forms a small, virtual, erect image.
Why is the object distance taken as negative in mirror problems?
By the New Cartesian sign convention, distances measured against the direction of incident light are negative. Since the object is always in front of the mirror (opposite to where light travels after reflection), its distance u is negative in almost all NDA numericals.
What does a negative image distance mean?
A negative v means the image forms in front of the mirror, where it can be caught on a screen, so the image is real. A positive v means the image is behind the mirror and is virtual.
Which mirror is used in vehicle rear-view mirrors and why?
A convex mirror is used because it always gives an erect, diminished image and a very wide field of view, letting the driver see more traffic behind in a small mirror.
How is focal length related to radius of curvature?
The focal length is half the radius of curvature: f = R/2. So if a spherical mirror has R = 30 cm, its focal length is 15 cm.
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