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NDA Physics · Light and Optics

Reflection and Mirrors

Light bounces off a surface obeying two laws (angle in = angle out, all in one plane). A plane mirror gives a virtual, erect, laterally-inverted, same-size image; spherical mirrors (concave converging, convex diverging) form images set by where the object sits relative to F and C.

All Light and Optics notesNDA Physics strategy

Why this matters

Eighteen PYQs and the chapter's home for sign-convention numerics. The recurring tests are: the laws of reflection, the plane-mirror image properties (and the half-your-height result), R = 2f, the image-formation table for concave and convex mirrors, and the mirror formula with magnification. Two of the three HARD questions live here, both carried by image-formation reasoning.

Concept 1 of 6

Light rays and the laws of reflection

Intuition

Light travels in straight lines (rays) until it meets a surface. When it bounces off, two simple rules always hold: it turns back by exactly the angle it came in at, and the incoming ray, the reflected ray, and the line perpendicular to the surface (the normal) all lie flat in one plane.

Definition

Light is an electromagnetic wave that travels in straight lines in a uniform medium. On reflection:

  • The angle of incidence equals the angle of reflection — both measured from the normal (the line perpendicular to the surface), not from the surface itself.
  • The incident ray, reflected ray, and normal all lie in one plane.

These laws hold for every mirror, flat or curved.

Worked example

A ray strikes a plane mirror making a 30° angle with the mirror surface. What is the angle of reflection?
  1. Angles in reflection are measured from the NORMAL, not the surface.
  2. If the ray makes 30° with the surface, it makes 90°−30°=60°90° - 30° = 60° with the normal — so the angle of incidence is 60°.
  3. By the law of reflection, the angle of reflection equals the angle of incidence.
Answer:60° (measured from the normal).
Practice this conceptself-check · 3 quick reps

Try it yourself

A ray hits a mirror along the normal (perpendicular to the surface). At what angle does it reflect?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    Angle of incidence is measured from the surface or the normal?
  2. 2.
    If the angle of incidence is 35°, the angle of reflection is…
  3. 3.
    A ray makes 50° with a mirror surface. Angle of incidence?

Measure angles from the normal, not the surface

The single most common reflection error: a ray quoted as making angle θ with the mirror SURFACE has angle of incidence (90° − θ). NDA likes to state the surface angle and watch you forget to convert.
Drill 1 more on light rays and the laws of reflection

Concept 2 of 6

Plane mirror images

Intuition

Stand in front of a flat mirror: your image looks the same size, stands the same way up, appears as far behind the glass as you are in front, and your left hand looks like the image's right hand. The image is virtual — you cannot catch it on a screen.

Definition

A plane mirror image is:

  • Virtual (formed behind the mirror, cannot be projected on a screen),
  • Erect (the same way up),
  • Same size as the object,
  • Laterally inverted (left ↔ right swapped),
  • as far behind the mirror as the object is in front.

A periscope uses two plane mirrors and works purely by reflection. To see your full height you need a mirror only half your height, fixed at the right level — this is independent of how far you stand.

Worked example

A girl 1.6 m tall wants to see her complete image in a fixed plane mirror on the wall. What is the minimum height of mirror she needs?
  1. The minimum mirror height to see a full image is exactly half the person's height — a result of the geometry of equal incidence and reflection angles.
  2. Minimum height =1.6/2=0.8= 1.6 / 2 = 0.8 m.
  3. This does not depend on her distance from the mirror.
Answer:0.8 m.
Practice this conceptself-check · 4 quick reps

Try it yourself

Which way is a plane-mirror image inverted — top-to-bottom or left-to-right?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    Is a plane-mirror image real or virtual?
  2. 2.
    Minimum mirror height to see your full 1.5 m height?
  3. 3.
    A periscope works on which phenomenon?
  4. 4.
    Plane-mirror image size compared to object?

From the bank · past-year question

Example 2Light and OpticsMODERATE
Sita, 1·5 m high, stands before a plane mirror fixed on a wall to view her full image. What should be the minimum height of the plane mirror so that Sita can view her image fully?

[Q55 · Sep · 2023]

Virtual + erect + same-size — and only laterally inverted

Students often say a plane mirror 'inverts' the image and picture it upside down. It is ERECT. The only swap is left ↔ right (lateral inversion). Size is unchanged.

Half your height — distance does not matter

The minimum mirror height is always half the object height, no matter how far back you stand. Distractors tempt you with the full height or a distance-dependent answer.
Drill 4 more on plane mirror images

Concept 3 of 6

Spherical mirrors — pole, focus, centre, and R = 2f

Intuition

A spherical mirror is a slice of a shiny sphere. Its centre point is the pole P; the centre of the original sphere is C (the centre of curvature); halfway between sits the focus F. A concave mirror caves inward and converges light; a convex mirror bulges out and diverges light. The focal length is always half the radius of curvature.

Definition

Key points on a spherical mirror: pole (P) — the centre of the reflecting surface; centre of curvature (C) — centre of the sphere it is cut from; focus (F) — the point where rays parallel to the axis converge (concave) or appear to diverge from (convex); radius of curvature (R) = PC.

  • Relation: R=2fR = 2f, i.e. f=R/2f = R/2.
  • A concave mirror is converging; a convex mirror is diverging.
  • A plane mirror is the limiting case R→∞R \to \infty, so f→∞f \to \infty — which is why the mirror formula reduces to the plane-mirror equation there.

Focal length and radius of curvature

f=R2f = \dfrac{R}{2}
  • ffocal length
  • Rradius of curvature (= PC)

Worked example

A concave mirror has a radius of curvature of 40 cm. What is its focal length?
  1. Use f=R/2f = R/2.
  2. f=40/2=20f = 40 / 2 = 20 cm.
Answer:20 cm.
Practice this conceptself-check · 4 quick reps

Try it yourself

For a spherical mirror, how does the focal length relate to the radius of curvature, and what happens to f for a plane mirror?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    Focal length of a mirror with R = 30 cm?
  2. 2.
    Radius of curvature of a mirror with f = 12 cm?
  3. 3.
    A concave mirror is converging or diverging?
  4. 4.
    For a plane mirror, focal length is…

From the bank · past-year question

Example 3Light and OpticsEASY
The correct relation between the radius of curvature R and focal length f of a spherical mirror is

[Q86 · Apr · 2020]

R = 2f, so f = R/2 — not f = 2R

The focus is HALFWAY between the pole and the centre of curvature, so f is HALF of R. Flipping it to f = 2R is a classic slip.

Concept 4 of 6

Concave mirror — image formation

Intuition

A concave mirror converges light, so where the image forms — and whether it is real or virtual, enlarged or shrunk — depends entirely on where the object sits relative to F and C. Bring the object closer than F and the image flips to virtual, erect and magnified (that is the shaving/make-up mirror). That is why concave mirrors are used in vehicle headlights — a source at F sends out a parallel beam.

Definition

Concave-mirror image as the object moves in:

  • Beyond C: real, inverted, diminished, between F and C.
  • At C: real, inverted, same size, at C.
  • Between C and F: real, inverted, magnified, beyond C.
  • At F: image at infinity (used in headlights/searchlights — source at F gives a parallel beam).
  • Between F and P: virtual, erect, magnified, behind the mirror.

An object exactly at the focus does NOT give an image between F and P — that combination is impossible.

CFPobjectimageObject beyond C: real, inverted, diminished image between F and C

A concave mirror converges light. With the object beyond C the image is real, inverted and smaller, formed between F and C.

Worked example

Where is the image formed when an object is placed exactly at the centre of curvature of a concave mirror, and what is its nature?
  1. At C, the image forms at C itself (the ray through C retraces, and the parallel ray reflects through F, meeting back at C).
  2. It is real and inverted.
  3. It is the same size as the object (magnification 1).
Answer:At C — real, inverted, same size.
Practice this conceptself-check · 4 quick reps

Try it yourself

An object is placed between the focus F and the pole P of a concave mirror. State the three properties of the image.

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    Object beyond C in a concave mirror — image is enlarged or diminished?
  2. 2.
    Object at F of a concave mirror — image forms where?
  3. 3.
    Why is a concave mirror used in a headlight?
  4. 4.
    Object between F and P of a concave mirror — image real or virtual?

From the bank · past-year question

Example 4Light and OpticsMODERATE
In case of a concave mirror, if an object is kept between principal focus F and pole P of the mirror, then which one of the following statements about the image is NOT correct?

[Q150 · Apr · 2020]

Object at F gives the image at infinity, not between F and P

When an object sits between F and P the image IS virtual/erect/magnified — but it is the object at F (not the image) that goes to infinity. 'Image at infinity' is the false statement when the object is between F and P.

Only inside F does a concave mirror give a virtual image

Everywhere from infinity down to F the concave mirror gives a REAL, inverted image. The image only becomes virtual and erect once the object crosses inside the focus.
Drill 4 more on concave mirror — image formation

Concept 5 of 6

Convex mirror — always virtual, erect, diminished

Intuition

A convex mirror bulges toward you and spreads light out, so it can never bring rays to a real focus in front of it. Wherever the object is, the image is virtual, the right way up, and smaller — squeezed into the small space between the pole and the focus behind the mirror. Shrinking the scene is exactly what gives a wide field of view, which is why it is the vehicle rear-view mirror.

Definition

For a convex mirror, for every real object position:

  • the image is virtual,
  • erect,
  • diminished (smaller than the object),
  • located between the pole P and the focus F, behind the mirror.

It can never form a real or inverted image. The wide field of view makes it ideal for rear-view mirrors and at blind corners.

FCPobjectimageAlways virtual, erect, diminished — between P and F, behind the mirror

A convex mirror diverges light, so it always gives a virtual, erect, diminished image — wherever the object is. That wide field of view is why it is used as a vehicle rear-view mirror.

Worked example

An object is moved from far away toward a convex mirror. Describe how the image changes.
  1. A convex mirror always gives a virtual, erect, diminished image between P and F.
  2. As the object approaches, the image stays virtual and erect but grows slightly (still smaller than the object) and moves toward the pole.
  3. It never becomes real or inverted at any position.
Answer:Always virtual, erect and diminished; it grows a little and moves toward P as the object nears.
Practice this conceptself-check · 4 quick reps

Try it yourself

A mirror always forms a virtual, erect, diminished image between its pole and focus, no matter where the object is. What type of mirror is it?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    Nature of a convex-mirror image (three words)?
  2. 2.
    Can a convex mirror form an inverted image?
  3. 3.
    Which mirror is used as a vehicle rear-view mirror?
  4. 4.
    A convex-mirror image lies between which two points?

From the bank · past-year question

Example 5Light and OpticsMODERATE
An object is placed between infinity and the pole (P) of a convex mirror. The position of the image is

[Q126 · Apr · 2025]

A convex mirror NEVER inverts

Because the image is always virtual and erect, a convex mirror can never produce an inverted image. Any option claiming an inverted convex-mirror image is the wrong statement.
Drill 3 more on convex mirror — always virtual, erect, diminished

Concept 6 of 6

Mirror formula and magnification

Intuition

The mirror formula ties object distance, image distance and focal length in one equation; magnification then tells you how big and which way up the image is. The whole game is signs: with the New Cartesian convention, distances measured against the incoming light are negative, so a concave mirror's f is negative and a convex mirror's f is positive.

Definition

Mirror formula: 1v+1u=1f\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}, where distances follow the New Cartesian sign convention (measured from the pole; distances against the incident light are negative). Magnification: m=h′h=−vum = \dfrac{h'}{h} = -\dfrac{v}{u}.

  • m<0m < 0: real, inverted image. m>0m > 0: virtual, erect image.
  • ∣m∣>1|m| > 1: magnified; ∣m∣<1|m| < 1: diminished.

Concave mirror: ff is negative. Convex mirror: ff is positive.

Mirror formula and magnification

1v+1u=1f,m=−vu\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}, \qquad m = -\dfrac{v}{u}
  • uobject distance (from pole)
  • vimage distance (from pole)
  • ffocal length (−ve concave, +ve convex)
  • mmagnification (h'/h)

Worked example

An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find the image distance and magnification.
  1. Sign convention: u=−30u = -30 cm, f=−20f = -20 cm (concave).
  2. 1v=1f−1u=1−20−1−30=−360+260=−160\dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{u} = \dfrac{1}{-20} - \dfrac{1}{-30} = -\dfrac{3}{60} + \dfrac{2}{60} = -\dfrac{1}{60}.
  3. So v=−60v = -60 cm (real image, in front of the mirror).
  4. m=−v/u=−(−60)/(−30)=−2m = -v/u = -(-60)/(-30) = -2: inverted and twice the size.
Answer:v=−60v = -60 cm; m=−2m = -2 (real, inverted, magnified ×2).
Practice this conceptself-check · 4 quick reps

Try it yourself

An object is placed 15 cm in front of a convex mirror of focal length 10 cm. Find the image distance and the magnification.

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

  1. 1.
    Sign of f for a concave mirror?
  2. 2.
    A magnification of −2 means the image is…
  3. 3.
    Does the mirror formula 1/v + 1/u = 1/f apply to lenses too?
  4. 4.
    m = +0.5 means the image is…

From the bank · past-year question

Example 6Light and OpticsMODERATE
Spherical mirror formula relating an object distance 'u', image distance 'v' and focal length of mirror 'f' may be applied to a plane mirror when

[Q136 · Sep · 2021]

Sign convention is the whole game

Almost every wrong numeric answer comes from a sign slip. Concave f is negative, convex f is positive, real distances in front of the mirror are negative. Write the signs down BEFORE substituting.

Magnification sign tells you real vs virtual

Negative m = real and inverted; positive m = virtual and erect. Don't read |m| alone and forget the sign — it carries the orientation.
Drill 1 more on mirror formula and magnification

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Watch out for (9)

Mastery check — 5 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Light and OpticsHARD
Two plane mirrors XY and YZ (XY⊥YZXY \perp YZ) joined at their edge. A light ray falls on one of the mirrors and is reflected back parallel to its original path. The two mirrors are now rotated by an angle θ\theta to their new position X'YZ', and the new reflected ray is at an angle α\alpha from the original reflected ray. Then :

[Q86 · Apr · 2023]

Example 2Light and OpticsEASY
Which one of the following is the natural phenomenon based on which a simple periscope works?

[Q61 · Apr · 2018]

Example 3Light and OpticsEASY
A point object is placed at the centre of curvature of a spherical concave mirror. Which one among the following would be the correct location of image formed ?

[Q89 · Sep · 2024]

Example 4Light and OpticsEASY
An object is placed in front of a convex mirror. Which one of the following statements is correct?

[Q121 · Sep · 2018]

Example 5Light and OpticsEASY
A lens has a power of +2·0 Dioptre. Which one of the following statements about the lens is true?

[Q142 · Apr · 2020]

Drill every past-year question on this subtopic

18 questions from the bank — paginated, with cart and Word-export support.

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