🪞 Reflection of Light is a scoring chapter in AMU — 2–3 questions every year. Mirror formula numericals, sign convention, image characteristics in plane/concave/convex mirrors, and ray diagrams are the core focus. This mega guide covers everything with 18+ PYQs, 18+ solved numericals, and step-by-step solutions. Let's master it! 🔥
1) Nature of Light
Light is a form of energy that enables us to see. It is an electromagnetic wave that does not require a medium to travel.
Key properties of light:
Speed of light in vacuum (c) = 3 × 10⁸ m/s
Light travels in straight lines → rectilinear propagation
Light behaves as both wave (EM wave) and particle (photon) — dual nature
Wavelength range of visible light: 400 nm (violet) to 700 nm (red)
Frequency range: ~4.3 × 10¹⁴ Hz to ~7.5 × 10¹⁴ Hz
🟡 Senior's Tip:
The speed of light is the maximum speed in the universe. It takes about 8 minutes and 20 seconds for sunlight to reach Earth (distance = 1.5 × 10¹¹ m). This is why we see the Sun as it was 8 minutes ago! When you see a star, you're looking into the past.
The speed of light is the maximum speed in the universe. It takes about 8 minutes and 20 seconds for sunlight to reach Earth (distance = 1.5 × 10¹¹ m). This is why we see the Sun as it was 8 minutes ago! When you see a star, you're looking into the past.
🔥 AMU PYQ: The speed of light in vacuum is:
(A) 3 × 10⁶ m/s (B) 3 × 10⁸ m/s (C) 3 × 10¹⁰ m/s (D) 3 × 10⁵ m/s
Ans: B (3 × 10⁸ m/s — must memorize!)
(A) 3 × 10⁶ m/s (B) 3 × 10⁸ m/s (C) 3 × 10¹⁰ m/s (D) 3 × 10⁵ m/s
Ans: B (3 × 10⁸ m/s — must memorize!)
2) Laws of Reflection — Complete Explanation
Reflection is the phenomenon of light bouncing back into the same medium after striking a surface. There are two laws that govern all reflection — whether from a plane mirror, a concave mirror, or a rough surface.
Two laws of reflection:
Law 1: Angle of incidence (i) = Angle of reflection (r)
Law 2: The incident ray, the reflected ray, and the normal all lie in the SAME plane
🟡 Senior's Tip — Understanding Law 2:
The incident ray and the normal define a plane. The reflected ray must lie in that same plane. It cannot pop out of that plane. This is why 3D geometry matters in reflection — you can't reflect light "out of the page" if the incident ray and normal are in the page.
The incident ray and the normal define a plane. The reflected ray must lie in that same plane. It cannot pop out of that plane. This is why 3D geometry matters in reflection — you can't reflect light "out of the page" if the incident ray and normal are in the page.
Verification of Laws of Reflection using a Plane Mirror:
- A white sheet of paper is placed on a drawing board with a plane mirror standing vertically on it
- Pins are placed to mark the incident ray, and the reflected ray is traced by viewing from the other side
- Angles are measured using a protractor — i and r are found to be equal (verifying Law 1)
- The incident ray, reflected ray, and normal are all in the plane of the paper (verifying Law 2)
🔥 AMU PYQ: According to laws of reflection, angle of incidence is equal to:
(A) Angle of refraction (B) Angle of reflection (C) 90° − angle of incidence (D) Critical angle
Ans: B (i = r)
(A) Angle of refraction (B) Angle of reflection (C) 90° − angle of incidence (D) Critical angle
Ans: B (i = r)
3) Regular vs Diffused Reflection — Comparison
| Property | Regular (Specular) Reflection | Diffused (Irregular) Reflection |
|---|---|---|
| Surface | Smooth, polished (plane mirror, still water, polished metal) | Rough, uneven (paper, wall, cloth, wood, unpolished surface) |
| Parallel rays after reflection | Remain parallel → clear image formed | Scatter in different directions → no image |
| Image | Clear, sharp image is formed | No image — object becomes visible |
| Laws obeyed? | Yes (i = r for each ray) | Yes (each ray individually obeys i = r, but normals point in different directions) |
| Example | Looking in a mirror, seeing reflection in water | Seeing a book, seeing a wall, visibility of non-luminous objects |
| Application | Periscope, kaleidoscope, telescopes | We see objects around us because of diffused reflection |
🟡 Senior's Insight — Why can we see a table?
A table is NOT a light source. We see it because light from the Sun/bulb falls on it and undergoes diffused reflection — the scattered light enters our eyes. If the table were a perfect mirror, we would only see the reflection of the light source, not the table itself!
A table is NOT a light source. We see it because light from the Sun/bulb falls on it and undergoes diffused reflection — the scattered light enters our eyes. If the table were a perfect mirror, we would only see the reflection of the light source, not the table itself!
4) Image Formation by a Plane Mirror — Detailed
Characteristics of image in a plane mirror:
① Virtual (cannot be obtained on a screen)
② Erect (same orientation as object)
③ Same size as object (m = +1)
④ Laterally inverted (left ↔ right reversed)
⑤ Image distance = Object distance (v = −u)
⑥ Image is as far behind the mirror as the object is in front
Field of View of a Plane Mirror:
The field of view is the region visible to an observer looking into a plane mirror. It depends on the size of the mirror and the position of the observer. A smaller mirror gives a narrower field of view, which is why rear-view mirrors in vehicles are convex (to give a wider field).
Multiple Images — Mirrors at an Angle:
When two plane mirrors are placed at an angle θ, the number of images formed is:
n = 360°/θ − 1 (if 360/θ is even)
n = 360°/θ (if 360/θ is odd and object is not on bisector)
Examples:
θ = 90° → n = 360/90 − 1 = 4 − 1 = 3 images
θ = 60° → n = 360/60 − 1 = 6 − 1 = 5 images
θ = 0° (parallel) → infinite images (barber shop effect)
Uses of Plane Mirrors:
- Periscope: Two plane mirrors at 45° — used in submarines to see above water surface
- Kaleidoscope: Multiple plane mirrors at angles to create beautiful patterns (toy)
- Dressing table mirror: To see our own reflection
- Optical instruments: Used in microscopes, telescopes, periscopes, and rangefinders
- Solar cookers: Plane mirrors are used to reflect and concentrate sunlight
🔥 AMU PYQ: The image formed by a plane mirror is:
(A) Real and inverted (B) Virtual and erect (C) Real and erect (D) Virtual and inverted
Ans: B (virtual, erect, same size, laterally inverted)
(A) Real and inverted (B) Virtual and erect (C) Real and erect (D) Virtual and inverted
Ans: B (virtual, erect, same size, laterally inverted)
🔥 AMU PYQ: Number of images formed when two mirrors are at 60°:
(A) 3 (B) 5 (C) 6 (D) 4
Ans: B (n = 360/60 − 1 = 5, since 360/60 = 6 which is even)
(A) 3 (B) 5 (C) 6 (D) 4
Ans: B (n = 360/60 − 1 = 5, since 360/60 = 6 which is even)
5) Spherical Mirrors — Terminology & Types
Spherical mirrors are mirrors whose reflecting surfaces are part of a sphere. There are two types: concave (curved inward) and convex (curved outward).
Key Terms — MUST Memorize:
| Term | Symbol | Definition |
|---|---|---|
| Pole | P | Centre point of the mirror surface |
| Centre of Curvature | C | Centre of the sphere from which the mirror is cut |
| Radius of Curvature | R | Distance from P to C (R = 2f) |
| Principal Focus | F | Point where parallel rays converge (concave) or appear to diverge (convex) |
| Focal Length | f | Distance from P to F (f = R/2) |
| Principal Axis | — | Line joining P, F, and C |
| Aperture | — | Diameter of the mirror (width of reflecting surface) |
Fundamental relationship:
f = R / 2
R = 2f
| Property | Concave Mirror (Converging) | Convex Mirror (Diverging) |
|---|---|---|
| Shape | Curved inward (like a cave — "concave = cave") | Curved outward (bulging out) |
| Focus type | Real (in front of mirror) | Virtual (behind mirror) |
| Focal length (sign) | Negative (f < 0) | Positive (f > 0) |
| Image nature | Real OR virtual (depends on object position) | Always virtual, erect, diminished |
| Uses | Shaving mirror, dentist mirror, torch/headlight, solar cooker, telescope | Rear-view mirror, vigilance mirror, street light reflectors |
6) Ray Diagrams — Rules for Spherical Mirrors ⭐
To locate the image formed by a spherical mirror, we use ray diagrams. Any two of the following rays are sufficient:
Rule 1 — Ray parallel to principal axis:
After reflection, passes through F (in concave) OR appears to come from F (in convex)
Rule 2 — Ray passing through F:
After reflection, becomes parallel to principal axis
Rule 3 — Ray passing through C:
After reflection, retraces its path (strikes normally, i = 0, r = 0)
Rule 4 — Ray striking at the pole P:
Reflects with same angle on the other side of principal axis (i = r)
🟡 Senior's Tip — Drawing ray diagrams:
• Always draw the mirror vertically with a slight curve
• Mark P, F, and C clearly on the principal axis
• Use an arrow for the object (point up or down)
• Use a different colour/style for reflected rays
• Extend reflected rays behind the mirror as dashed lines for virtual images
• The point where reflected rays actually meet (or appear to meet) is the image location
• Always draw the mirror vertically with a slight curve
• Mark P, F, and C clearly on the principal axis
• Use an arrow for the object (point up or down)
• Use a different colour/style for reflected rays
• Extend reflected rays behind the mirror as dashed lines for virtual images
• The point where reflected rays actually meet (or appear to meet) is the image location
7) Image Formation by Concave Mirror — All 6 Cases ⭐
| Case | Object Position | Image Position | Nature | Size |
|---|---|---|---|---|
| 1 | At infinity | At F | Real, inverted | Highly diminished (point-sized) |
| 2 | Beyond C (> 2f) | Between C and F (f < v < 2f) | Real, inverted | Diminished (m < 1) |
| 3 | At C (2f) | At C (v = 2f) | Real, inverted | Same size (m = 1) |
| 4 | Between C and F (f < u < 2f) | Beyond C (v > 2f) | Real, inverted | Enlarged (m > 1) |
| 5 | At F (u = f) | At infinity | — | Highly enlarged (parallel rays) |
| 6 | Between P and F (u < f) | Behind mirror (v > 0, virtual) | Virtual, erect | Enlarged (m > 1) |
🟡 Senior's Memory Trick — "CIR VED" for Concave:
• Object at C → image at C (same size)
• Object at Infinity → image at F (point)
• Object between P and F → image Virtual and Enlarged behind mirror
• Object beyond C → image Diminished between C and F
The KEY case for AMU: Object between P and F → Virtual, erect, enlarged image (shaving mirror/dentist mirror application!)
• Object at C → image at C (same size)
• Object at Infinity → image at F (point)
• Object between P and F → image Virtual and Enlarged behind mirror
• Object beyond C → image Diminished between C and F
The KEY case for AMU: Object between P and F → Virtual, erect, enlarged image (shaving mirror/dentist mirror application!)
🔥 AMU PYQ: To get an enlarged and erect image from a concave mirror, object must be placed:
(A) At C (B) Beyond C (C) Between P and F (D) At F
Ans: C (only case that gives virtual, erect, enlarged image)
(A) At C (B) Beyond C (C) Between P and F (D) At F
Ans: C (only case that gives virtual, erect, enlarged image)
8) Image Formation by Convex Mirror — 2 Cases
| Case | Object Position | Image Position | Nature | Size |
|---|---|---|---|---|
| 1 | At infinity | At F (behind mirror) | Virtual, erect | Highly diminished |
| 2 | Anywhere in front | Between P and F (behind mirror) | Virtual, erect | Diminished (m < 1) |
🟡 Senior's Tip — Convex Mirror is ALWAYS the same:
No matter where you place the object, a convex mirror ALWAYS gives:
✅ Virtual ✅ Erect ✅ Diminished (smaller) image
This is why it's perfect for rear-view mirrors — you always see a smaller, upright image of all the traffic behind you with a wide field of view.
No matter where you place the object, a convex mirror ALWAYS gives:
✅ Virtual ✅ Erect ✅ Diminished (smaller) image
This is why it's perfect for rear-view mirrors — you always see a smaller, upright image of all the traffic behind you with a wide field of view.
🔥 AMU PYQ: The image formed by a convex mirror is always:
(A) Real and inverted (B) Virtual and erect (C) Real and erect (D) Virtual and inverted
Ans: B (always virtual, erect, and diminished for any object position)
(A) Real and inverted (B) Virtual and erect (C) Real and erect (D) Virtual and inverted
Ans: B (always virtual, erect, and diminished for any object position)
9) Mirror Formula & Magnification ⭐
Mirror formula — THE most important equation:
1/f = 1/u + 1/v
f = focal length
u = object distance (from pole P)
v = image distance (from pole P)
Magnification (m):
m = hᵢ / hₒ = −v / u
hᵢ = image height, hₒ = object height
|m| > 1 → enlarged image
|m| = 1 → same size
|m| < 1 → diminished image
m = +ve → virtual, erect image
m = −ve → real, inverted image
10) Cartesian Sign Convention — CRITICAL ⭐
❌ This is where 90% of students lose marks! Get this RIGHT.
Rules of Cartesian Sign Convention:
1. Pole (P) of the mirror is the ORIGIN
2. Principal axis is the X-axis
3. Distances measured in direction of incident light → POSITIVE (+ve)
4. Distances measured opposite to incident light → NEGATIVE (−ve)
5. Heights above principal axis → POSITIVE (+ve)
6. Heights below principal axis → NEGATIVE (−ve)
Quick Reference Table:
• u (object distance) → ALWAYS −ve (object in front of mirror)
• f for CONCAVE mirror → −ve (real focus in front)
• f for CONVEX mirror → +ve (virtual focus behind)
• v for CONCAVE → real image: −ve, virtual image: +ve
• v for CONVEX → ALWAYS +ve (image behind mirror)
• hₒ (object height) → ALWAYS +ve
• hᵢ (image height) → erect: +ve, inverted: −ve
🟡 Senior's Rule of Thumb:
If the object/image is on the same side as the incident light (in front of mirror) → distance is −ve
If the object/image is on the opposite side (behind mirror) → distance is +ve
Because incident light travels from left to right in diagrams, and the mirror is at the origin, everything in front = negative, everything behind = positive.
If the object/image is on the same side as the incident light (in front of mirror) → distance is −ve
If the object/image is on the opposite side (behind mirror) → distance is +ve
Because incident light travels from left to right in diagrams, and the mirror is at the origin, everything in front = negative, everything behind = positive.
11) Uses of Spherical Mirrors — Detailed Applications
A. Concave Mirror Applications:
| Use | How it works | Object position |
|---|---|---|
| Shaving mirror / Makeup mirror | Produces enlarged, erect virtual image | Between P and F |
| Dentist's mirror | Enlarged view of teeth | Between P and F |
| Torch / Headlight / Spotlight | Bulb at F → parallel beam of light | Bulb at F |
| Solar concentrator / Solar cooker | Large concave mirror focuses sunlight at F → high temperature | Sun at infinity → image at F |
| Reflecting telescope | Concave mirror collects light from distant stars | Stars at infinity → image at F |
| ENT specialist's head mirror | Concave mirror with hole focuses light into ear/nose | Light source at focus |
B. Convex Mirror Applications:
| Use | Why convex? |
|---|---|
| Rear-view mirror (vehicles) | Always gives erect, diminished image with WIDE field of view. "Objects in mirror are closer than they appear" |
| Vigilance / Security mirror | Convex mirrors at corners in shops/hospitals to see around corners |
| Street light reflectors | Convex mirror spreads light over a wider area |
🟡 Senior's Tip — "Objects may appear closer than they are":
This warning is written on car side mirrors (convex). Because the image is diminished, it appears farther away. But in reality, the object (car behind you) is CLOSER than the image suggests. Always check blind spots!
This warning is written on car side mirrors (convex). Because the image is diminished, it appears farther away. But in reality, the object (car behind you) is CLOSER than the image suggests. Always check blind spots!
🔥 AMU PYQ: Which mirror is used as a rear-view mirror in vehicles?
(A) Plane (B) Concave (C) Convex (D) Both B and C
Ans: C (convex gives wider field of view, always erect and diminished)
(A) Plane (B) Concave (C) Convex (D) Both B and C
Ans: C (convex gives wider field of view, always erect and diminished)
🔥 AMU PYQ: A dentist uses which mirror to see enlarged image of teeth?
(A) Plane (B) Concave (C) Convex (D) None
Ans: B (concave mirror gives enlarged virtual image when object is between P and F)
(A) Plane (B) Concave (C) Convex (D) None
Ans: B (concave mirror gives enlarged virtual image when object is between P and F)
12) PYQ Battle — 18 AMU Past Questions on Reflection
Q1. According to laws of reflection, angle of incidence is equal to:
(A) Angle of refraction (B) Angle of reflection (C) 90° − i (D) Critical angle
Ans: B
(A) Angle of refraction (B) Angle of reflection (C) 90° − i (D) Critical angle
Ans: B
Q2. The image formed by a plane mirror is:
(A) Real and inverted (B) Virtual and erect (C) Real and erect (D) Virtual and inverted
Ans: B
(A) Real and inverted (B) Virtual and erect (C) Real and erect (D) Virtual and inverted
Ans: B
Q3. The mirror formula is:
(A) 1/f = 1/u − 1/v (B) 1/f = 1/u + 1/v (C) 1/f = u + v (D) f = uv/(u+v)
Ans: B
(A) 1/f = 1/u − 1/v (B) 1/f = 1/u + 1/v (C) 1/f = u + v (D) f = uv/(u+v)
Ans: B
Q4. For a concave mirror, focal length = 10 cm. Object at 30 cm. Image at?
Ans: v = −15 cm (real, between C and F, diminished)
1/v = 1/f − 1/u = 1/(−10) − 1/(−30) = −1/10 + 1/30 = −2/30 = −1/15Ans: v = −15 cm (real, between C and F, diminished)
Q5. A convex mirror has f = +20 cm. Object at 10 cm. Find v.
Ans: v = +6.67 cm (virtual, behind mirror)
1/v = 1/f − 1/u = 1/20 − 1/(−10) = 1/20 + 1/10 = 3/20Ans: v = +6.67 cm (virtual, behind mirror)
Q6. An object 5 cm tall is at 15 cm from a concave mirror (f = 10 cm). Find image height.
v = −30 cm (as solved above)
m = −v/u = −(−30)/(−15) = −2
hᵢ = m × hₒ = −2 × 5 = −10 cm (inverted, enlarged)
Q7. The focal length of a mirror is +15 cm. The mirror is:
(A) Concave (B) Convex (C) Plane (D) Cannot determine
Ans: B (positive f → convex mirror)
(A) Concave (B) Convex (C) Plane (D) Cannot determine
Ans: B (positive f → convex mirror)
Q8. The radius of curvature of a mirror is 40 cm. Focal length is:
(A) 20 cm (B) 40 cm (C) 80 cm (D) 10 cm
Ans: A (f = R/2 = 20 cm)
(A) 20 cm (B) 40 cm (C) 80 cm (D) 10 cm
Ans: A (f = R/2 = 20 cm)
Q9. A concave mirror forms an enlarged virtual image when object is:
(A) At C (B) Beyond C (C) Between P and F (D) At F
Ans: C
(A) At C (B) Beyond C (C) Between P and F (D) At F
Ans: C
Q10. Magnification m = −v/u. If m = −2, the image is:
(A) Virtual and erect (B) Real and inverted (C) Virtual and inverted (D) Real and erect
Ans: B (negative m → real & inverted)
(A) Virtual and erect (B) Real and inverted (C) Virtual and inverted (D) Real and erect
Ans: B (negative m → real & inverted)
Q11. The speed of light in vacuum is:
(A) 3 × 10⁶ m/s (B) 3 × 10⁸ m/s (C) 3 × 10¹⁰ m/s (D) 3 × 10⁵ m/s
Ans: B
(A) 3 × 10⁶ m/s (B) 3 × 10⁸ m/s (C) 3 × 10¹⁰ m/s (D) 3 × 10⁵ m/s
Ans: B
Q12. Which mirror always produces a diminished and erect image?
(A) Plane (B) Concave (C) Convex (D) Both B and C
Ans: C
(A) Plane (B) Concave (C) Convex (D) Both B and C
Ans: C
Q13. If u = −30 cm and f = −10 cm for a concave mirror, the image is at:
Ans: v = −15 cm (real, between C and F)
Ans: v = −15 cm (real, between C and F)
Q14. An object placed at C of a concave mirror gives image at:
(A) At F (B) At C (C) Beyond C (D) Behind mirror
Ans: B (same size, real, inverted)
(A) At F (B) At C (C) Beyond C (D) Behind mirror
Ans: B (same size, real, inverted)
Q15. Number of images formed by two mirrors at 90°:
(A) 2 (B) 3 (C) 4 (D) 5
Ans: B (n = 360/90 − 1 = 3)
(A) 2 (B) 3 (C) 4 (D) 5
Ans: B (n = 360/90 − 1 = 3)
Q16. Which is used in a solar cooker to concentrate sunlight?
(A) Plane mirror (B) Concave mirror (C) Convex mirror (D) Prism
Ans: B (concave focuses sunlight at F → high temperature)
(A) Plane mirror (B) Concave mirror (C) Convex mirror (D) Prism
Ans: B (concave focuses sunlight at F → high temperature)
Q17. A plane mirror produces an image that is:
(A) Laterally inverted (B) Not inverted (C) Real (D) Diminished
Ans: A (laterally inverted = left-right reversal)
(A) Laterally inverted (B) Not inverted (C) Real (D) Diminished
Ans: A (laterally inverted = left-right reversal)
Q18. Magnification of a plane mirror is:
(A) 0 (B) +1 (C) −1 (D) ∞
Ans: B (m = +1 for plane mirror, same size, erect, virtual)
(A) 0 (B) +1 (C) −1 (D) ∞
Ans: B (m = +1 for plane mirror, same size, erect, virtual)
13) Practice Problems — 18 Numericals with Step-by-Step Solutions
Problem 1: Find the focal length of a concave mirror whose radius of curvature is 30 cm.
f = R/2 = 30/2 = 15 cm (f is negative for concave → f = −15 cm)
Problem 2: An object is placed at 25 cm from a concave mirror of f = 15 cm. Find image position and nature.
u = −25 cm, f = −15 cm
1/v = 1/f − 1/u = 1/(−15) − 1/(−25) = −1/15 + 1/25 = (−5 + 3)/75 = −2/75
v = −37.5 cm (real, inverted, beyond C)
Problem 3: A convex mirror of f = 30 cm has an object at 20 cm. Find v and nature.
u = −20 cm, f = +30 cm
1/v = 1/f − 1/u = 1/30 − 1/(−20) = 1/30 + 1/20 = (2 + 3)/60 = 5/60 = 1/12
v = +12 cm (virtual, behind mirror, diminished, erect)
Problem 4: A concave mirror forms a real image at 40 cm when object is at 20 cm. Find f.
u = −20 cm, v = −40 cm (real → −ve)
1/f = 1/u + 1/v = 1/(−20) + 1/(−40) = −1/20 − 1/40 = −3/40
f = −13.33 cm
Problem 5: An object 2 cm high is at 10 cm from a convex mirror (f = 15 cm). Find image height.
1/v = 1/15 − 1/(−10) = 1/15 + 1/10 = 5/30 = 1/6 → v = +6 cm
m = −v/u = −6/(−10) = +0.6
hᵢ = m × hₒ = 0.6 × 2 = +1.2 cm (erect, diminished)
Problem 6: Where should an object be placed in front of a concave mirror (f = 12 cm) to get a real image 3 times the size?
m = −3 (real → negative)
m = −v/u → −3 = −v/u → v = 3u
But v is also negative (real): v = 3u (where u is −ve)
1/f = 1/u + 1/v → 1/(−12) = 1/u + 1/(3u)
−1/12 = 1/u + 1/(3u) = 4/(3u)
−3u = 48 → u = −16 cm
Problem 7: A convex mirror produces a virtual image half the size of the object. If f = 20 cm, find u.
m = +1/2 (virtual, erect → positive)
m = −v/u → 1/2 = −v/u → v = −u/2
For convex mirror, v is +ve, so v = −u/2 must be +ve → u is −ve (which is always true)
Wait: m = −v/u → 1/2 = −v/(−u) → 1/2 = v/u → v = u/2
Since v is +ve for convex, u/2 = +ve, so u = +ve? No, u is always −ve.
Let u = −x, then m = −v/(−x) = v/x = 1/2 → v = x/2
1/f = 1/u + 1/v → 1/20 = 1/(−x) + 1/(x/2) = −1/x + 2/x = 1/x
x = 20 → u = −20 cm
Problem 8: Find R for a concave mirror with f = 25 cm.
R = 2f = 2 × 25 = 50 cm
Problem 9: A candle 5 cm tall is at 15 cm from a concave mirror (f = 10 cm). Find image position, size, and nature.
1/v = 1/(−10) − 1/(−15) = −1/10 + 1/15 = (−3 + 2)/30 = −1/30
v = −30 cm (real, inverted, beyond C)
m = −v/u = −(−30)/(−15) = −2
hᵢ = −2 × 5 = −10 cm (inverted, enlarged)
Problem 10: A convex mirror has R = 40 cm. Object at 30 cm. Find v, m, and nature.
f = R/2 = 40/2 = +20 cm (convex)
1/v = 1/20 − 1/(−30) = 1/20 + 1/30 = 5/60 = 1/12
v = +12 cm (virtual behind mirror)
m = −v/u = −12/(−30) = +0.4 (diminished, erect)
Problem 11: Two plane mirrors are at 45°. Find the number of images.
n = 360/45 − 1 = 8 − 1 = 7 images
Problem 12: An object is placed at 50 cm from a concave mirror (f = 20 cm). Find v and magnification.
1/v = 1/(−20) − 1/(−50) = −1/20 + 1/50 = (−5 + 2)/100 = −3/100
v = −33.33 cm
m = −(−33.33)/(−50) = 33.33/(−50) = −0.667 (real, diminished, inverted)
Problem 13: A concave mirror produces an image on a screen placed 30 cm in front. If object is at 15 cm, find f.
v = −30 cm, u = −15 cm
1/f = 1/(−15) + 1/(−30) = −1/15 − 1/30 = −3/30 = −1/10
f = −10 cm
Problem 14: A 2 cm pin is placed at 8 cm from a concave mirror (f = 12 cm). Find image position and size.
u = −8 cm, f = −12 cm, u < f → virtual image
1/v = 1/(−12) − 1/(−8) = −1/12 + 1/8 = (−2 + 3)/24 = 1/24
v = +24 cm (behind mirror, virtual)
m = −v/u = −24/(−8) = +3
hᵢ = 3 × 2 = +6 cm (erect, enlarged, virtual)
Problem 15: A convex mirror has f = 25 cm. Where should an object be placed to get an image at 10 cm behind mirror?
v = +10 cm (behind mirror), f = +25 cm
1/u = 1/v − 1/f = 1/10 − 1/25 = (5 − 2)/50 = 3/50
u = 50/3 = +16.67 cm → but u must be −ve!
Actually: 1/u = 1/v − 1/f = 1/10 − 1/25 = 3/50 → u = 50/3 cm
Since u is in front, u = −16.67 cm
Problem 16: The image formed by a convex mirror is 1/3rd the size of object. If f = 18 cm, find u.
m = +1/3 = −v/u → v = −u/3
But v is +ve for convex → v = −u/3 means u must be −ve
Let u = −x, then v = x/3
1/18 = 1/(−x) + 1/(x/3) = −1/x + 3/x = 2/x
x = 36, u = −36 cm
Problem 17: A concave mirror of R = 40 cm forms a real image at 30 cm. Find u.
f = −20 cm, v = −30 cm
1/u = 1/f − 1/v = 1/(−20) − 1/(−30) = −1/20 + 1/30 = (−3 + 2)/60 = −1/60
u = −60 cm
Problem 18: A 10 cm object is placed at 20 cm from a convex mirror (f = 20 cm). Find image characteristics.
1/v = 1/20 − 1/(−20) = 1/20 + 1/20 = 1/10 → v = +10 cm
m = −10/(−20) = +0.5
hᵢ = 0.5 × 10 = +5 cm
Nature: virtual, erect, diminished (behind mirror)
14) Common Mistakes ❌ — Don't Lose Marks!
❌ Mistake 1: Forgetting the sign of u (always negative).
✅ Fix: u is ALWAYS negative for both concave and convex mirrors because the object is placed in front of the mirror (opposite to incident light direction).
✅ Fix: u is ALWAYS negative for both concave and convex mirrors because the object is placed in front of the mirror (opposite to incident light direction).
❌ Mistake 2: Confusing focal length sign: concave = −ve, convex = +ve.
✅ Fix: Concave has REAL focus in front → −ve. Convex has VIRTUAL focus behind → +ve.
✅ Fix: Concave has REAL focus in front → −ve. Convex has VIRTUAL focus behind → +ve.
❌ Mistake 3: Confusing mirror formula with lens formula.
✅ Fix: Mirror: 1/f = 1/u + 1/v. Lens: 1/f = 1/v − 1/u. DIFFERENT!
✅ Fix: Mirror: 1/f = 1/u + 1/v. Lens: 1/f = 1/v − 1/u. DIFFERENT!
❌ Mistake 4: Thinking m = v/u for mirrors (that's for lenses).
✅ Fix: For mirrors: m = −v/u. For lenses: m = v/u. The minus sign is IMPORTANT.
✅ Fix: For mirrors: m = −v/u. For lenses: m = v/u. The minus sign is IMPORTANT.
❌ Mistake 5: Confusing real and virtual images.
✅ Fix: Real image: can be obtained on screen, inverted, v is −ve for concave. Virtual image: cannot be obtained on screen, erect, v is +ve.
✅ Fix: Real image: can be obtained on screen, inverted, v is −ve for concave. Virtual image: cannot be obtained on screen, erect, v is +ve.
❌ Mistake 6: Forgetting that in sign convention, distances are measured from pole P.
✅ Fix: Always measure from P (pole of mirror). Not from the object or from F.
✅ Fix: Always measure from P (pole of mirror). Not from the object or from F.
❌ Mistake 7: Using f = R/2 but forgetting the sign.
✅ Fix: f = R/2 gives magnitude. Then apply sign: concave → negative, convex → positive.
✅ Fix: f = R/2 gives magnitude. Then apply sign: concave → negative, convex → positive.
❌ Mistake 8: Thinking plane mirror has f = 0 or infinite.
✅ Fix: Plane mirror can be considered as a spherical mirror with R → ∞, so f → ∞. 1/f ≈ 0.
✅ Fix: Plane mirror can be considered as a spherical mirror with R → ∞, so f → ∞. 1/f ≈ 0.
15) Quick Revision — One-Liners
- Light speed in vacuum: 3 × 10⁸ m/s. EM wave. Rectilinear propagation.
- Laws of reflection: i = r. Incident, reflected, normal in same plane.
- Regular reflection → smooth surface → clear image. Diffused → rough surface → no image, but object visible.
- Plane mirror: virtual, erect, same size, laterally inverted, v = −u, m = +1.
- Number of images: n = 360/θ − 1 (if even). Two parallel mirrors → infinite images.
- Concave (converging): f = −ve, R = 2f. Real focus in front.
- Convex (diverging): f = +ve, R = 2f. Virtual focus behind.
- Mirror formula: 1/f = 1/u + 1/v. Sign convention is CRITICAL.
- Magnification: m = −v/u = hᵢ/hₒ. m > 0 → virtual & erect. m < 0 → real & inverted.
- Concave: object between P and F → virtual, erect, enlarged (shaving/dentist mirror).
- Concave: object at C → image at C, same size, real, inverted.
- Concave: object beyond C → image between C and F, diminished, real, inverted.
- Concave: object at F → parallel rays → image at infinity.
- Convex: ALWAYS virtual, erect, diminished. Used in rear-view mirrors.
- Field of view: convex > plane > concave. Convex gives widest view.
- u is ALWAYS negative. f is negative for concave, positive for convex.
- Uses: concave → torch, solar cooker, telescope, dentist. Convex → rear-view, security.
✅ Reflection of Light — Fully Covered! You now have a complete reference with theory, all image formation cases, sign convention, mirror formula, 18 PYQs, 18 solved numericals, 8 common mistakes, and quick revision. Master the sign convention and you're ready for AMU! 🪞🔥