Chapter 5 of 13

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Andhra Pradesh (BIEAP)Class 10 Physical Science★ AP Board (BSEAP) SSC Physical Science · ~8 marks · Board: AP Board

Reflection of Light by Different Surfaces

LAWS OF REFLECTION. Plane mirrors — image characteristics. SPHERICAL MIRRORS — concave (converging) and convex (diverging). MIRROR FORMULA (1/f = 1/u + 1/v). MAGNIFICATION. Sign convention. Ray diagrams for all cases. AP Board Class 10 Physical Science.

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By the end of this chapter you'll be able to…

1State and apply the laws of reflection
2Distinguish plane, concave, and convex mirrors; identify focal length and centre of curvature
3Draw ray diagrams to locate images formed by concave and convex mirrors
4Apply the mirror formula: 1/f = 1/v + 1/u with proper sign convention
5Calculate magnification and interpret image characteristics (real/virtual, erect/inverted, magnified/diminished)

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Why this chapter matters

Reflection of Light covers mirrors (plane and curved) and is tested extensively in AP SSC. The mirror formula, magnification formula, and ray diagram skills are all tested. Concave and convex mirrors have different uses (concave: shaving mirror, solar cooker, headlights; convex: rear-view mirror) that appear as 2-mark application questions. Image formation by mirrors and the relationship between image characteristics and object position must be mastered for 6–8 marks.

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AP Board Class 9 Science: light, reflection, basic optics

Reflection of Light — Class 10 Physical Science

"Light travels in straight lines. When it hits a surface, it BOUNCES. This simple fact — reflection — is why you can see yourself in a mirror, why car headlights work, and why dentists can see the back of your teeth."

1. Laws of Reflection

Angle of incidence (i) = Angle of reflection (r). Measured from the NORMAL (perpendicular to the surface).
The INCIDENT ray, REFLECTED ray, and NORMAL all lie in the SAME PLANE.

2. Plane Mirror

Image characteristics: VIRTUAL (cannot be caught on a screen). ERECT (upright). Same SIZE as the object. LATERALLY INVERTED (left ↔ right swapped). As far BEHIND the mirror as the object is in FRONT. 'Your reflection raises its LEFT hand when you raise your RIGHT. Ambulances have "ECNALUBMA" written on the front — so drivers see "AMBULANCE" in their rear-view mirror!'

3. Spherical Mirrors

	Concave Mirror	Convex Mirror
Shape	Curved INWARD (like a bowl)	Curved OUTWARD (bulging)
Effect on parallel rays	CONVERGES to a point (FOCUS)	DIVERGES (appears to come from focus BEHIND mirror)
Uses	Torches, shaving mirrors, dentist mirrors, solar furnaces	Rear-view mirrors (cars, bikes). Shop security mirrors.
Image types	REAL or VIRTUAL. Magnified or diminished.	ALWAYS virtual, diminished, erect.

Key Definitions

Pole (P) : Centre of the mirror's surface. Centre of Curvature (C) : Centre of the sphere. Radius of Curvature (R) : Distance PC. Focus (F) : Midpoint of PC. Focal Length (f) = R/2.

Ray Diagrams — Rules for Drawing

Ray PARALLEL to principal axis → after reflection, passes through FOCUS (concave) or APPEARS to come from focus (convex).
Ray passing through FOCUS → after reflection, becomes parallel to principal axis.
Ray passing through CENTRE OF CURVATURE → retraces its path (strikes mirror normally).
Ray incident at the POLE → reflected at EQUAL angle.

Mirror Formula: 1/f = 1/u + 1/v

f = focal length (negative for concave, positive for convex). u = object distance (ALWAYS negative — object is in front of mirror). v = image distance (positive for real images, negative for virtual).

Magnification: m = −v/u = h'/h (h' = image height, h = object height).

m > 0 → ERECT (virtual). m < 0 → INVERTED (real). |m| > 1 → MAGNIFIED. |m| < 1 → DIMINISHED.

Sign Convention (Cartesian)

All distances measured from POLE. Distances in direction of incident light → NEGATIVE (u is always negative). Opposite direction → POSITIVE. Heights above principal axis → POSITIVE. Below → NEGATIVE.

4. Concave Mirror — Image Cases

Object Position	Image Position	Size	Nature
At infinity	At F	Highly diminished	REAL, inverted
Beyond C	Between F and C	Diminished	REAL, inverted
At C	At C	Same size	REAL, inverted
Between C and F	Beyond C	Magnified	REAL, inverted
At F	At infinity	Highly magnified	REAL, inverted
Between P and F	BEHIND mirror	Magnified	VIRTUAL, erect

'Only the LAST case (object between P and F) produces a VIRTUAL, MAGNIFIED image — this is why concave mirrors are used as shaving mirrors and dentist mirrors.'

5. Convex Mirror — Always the Same

Image is ALWAYS: Virtual. Erect. Diminished. Behind the mirror (between P and F). 'Convex mirrors give a WIDER field of view — but images are SMALLER. This is why they're used as rear-view mirrors: "Objects in the mirror are closer than they appear."'

6. Common Mistakes

Sign convention errors: 'u is ALWAYS negative. f is negative for concave, positive for convex. v is negative for virtual images.'
'Centre of curvature = focus' — C is at distance R from pole. F is at R/2.
Drawing the wrong ray: 'A ray through FOCUS becomes parallel. A ray through CENTRE bounces back. These are DIFFERENT.'

7. AP SSC Exam Focus

Topic	Marks
Mirror formula problems	3-4
Ray diagrams (concave)	4-5
Image characteristics	3-4
Uses of mirrors	2-3

8. Worked Numerical Problems — Mirror Formula and Magnification

Example 1: An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the image position and nature. Solution: u = −15 cm, f = −10 cm (concave → f negative). 1/f = 1/u + 1/v → 1/v = 1/f − 1/u = 1/(−10) − 1/(−15) = −1/10 + 1/15 = (−3+2)/30 = −1/30. v = −30 cm. m = −v/u = −(−30)/(−15) = −2. 'v is NEGATIVE — image is REAL (in front of mirror). m = −2 — image is INVERTED and MAGNIFIED (2×).'

Example 2: An object is placed 20 cm in front of a concave mirror of focal length 15 cm. Find the image position, nature, and magnification. Solution: u = −20 cm, f = −15 cm. 1/v = 1/f − 1/u = 1/(−15) − 1/(−20) = −1/15 + 1/20 = (−4+3)/60 = −1/60. v = −60 cm. m = −v/u = −(−60)/(−20) = −3. 'Image is REAL, INVERTED, MAGNIFIED (3×), at 60 cm in front of mirror. Object is between C and F.'

Example 3: A convex mirror has focal length 20 cm. An object is placed 30 cm in front. Find the image position and magnification. Solution: u = −30 cm, f = +20 cm (convex → f positive). 1/v = 1/f − 1/u = 1/20 − 1/(−30) = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12. v = +12 cm. m = −v/u = −12/(−30) = +0.4. 'v is POSITIVE — image is VIRTUAL (behind mirror). m = +0.4 — image is ERECT and DIMINISHED. Exactly what a convex mirror always produces.'

Example 4: A concave mirror forms a real, inverted image of the same size as the object. Where is the object placed? Solution: For SAME SIZE, real, inverted image → object must be at CENTRE OF CURVATURE (C). u = R = 2f. 'Object at C: image at C. Same size. Real. Inverted.'

9. Uses of Mirrors — Detailed

Concave Mirror Uses:

Shaving mirror / Make-up mirror: Object placed BETWEEN P and F → VIRTUAL, ERECT, MAGNIFIED image. You see an enlarged view of your face.
Dentist's mirror: Concave mirror on a handle — gives MAGNIFIED view of teeth.
Torch / Headlight: Bulb placed at FOCUS → reflected rays become PARALLEL → narrow, powerful beam.
Solar Furnace: Large concave reflector CONCENTRATES sunlight at the FOCUS → very HIGH TEMPERATURE (used to heat water, cook food, or generate steam).
Reflecting Telescopes: Concave mirror as the PRIMARY MIRROR to collect light from distant stars.

Convex Mirror Uses:

Rear-view mirror in vehicles: Gives a WIDER field of view — driver can see more of the traffic behind. Images are VIRTUAL, ERECT, and DIMINISHED — so "objects in mirror are closer than they appear."
Security mirrors in shops: Wide field of view — one mirror can monitor a large area.

10. Magnification — Special Cases

m > 1: Image is MAGNIFIED (larger than object). Example: shaving mirror (object between P and F). m = 1: Same size. Example: concave mirror with object at C. m < 1: DIMINISHED (smaller). Example: convex mirror (always). Concave mirror with object beyond C. m > 0: ERECT image (virtual). Example: convex mirror. Concave mirror with object between P and F. m < 0: INVERTED image (real). Example: concave mirror with object beyond F.

'When solving numerical problems: start by writing u = −(given distance). Decide f = −R/2 (concave) or +R/2 (convex). Then use the mirror formula. Check the sign of v to determine real/virtual. Calculate m to find magnification and orientation.'

11. Self-Test

Q1: A concave mirror has focal length 10 cm. Where should an object be placed to get a REAL, INVERTED, SAME-SIZE image? A1: At the CENTRE OF CURVATURE (C). R = 2f = 20 cm. Object distance u = 20 cm (in front of mirror).

Q2: Why do convex mirrors give a wider field of view? A2: Convex mirrors curve OUTWARD. They diverge incoming light rays. This allows them to COLLECT light from a WIDER angle and present a MINIATURE view of the entire scene. 'The curved surface acts like a wide-angle lens.'

Q3: A concave mirror produces a virtual image. Where is the object placed? A3: Between POLE (P) and FOCUS (F). Only this case gives a VIRTUAL, ERECT, MAGNIFIED image.

Q4: An object is placed 10 cm from a convex mirror of focal length 15 cm. Find the image distance. A4: u = −10 cm, f = +15 cm. 1/v = 1/f − 1/u = 1/15 − 1/(−10) = 1/15 + 1/10 = (2+3)/30 = 5/30 = 1/6. v = +6 cm. Image is 6 cm BEHIND the mirror.

Q5: Calculate the magnification when the image distance is −30 cm and object distance is −15 cm. Describe the image. A5: m = −v/u = −(−30)/(−15) = 30/(−15) = −2. m = −2 — Image is REAL, INVERTED, MAGNIFIED (2×).

Q6: A dentist uses a concave mirror of focal length 2 cm. At what distance should the tooth be placed from the mirror to get a magnified image? A6: To get a MAGNIFIED, VIRTUAL image: object must be BETWEEN P and F. So tooth should be placed LESS THAN 2 cm from the mirror (u < f).

Q7: The radius of curvature of a convex mirror used as a rear-view mirror is 3 m. A car is 5 m behind the mirror. Find the position of the image. A7: R = +3 m → f = +1.5 m. u = −5 m. 1/v = 1/f − 1/u = 1/1.5 − 1/(−5) = 1/1.5 + 1/5 = 0.667 + 0.2 = 0.867. v = +1.15 m. Image is 1.15 m BEHIND the mirror — VIRTUAL, ERECT, DIMINISHED.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Mirror Formulas and Sign Convention

MIRROR FORMULA: 1/f = 1/v + 1/u. MAGNIFICATION: m = −v/u = h'/h. SIGN CONVENTION (New Cartesian): All distances from POLE. Incident light direction = positive (+). Against = negative (−). Object ALWAYS on left → u always NEGATIVE. For CONCAVE mirror: f is NEGATIVE (centre of curvature in front). For CONVEX mirror: f is POSITIVE (centre of curvature behind mirror). FOCAL LENGTH: f = R/2 (R = radius of curvature). RAY RULES: (1) Ray parallel to PA → reflects through F (concave) or appears from F (convex). (2) Ray through F → reflects parallel to PA. (3) Ray through C → reflects back through C. (4) Ray at pole → reflects at equal angle to PA. IMAGE CHARACTERISTICS: If m is negative → inverted. If |m|>1 → magnified. m positive → erect.

USES OF MIRRORS: Concave: shaving/makeup mirror (erect, magnified virtual image when object inside F). Searchlights/torches/headlights (object at F → parallel reflected beam). Solar cooker (concentrates parallel rays at F). ENT doctor's mirror. Convex: rear-view mirror (always gives erect, diminished, virtual image — wider field of view). IMPORTANT: Convex mirror NEVER forms a real image. It always forms virtual, erect, diminished images. AP SSC tests: 'Why do we use convex mirrors as rear-view mirrors?' → Because they form erect, diminished images with wider field of view.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Using positive focal length for concave mirror

✓ In the New Cartesian sign convention, the CONCAVE mirror has its focal point IN FRONT of the mirror (same side as the object). Since distances in front of the mirror are NEGATIVE (against incident light), the focal length of a concave mirror is NEGATIVE (f < 0). The focal length of a CONVEX mirror is POSITIVE (f > 0) because its focal point is behind the mirror (in the direction of incident light). Always identify the type of mirror first, then assign the correct sign to f.

Practice problems

Work through this chapter's problems as a readiness check — reveal each solution, mark yourself honestly, and get your gap report at the end.

Readiness check

Are you exam-ready for Reflection of Light by Different Surfaces?

1 problems from this chapter. Try each one, reveal the worked solution, mark yourself honestly — get your gap report at the end.

1 questions~2 min

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Laws of reflection: (1) Angle of incidence = angle of reflection. (2) Incident ray, reflected ray, and normal at the point of incidence lie in the same plane.
•New Cartesian sign convention: all distances from POLE of mirror. In FRONT of mirror = NEGATIVE. Behind mirror = POSITIVE.
•Concave mirror: focal length f is NEGATIVE (focus is in front of mirror). Convex mirror: f is POSITIVE (focus is behind mirror).
•Mirror formula: 1/f = 1/v + 1/u. Magnification m = -v/u. If m is negative → image is INVERTED. If |m| > 1 → ENLARGED. If |m| < 1 → DIMINISHED.
•Real image: formed in FRONT of mirror (rays actually converge). Virtual image: formed BEHIND mirror (rays appear to diverge from there).
•Concave mirror image positions: (i) Object at infinity → image at F (real, point). (ii) Object beyond C → image between F and C (real, inverted, diminished). (iii) Object at C → image at C (real, inverted, same size). (iv) Object between C and F → image beyond C (real, inverted, enlarged). (v) Object at F → image at infinity. (vi) Object between F and P → image behind mirror (virtual, erect, enlarged).
•Convex mirror: image is ALWAYS virtual, erect, and diminished, regardless of object position. Image is always behind the mirror.
•Uses of concave mirror: shaving/makeup (magnified virtual image), headlights (parallel beam), solar furnaces, ENT doctor's reflector.
•Uses of convex mirror: rear-view mirrors in vehicles (wide field of view), shop security mirrors.
•Radius of curvature R = 2f (centre of curvature is twice the focal length from the pole).

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Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Medical endoscopes and otoscopes

ENT doctors use a small concave mirror (with a hole) on their forehead to focus a beam of light into the patient's ear or throat. The concave mirror concentrates the light from a lamp into a parallel beam — the same property used in torches and car headlights. This is a direct clinical application of the concave mirror's converging property.

Solar concentrators and renewable energy

Large-scale solar thermal power plants use arrays of curved (parabolic) concave mirrors to focus sunlight onto a central receiver tube, heating a fluid to 400°C+ to drive a steam turbine. This is the principle of a solar furnace applied at industrial scale. India's National Solar Mission has installed several such concentrated solar power plants, including in Rajasthan.

Telescope mirrors and astronomy

All reflecting telescopes (including the Hubble Space Telescope and the James Webb Space Telescope) use large concave mirrors to collect and focus light from distant stars. The larger the mirror, the more light it collects, and the dimmer the objects it can detect. This is the concave mirror's image-at-infinity-to-focal-point property put to extraordinary use.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Sign convention: always state which sign convention you are using (New Cartesian) and apply it consistently. Losing a sign loses the entire mark for that calculation.

After calculating v, always state whether the image is real or virtual (from the sign of v), inverted or erect (from the sign of m), and enlarged or diminished (from |m|). The 'nature of image' requires all three descriptors.

Ray diagrams: draw two standard rays for any mirror problem. (1) Ray parallel to principal axis → reflects through F (concave) or appears to come from F (convex). (2) Ray through C → reflects back along itself. The intersection point is the image.

Uses of mirrors (2-mark question): always write one use of CONCAVE and one use of CONVEX, with a brief reason for each. Stating the use without the reason earns only half the marks.

Practice mirror formula with both concave and convex mirrors. Students who only practice one type are caught off guard by the other in the exam.

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

STRETCH

Research parabolic mirrors vs spherical mirrors — spherical mirrors suffer from spherical aberration (rays far from the axis are not focused at exactly the same point as paraxial rays), which blurs the image. Parabolic mirrors have zero spherical aberration for parallel incoming rays — which is why astronomical telescopes use parabolic mirrors, not spherical ones.

STRETCH

Investigate the Hubble Space Telescope's initial spherical aberration problem (1990) — the mirror was ground to incorrect specifications, giving blurry images. The Corrective Optics Space Telescope Axial Replacement (COSTAR) was installed in 1993 to fix the aberration optically. This is a famous case study in precision optics.

STRETCH

Explore the physics of a 'magic mirror' — a special concave mirror that forms a real, life-size image in the air in front of the mirror at twice the focal length. This is the principle used in some 3D display technologies and coin levitation illusions.

STRETCH

Research corner reflectors — arrangements of three mutually perpendicular plane mirrors that reflect any incoming ray exactly back in the direction it came from, regardless of angle of incidence. These are placed on the Moon (by Apollo missions) and on road safety signs; laser pulses bounced off lunar corner reflectors measure the Earth-Moon distance to millimetre accuracy.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

AP Board SSC (Class 10)High — mirror formula calculation and ray diagrams are standard 4+2 mark questions in almost every AP SSC paper

JEE Main / Advanced (Physics)Very High — Ray Optics is a high-weight chapter in Class 12 Physics; mirror formula is the starting point

AP EAMCET (Engineering)High — optics (reflection, refraction, lenses) is tested in Class 12 Physics section of EAMCET

NTSE (Science section)Moderate — reflection concepts and mirror uses appear in NTSE Stage I science

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

A concave mirror converges reflected rays — they actually meet at a point in front of the mirror, forming a real image that can be projected on a screen. A convex mirror diverges reflected rays — they spread outward and never actually meet. However, our brain traces the rays backward to where they appear to come from (behind the mirror), creating a virtual image that cannot be projected. The key is whether reflected rays converge (real) or diverge (virtual).

The inside (bowl) of a spoon is CONCAVE — when you hold it close to your face (object between F and P), it forms a virtual, erect, enlarged image (like a concave mirror used as a makeup mirror). When you move far away (object beyond C), it forms a real, inverted, diminished image. The back of the spoon is CONVEX — it always forms a virtual, erect, diminished image regardless of distance. This is why the back of the spoon always shows a wide-angle, smaller-than-life reflection.

The New Cartesian Convention treats the incident light direction as positive. For mirrors, light travels from the object toward the mirror — so the object side is the NEGATIVE direction (opposite to the assumed positive direction which is behind the mirror). This is a convention, not a physical law — the important thing is to apply it CONSISTENTLY. With this convention: real images (in front of mirror) have negative v, virtual images (behind mirror) have positive v. Focal length of concave mirror is negative, convex mirror is positive.

As the candle moves from infinity toward the focal point: The real image starts at F (tiny point) when the candle is at infinity → moves further and further from the mirror as the candle approaches F → when the candle is exactly at F, the image goes to infinity (parallel reflected rays). When the candle goes inside F, suddenly the image appears behind the mirror as a virtual, erect, enlarged image. This dramatic change at the focal point is why the focal point is a special location.

A convex mirror provides a WIDER FIELD OF VIEW than a plane mirror of the same size — it can show more of the road behind the car. The diminished (smaller) image is a tradeoff — objects appear farther than they are. This is why car rear-view mirrors have the warning 'Objects in mirror are closer than they appear.' A plane mirror would give accurate size but a narrower field of view — potentially missing vehicles in adjacent lanes.

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