CBSE Class 10 Science Light Reflection and Refraction Notes

Key Topics in This Chapter

• Reflection of Light — laws of reflection, plane mirror, spherical mirrors

• Concave Mirror — image formation at all object positions, uses

• Convex Mirror — image formation, uses

• Mirror Formula and Magnification — numericals

• Refraction of Light — laws of refraction, Snell's Law, refractive index

• Refraction through glass slab — lateral displacement

• Lenses — convex (converging) and concave (diverging) lenses

• Convex Lens — image formation at all object positions

• Concave Lens — image formation

• Lens Formula, Magnification, and Power of a Lens — numericals

LAW 1:  The angle of incidence = The angle of reflection

        ∠i  =  ∠r

        (both angles measured from the NORMAL to the surface at the point of incidence)

LAW 2:  The incident ray, the reflected ray, and the normal to the surface

        at the point of incidence all lie in the SAME PLANE.

Normal = line perpendicular to the reflecting surface at the point where light strikes.

Plane Mirror — Image Properties (Memorise All 6)

1. Virtual — image cannot be obtained on a screen; formed behind the mirror

2. Erect — right-side up (same orientation as the object)

3. Laterally inverted — left and right are swapped (left hand appears as right hand)

4. Same size as object — magnification = +1

5. As far behind the mirror as the object is in front

6. Image distance = Object distance  (|v| = |u|)

Term

Symbol

Definition

Centre of Curvature

C

Centre of the sphere of which the mirror is a part. Located in front of concave mirror, behind convex mirror.

Radius of Curvature

R

Radius of sphere of which mirror is part. R = 2f (twice the focal length).

Pole

P

Midpoint / geometric centre of the reflecting surface of the mirror.

Principal Axis

—

Imaginary straight line passing through C, F, and P — the axis of symmetry.

Focus (Principal Focus)

F

Point where all rays parallel to principal axis converge (concave) or appear to diverge from (convex) after reflection.

Focal Length

f

Distance from Pole (P) to Focus (F) along the principal axis. f = R/2.

Aperture

—

Diameter of the reflecting surface. Larger aperture = more light collected.

Key relationship:  R  =  2f   →   f  =  R / 2

For CONCAVE mirror:  f is NEGATIVE (focus in front of mirror — same side as object)

For CONVEX mirror:   f is POSITIVE (focus behind mirror — opposite side to object)

(Using New Cartesian Sign Convention — see Section 3.2)

New Cartesian Sign Convention — The Complete Rules

1. All distances are measured from the POLE (P) of the mirror (or optical centre of lens).

2. Distances measured in the DIRECTION OF INCIDENT LIGHT are POSITIVE (+).

3. Distances measured AGAINST the direction of incident light are NEGATIVE (−).

4. Heights measured UPWARD from the principal axis are POSITIVE (+).

5. Heights measured DOWNWARD from the principal axis are NEGATIVE (−).

Incident light travels LEFT TO RIGHT (standard convention):

  → Objects are placed to the LEFT of the mirror → object distance u is always NEGATIVE

  → For CONCAVE mirror: f is NEGATIVE, R is NEGATIVE

  → For CONVEX mirror: f is POSITIVE, R is POSITIVE

MEMORY AID: Object is ALWAYS to the left → u is ALWAYS negative for mirrors.

Rule

Incident Ray

Reflected Ray

Rule 1

Parallel to the principal axis

Passes through F (concave) or appears to come from F (convex)

Rule 2

Passes through F (concave) or directed toward F (convex)

Emerges parallel to the principal axis

Rule 3

Passes through C (or directed toward C for convex)

Retraces its path back through C (reflects along same line)

Object Position

Image Position

Image Size

Image Nature

Uses

At infinity (∞)

At F (focal point)

Highly diminished (point image)

Real, Inverted

Reflecting telescopes, solar furnaces

Beyond C (beyond 2f)

Between F and C

Diminished (smaller than object)

Real, Inverted

Used in rear-view mirrors — NO; this is concave.

At C (at 2f)

At C (at 2f)

Same size as object

Real, Inverted

Used in ERG machines (medical)

Between C and F

Beyond C (beyond 2f)

Enlarged (magnified)

Real, Inverted

Projectors, headlights (object at F gives parallel beam)

At F

At infinity (∞)

Highly enlarged

Real, Inverted

Searchlights, vehicle headlights (parallel beam produced)

Between F and P

Behind the mirror

Enlarged (magnified)

Virtual, Erect

Shaving/make-up mirrors, dental mirrors (magnified upright image)

Concave Mirror — Key Facts for Board Exam

• Only when object is BETWEEN F and P does concave mirror give a VIRTUAL, ERECT image.

• All other positions give REAL, INVERTED images.

• As object moves from infinity toward mirror, image moves from F toward infinity (then virtual).

• At F: image at infinity → parallel beam of light produced (used in searchlights, headlights).

• Uses: Shaving mirror, dental mirror, solar furnace, reflector in torches/headlights.

Object Position

Image Position

Image Size

Image Nature

At infinity (∞)

At F (behind mirror)

Highly diminished (point image)

Virtual, Erect

Anywhere between infinity and P

Between F and P (behind mirror)

Diminished (smaller than object)

Virtual, Erect

Convex Mirror — Why Used as Rear-View Mirror in Vehicles

1. Always gives ERECT (right-side up) image — driver sees correctly oriented view.

2. Always gives DIMINISHED image — wider field of view (see more of the road behind).

3. Always VIRTUAL — driver knows image is behind the mirror; no confusion about distance.

Limitation: Objects appear further away than they are (because image is diminished).

That is why rear-view mirrors say: 'Objects in mirror are closer than they appear.'

MIRROR FORMULA:

  1/v  +  1/u  =  1/f

where:

  v = image distance (measured from pole P)

  u = object distance (measured from pole P)  [always negative for real objects]

  f = focal length  [negative for concave, positive for convex mirror]

Also:  f  =  R / 2  →  R  =  2f

MAGNIFICATION (m):

  m  =  Height of Image (h')  /  Height of Object (h)  =  −v / u

  m > 0 (positive):  Image is ERECT (same side up as object)

  m < 0 (negative):  Image is INVERTED

  |m| > 1:           Image is ENLARGED (magnified)

  |m| < 1:           Image is DIMINISHED (smaller than object)

  |m| = 1:           Image is SAME SIZE as object

Worked Numerical 3.1 — Concave Mirror

Problem: An object is placed 20 cm in front of a concave mirror of focal length 15 cm.

Find: (a) image distance (b) magnification (c) nature of image.

Given: u = −20 cm (object in front of mirror, negative by sign convention)

       f = −15 cm (concave mirror, negative by sign convention)

Using mirror formula:  1/v + 1/u = 1/f

  1/v + 1/(−20) = 1/(−15)

  1/v = 1/(−15) − 1/(−20) = −1/15 + 1/20

  1/v = (−4 + 3)/60 = −1/60

  v = −60 cm

Image is 60 cm in front of the mirror (v is negative → real image, same side as object).

Magnification: m = −v/u = −(−60)/(−20) = −3

Interpretation: m = −3 → Image is INVERTED (negative) and MAGNIFIED by 3× (|m| = 3 > 1).

Nature of image: REAL, INVERTED, ENLARGED (3 times the object size).

Worked Numerical 3.2 — Convex Mirror

Problem: An object 6 cm tall is placed 30 cm in front of a convex mirror with R = 40 cm.

Find: image distance, image height, and describe the image.

Given: u = −30 cm  (object in front of mirror, negative)

       R = +40 cm  (convex mirror, positive) → f = R/2 = +20 cm

       h = +6 cm   (object is upright, positive)

Mirror formula:  1/v = 1/f − 1/u = 1/20 − 1/(−30) = 1/20 + 1/30

  1/v = (3 + 2)/60 = 5/60 = 1/12

  v = +12 cm  (positive → image is behind the mirror → virtual image)

Magnification: m = −v/u = −(12)/(−30) = +0.4

Image height: h' = m × h = 0.4 × 6 = +2.4 cm

Image is VIRTUAL (behind mirror), ERECT (m positive), DIMINISHED (|m| < 1).

Image height = 2.4 cm (smaller than 6 cm object).

LAW 1:  The incident ray, the refracted ray, and the normal to the interface

        at the point of incidence all lie in the SAME PLANE.

LAW 2 (SNELL'S LAW):  The ratio of the sine of the angle of incidence

        to the sine of the angle of refraction is a constant for a given

        pair of media and a given colour of light:

        sin i / sin r  =  n₂₁  =  n₂ / n₁  =  constant

where:  i  = angle of incidence (in medium 1)

        r  = angle of refraction (in medium 2)

        n₁ = refractive index of medium 1

        n₂ = refractive index of medium 2

        n₂₁ = refractive index of medium 2 with respect to medium 1

Absolute Refractive Index (n) of a medium:

  n  =  Speed of light in vacuum (c)  /  Speed of light in medium (v)

  n  =  c / v

  n  =  3 × 10⁸ m/s  /  v

Snell's Law (extended form):

  n₁ × sin i  =  n₂ × sin r

  (This form makes calculations easier — use this version in numericals)

Also: n₂₁  =  n₂ / n₁  =  v₁ / v₂  =  λ₁ / λ₂

(speed in medium 1 / speed in medium 2 = refractive index of 2 w.r.t. 1)

Medium

Refractive Index (n)

Speed of Light (approx.)

Vacuum

1.000 (exact, by definition)

3.00 × 10⁸ m/s

Air

1.0003 (≈ 1.00 for calculations)

≈ 3.00 × 10⁸ m/s

Water

1.33

2.25 × 10⁸ m/s

Glass (crown)

1.50

2.00 × 10⁸ m/s

Glass (flint)

1.70

1.76 × 10⁸ m/s

Diamond

2.42

1.24 × 10⁸ m/s

Key Points — Refraction Through Glass Slab

• At entry (air → glass): ray bends TOWARD normal (denser medium, slower speed).

• At exit (glass → air): ray bends AWAY from normal (less dense medium, faster speed).

• Emergent ray is PARALLEL to incident ray (both surfaces are parallel).

• Lateral displacement: the perpendicular distance between incident and emergent rays.

• Lateral displacement INCREASES with: thicker slab, higher refractive index, larger angle of incidence.

• Net deviation of direction = 0° (parallel in, parallel out — just shifted sideways).

Term

Definition

Optical Centre (O)

The central point of the lens. Rays passing through O pass straight through without bending.

Principal Axis

Imaginary line passing through both centres of curvature and the optical centre.

Principal Focus (F)

For convex lens: point where parallel rays converge after refraction. For concave lens: point from which parallel rays appear to diverge after refraction.

Focal Length (f)

Distance from Optical Centre (O) to Principal Focus (F). Positive for convex, negative for concave (by sign convention).

Focal Plane

Plane perpendicular to principal axis passing through F. Objects at infinity form images in the focal plane.

Radius of Curvature

Radius of the sphere of which each lens surface is a part. R = 2f for thin lenses (approx.).

Sign Convention for Lenses:

  Object is always to the LEFT of lens  →  u is always NEGATIVE

  CONVEX (converging) lens:

    f is POSITIVE (focus on the right — transmission side, same as emergent light)

    Real images form on the RIGHT → v is POSITIVE for real images

    Virtual images form on the LEFT → v is NEGATIVE for virtual images

  CONCAVE (diverging) lens:

    f is NEGATIVE (focus on the left — same side as object)

    Images always virtual, on same side as object → v is always NEGATIVE

Rule

Incident Ray

Refracted Ray

Rule 1

Parallel to the principal axis

Passes through F₂ (far focus) for convex; appears to come from F₁ (near focus) for concave

Rule 2

Passes through F₁ (near focus) for convex; directed toward F₂ for concave

Emerges parallel to the principal axis

Rule 3

Passes through Optical Centre (O)

Passes through without any bending (straight line)

Object Position

Image Position

Image Size

Nature

Uses

At infinity (∞)

At F₂ (focal point)

Highly diminished

Real, Inverted

Telescope objective lens

Beyond 2F₁ (beyond 2f)

Between F₂ and 2F₂

Diminished

Real, Inverted

Camera lens (object far, image small on film)

At 2F₁ (at 2f)

At 2F₂ (at 2f)

Same size as object

Real, Inverted

Photocopier at 100% scale

Between F₁ and 2F₁

Beyond 2F₂

Enlarged

Real, Inverted

Film projector (slide/movie projector)

At F₁ (focal point)

At infinity (∞)

Highly enlarged

Real, Inverted

Searchlight / parallel beam production

Between F₁ and O

Same side as object (left of lens)

Enlarged

Virtual, Erect

Magnifying glass, reading lens

Convex Lens — Key Pattern

• Object BETWEEN F and O → Virtual, Erect, Enlarged (magnifying glass).

• All other positions → Real, Inverted images.

• At F: image at infinity (parallel beam). Beyond 2F: diminished. At 2F: same size. Between F and 2F: enlarged.

• SAME pattern as concave mirror — if you know one, you know the other.

Object Position

Image Position

Image Size

Nature

At infinity (∞)

At F₁ (same side as object)

Highly diminished (point image)

Virtual, Erect

Anywhere between infinity and O

Between F₁ and O (same side as object)

Diminished

Virtual, Erect

Concave Lens vs Convex Mirror — A Useful Parallel

Both concave lenses and convex mirrors ALWAYS produce:

  → Virtual, Erect, Diminished images

  → Images that are between F and the surface/optical centre

The key difference: convex mirror REFLECTS light; concave lens REFRACTS light.

Both are used where a wide field of view / smaller representation is needed.

LENS FORMULA:

  1/v  −  1/u  =  1/f

NOTE: Lens formula uses (1/v − 1/u) NOT (1/v + 1/u) like mirror formula.

This is the most common mix-up — memorise the difference.

where:

  v = image distance from optical centre O

  u = object distance from optical centre O  [always negative]

  f = focal length  [positive for convex, negative for concave]

MAGNIFICATION (m) for Lens:

  m  =  h' / h  =  v / u

NOTE: For lens, m = v/u (NOT −v/u as for mirrors).

  m > 0: Image is ERECT   |   m < 0: Image is INVERTED

  |m| > 1: Enlarged       |   |m| < 1: Diminished

Mirror Formula vs Lens Formula — Critical Difference

MIRROR:  1/v  +  1/u  =  1/f     and    m  =  −v/u

LENS:    1/v  −  1/u  =  1/f     and    m  =   v/u

The LENS formula has a MINUS sign between 1/v and 1/u.

The MIRROR magnification has a NEGATIVE sign: m = −v/u.

The LENS magnification has NO negative sign: m = v/u.

These two differences cause the majority of formula errors in board exams.

Worked Numerical 5.1 — Convex Lens (Magnifying Glass)

Problem: An object is placed 10 cm from a convex lens of focal length 15 cm.

Find image distance, magnification, and describe the image.

Given: u = −10 cm (object to left of lens, negative)

       f = +15 cm (convex lens, positive)

Lens formula:  1/v − 1/u = 1/f

  1/v − 1/(−10) = 1/15

  1/v + 1/10 = 1/15

  1/v = 1/15 − 1/10 = (2 − 3)/30 = −1/30

  v = −30 cm  (negative → image on same side as object → VIRTUAL)

Magnification: m = v/u = (−30)/(−10) = +3

Image is VIRTUAL (v negative), ERECT (m positive), ENLARGED by 3× (|m| = 3 > 1).

This is the magnifying glass configuration (object between F and O).

Worked Numerical 5.2 — Concave Lens

Problem: A concave lens has focal length 25 cm. Object placed 40 cm from lens.

Find image position and magnification.

Given: u = −40 cm, f = −25 cm (concave lens, negative)

1/v − 1/u = 1/f

  1/v − 1/(−40) = 1/(−25)

  1/v + 1/40 = −1/25

  1/v = −1/25 − 1/40 = (−8 − 5)/200 = −13/200

  v = −200/13 ≈ −15.4 cm

v is negative → image is on the SAME SIDE as object (left of lens) → VIRTUAL image.

Magnification: m = v/u = (−15.4)/(−40) = +0.385

Image is VIRTUAL, ERECT, DIMINISHED (m ≈ +0.39, so image is about 39% of object size).

POWER OF A LENS:

  P  =  1 / f

where f is the focal length in METRES.

  Unit of power: DIOPTRE (D)   [1 dioptre = 1 m⁻¹]

  CONVEX lens: f is POSITIVE → Power is POSITIVE

  CONCAVE lens: f is NEGATIVE → Power is NEGATIVE

COMBINATION OF LENSES (lenses placed in contact):

  P_total  =  P₁  +  P₂  +  P₃  + ...

  (The total power is the algebraic sum of individual powers)

  Equivalent focal length: 1/f = 1/f₁ + 1/f₂ + ...

Worked Numerical 6.1 — Power and Combination of Lenses

Problem: Two lenses — one convex of focal length 20 cm and one concave of focal length 40 cm

— are placed in contact. Find: (a) total power, (b) equivalent focal length.

Convex lens: f₁ = +20 cm = +0.20 m → P₁ = 1/0.20 = +5.0 D

Concave lens: f₂ = −40 cm = −0.40 m → P₂ = 1/(−0.40) = −2.5 D

(a) Total power:  P = P₁ + P₂ = 5.0 + (−2.5) = +2.5 D

(b) Equivalent focal length:  f = 1/P = 1/2.5 = 0.40 m = 40 cm

The combination acts as a CONVEX lens (P positive) of focal length 40 cm.

Power — Quick Reference

Power unit = Dioptre (D) = m⁻¹

Convex lens → Positive power (e.g., +3.5 D)

Concave lens → Negative power (e.g., −2.0 D)

Short focal length → HIGH power (bends light strongly)

Long focal length → LOW power (bends light weakly)

Spectacle prescriptions: +ve power = convex lens = treats hypermetropia (far-sightedness)

                         −ve power = concave lens = treats myopia (near-sightedness)

Feature

Concave Mirror

Convex Mirror

Reflecting surface

Inner (hollow) side — curves inward

Outer side — curves outward

Type

Converging mirror

Diverging mirror

Focus

Real focus — in front of mirror

Virtual focus — behind mirror

Focal length sign

-ve (negative)

+ ve (positive)

Image (generally)

Can be real or virtual

Always virtual, erect, diminished

Image when object beyond F

Real, inverted

Virtual, erect (always)

Image when object between F and P

Virtual, erect, enlarged

Virtual, erect, diminished

Uses

Shaving mirror, dental mirror, solar furnace, torch reflector, telescope

Rear-view mirror in vehicles, security mirrors in shops

Feature

Convex Lens

Concave Lens

Shape

Thicker at centre, thinner at edges

Thinner at centre, thicker at edges

Type

Converging lens

Diverging lens

Focus

Real focus — on transmission side

Virtual focus — on same side as object

Focal length sign

+ve (positive)

-ve (negative)

Power sign

Positive (+)

Negative (−)

Image (generally)

Can be real or virtual (at one position)

Always virtual, erect, diminished

Uses

Magnifying glass, camera, microscope, telescope eyepiece, projector

Spectacles for myopia (near-sightedness), Galilean telescope eyepiece

Aspect

Mirror Formula

Lens Formula

Formula

1/v + 1/u = 1/f

1/v − 1/u = 1/f

Magnification

m = −v/u

m = v/u

Reference point

Pole (P) of mirror

Optical Centre (O) of lens

Real image v sign

Negative (in front)

Positive (on far side of lens)

Virtual image v sign

Positive (behind mirror)

Negative (same side as object)

Concave/Convex f

Concave: f negative; Convex: f positive

Convex: f positive; Concave: f negative

Mistake

Why It Is Wrong

Correct Approach

Using +u for object distance

Object is always to the LEFT → against incident light direction

u is ALWAYS NEGATIVE for real objects in both mirrors and lenses

Using mirror formula for lenses

Formulas are different

Mirror: 1/v+1/u=1/f  |  Lens: 1/v−1/u=1/f  (note the minus sign for lens)

m = v/u for mirrors

Mirror magnification has a negative sign

Mirror: m = −v/u  |  Lens: m = v/u  (no negative for lens)

Concave mirror f is positive

Concave mirror focus is IN FRONT (real focus)

Concave mirror: f is NEGATIVE. Convex mirror: f is POSITIVE.

Convex lens f is negative

Convex lens focus is on far side (real focus, positive direction)

Convex lens: f is POSITIVE. Concave lens: f is NEGATIVE.

Power unit = cm⁻¹

Power requires focal length in METRES

P = 1/f (metres only). 1 D = 1 m⁻¹. Convert cm to m first!

Saying all mirror images are inverted

Concave mirror with object between F and P gives erect image

Concave: erect only when object between F and P. Convex: always erect.

Confusing lateral displacement with deviation

Glass slab causes shift, not direction change

Emergent ray is PARALLEL to incident ray (same direction) but laterally shifted.

Term / Formula

Definition / Value

Reflection

Bouncing of light off a surface back into the original medium

Laws of Reflection

∠i = ∠r; incident ray, reflected ray, normal are coplanar

Refraction

Bending of light as it passes from one medium to another due to change in speed

Snell's Law

n₁ sin i = n₂ sin r  (or sin i / sin r = n₂/n₁ = constant)

Refractive Index (n)

n = c/v = speed of light in vacuum / speed of light in medium

Refractive index of glass

≈ 1.50 (crown glass) to 1.70 (flint glass)

Refractive index of water

≈ 1.33

Centre of Curvature (C)

Centre of the sphere of which the mirror/lens surface is part

Focal Length (f)

Distance from pole (P) or optical centre (O) to focus (F). f = R/2

Concave mirror f

NEGATIVE  (focus in front, real focus)

Convex mirror f

POSITIVE  (focus behind, virtual focus)

Mirror Formula

1/v + 1/u = 1/f  (with sign convention)

Mirror Magnification

m = −v/u = h'/h

Convex lens f

POSITIVE  (focus on far side, real focus)

Concave lens f

NEGATIVE  (focus on near/object side, virtual focus)

Lens Formula

1/v − 1/u = 1/f  (note minus sign — differs from mirror)

Lens Magnification

m = v/u = h'/h  (no negative sign — differs from mirror)

Power of Lens (P)

P = 1/f  (f in metres). Unit: Dioptre (D) = m⁻¹

Convex lens power

POSITIVE (+)  e.g., +2.5 D

Concave lens power

NEGATIVE (−)  e.g., −3.0 D

Combined power

P_total = P₁ + P₂ + P₃ + ...  (algebraic sum)

Lateral Displacement

Perpendicular shift of emergent ray vs incident ray through a glass slab

R = 2f

Radius of curvature = 2 × focal length for both mirrors and lenses

Board Exam Strategy for Light — Reflection and Refraction

1. ALWAYS write sign convention first in any numerical — u is negative, state f sign clearly.

2. Mirror formula: 1/v + 1/u = 1/f  |  Lens formula: 1/v − 1/u = 1/f  — the minus is critical.

3. Mirror magnification: m = −v/u  |  Lens magnification: m = v/u  — no negative for lens.

4. Power must use f in METRES — always convert cm to m before calculating power.

5. For image nature: check sign of v (positive/negative) AND sign of m (positive/negative).

6. Ray diagrams: draw at least two rays; label all key points (P, F, C for mirrors; O, F₁, F₂ for lenses).

7. Concave mirror and convex lens: Object between F and P/O → Virtual, Erect, Enlarged (exam favourite).

8. Convex mirror and concave lens: ALWAYS virtual, erect, diminished — no exceptions.

9. For 5-mark numericals: Given → Formula → Sign convention statement → Substitution → Answer.

10. Image formation tables are worth memorising: they cover every diagram question possible.