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Chapter 9: Light Reflection and Refraction

Chapter 9 Science

Grade 10 Science · Chapter 9

Light — Reflection & Refraction

How mirrors form images, how light bends when it crosses media boundaries, and the mathematics behind lenses and mirrors — everything a Grade 10 student needs.

Reflection

Spherical Mirrors

Refraction

Lenses

Mirror & Lens Formulae

📋 Table of Contents

①Introduction to Light

②Laws of Reflection

③Spherical Mirrors & Key Terms

④Image Formation by Mirrors

⑤Mirror Formula & Magnification

⑥Refraction of Light

⑦Refractive Index & Snell’s Law

⑧Spherical Lenses

⑨Lens Formula & Power

⑩Worked Examples & Practice Sets

①	Introduction to Light

Light is the primary reason we are able to see the world around us. In a completely dark room, nothing is visible — but as soon as a light source is switched on, objects become visible because they reflect light back into our eyes. Transparent objects allow light to pass through them, while opaque objects reflect and absorb it.

A key observation about light is that it appears to travel in straight lines — a property called rectilinear propagation. The sharp shadow cast by an opaque object in the path of a point source of light is direct evidence of this.

Did you know? When an obstacle blocking light becomes extremely small, light actually bends around it — a phenomenon called diffraction. This shows that at a deeper level, light behaves as a wave. Even more surprisingly, under certain conditions it also behaves like a stream of particles. Modern physics reconciles both behaviours through quantum theory.

②	Laws of Reflection

When light strikes a polished reflecting surface such as a mirror, it bounces back according to two fundamental laws:

Law 1 — Angle of Incidence

↘		↙
∠i		∠r

Angle of incidence (∠i) = Angle of reflection (∠r)

Law 2 — Coplanar Rays

→

MIRROR
PLANE

→

Incident ray, reflected ray and normal all lie in the same plane.

These laws apply universally — to plane mirrors, concave mirrors, and convex mirrors alike. A plane mirror always forms an image that is virtual, erect, the same size as the object, and as far behind the mirror as the object is in front of it, with lateral inversion.

③	Spherical Mirrors & Key Terms

A spherical mirror has a curved reflective surface that forms part of a hollow sphere. There are two types:

🔴 Concave Mirror

		→→
Reflecting surface curves inward

Used in torches, shaving mirrors, solar furnaces, dentist mirrors.

🔵 Convex Mirror

→→
Reflecting surface curves outward

Used as rear-view (wing) mirrors in vehicles; wide field of view.

Key Terms Defined

Term	Symbol	Definition
Pole	P	Centre point of the reflecting surface of the mirror
Centre of Curvature	C	Centre of the sphere of which the mirror forms a part; lies outside the mirror
Radius of Curvature	R	Radius of the sphere; distance PC
Principal Axis	—	Straight line through P and C; normal to mirror at pole
Principal Focus	F	Point on principal axis where parallel rays converge (concave) or appear to diverge from (convex)
Focal Length	f	Distance from pole P to principal focus F; equal to R/2
Aperture	MN	Diameter of the reflecting surface (circular outline)

Key Relationship: For spherical mirrors with small apertures, R = 2f. The principal focus lies exactly halfway between the pole and the centre of curvature.

④	Image Formation by Mirrors

Concave Mirror — Image Summary Table

Object Position	Image Position	Size	Nature
At infinity	At F	Highly diminished (point)	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	Enlarged	Real & Inverted
At F	At infinity	Image not formed
Between P and F	Behind the mirror	Enlarged	Virtual & Erect

Convex Mirror — Image Summary Table

Object Position	Image Position	Size	Nature
At infinity	At F (behind mirror)	Highly diminished	Virtual & Erect
Between ∞ and P	Between P and F (behind mirror)	Diminished	Virtual & Erect

Why use a convex mirror as a rear-view mirror? Because it always produces a virtual, erect and diminished image regardless of object position — and it has a wider field of view than a plane mirror, helping the driver see more of the road behind them.

⑤	Mirror Formula & Magnification

Mirror Formula

1/v + 1/u = 1/f

where v = image distance, u = object distance, f = focal length

Magnification

m = h’/h = −v/u

m negative → real & inverted | m positive → virtual & erect

New Cartesian Sign Convention

All distances are measured from the pole (P). The principal axis is the x-axis:

Distances to the right of origin (+x direction)	POSITIVE (+)
Distances to the left of origin (−x direction)	NEGATIVE (−)
Heights above principal axis (+y direction)	POSITIVE (+)
Heights below principal axis (−y direction)	NEGATIVE (−)

⑥	Refraction of Light

Refraction is the bending of light when it passes from one transparent medium into another. This happens because light travels at different speeds in different media. Common examples include a pencil appearing bent when placed in a glass of water, or an object at the bottom of a pool appearing shallower than it really is.

Refraction at an Air-Glass Boundary

AIR (Rarer Medium)

↘

Incident ray

GLASS (Denser Medium)

↓

Refracted ray bends toward normal

Rule: Entering denser medium → bends TOWARD normal. Entering rarer medium → bends AWAY from normal.

Laws of Refraction

1	The incident ray, the refracted ray and the normal to the interface at the point of incidence all lie in the same plane.
2	Snell’s Law: For a given colour and a given pair of media, sin(i) / sin(r) = constant. This constant is the refractive index of the second medium with respect to the first.

When light travels through a rectangular glass slab, it refracts at the air-glass boundary (bending toward the normal) and refracts again at the glass-air boundary (bending away from the normal). The two refractions are equal and opposite, so the emergent ray is parallel to the incident ray but displaced sideways.

⑦	Refractive Index & Snell’s Law

The refractive index of a medium is a number that describes how much light slows down when entering that medium from vacuum. It is defined as the ratio of the speed of light in vacuum to the speed in the medium.

Absolute Refractive Index

n = c / v

c = speed of light in vacuum (3×10⁸ m/s), v = speed of light in the medium

Refractive Index of Common Materials

Material	Refractive Index (n)	Material	Refractive Index (n)
Air	1.0003	Crown Glass	1.52
Water	1.33	Rock Salt	1.54
Ice	1.31	Ruby	1.71
Kerosene	1.44	Sapphire	1.77
Turpentine Oil	1.47	Diamond	2.42

Optical Density: A medium with a higher refractive index is optically denser. Kerosene (n = 1.44) is optically denser than water (n = 1.33) even though water has greater mass density. Light travels faster in optically rarer media.

⑧	Spherical Lenses

A lens is a transparent material bounded by at least one spherical surface. Lenses refract light to form images.

Convex Lens (Converging)

→

↗
→
↘

Thicker at centre. Converges parallel rays to a focal point. Focal length is positive (+).

Concave Lens (Diverging)

→

↗
⬝
↘

Thicker at edges. Diverges parallel rays; appear to come from focal point. Focal length is negative (−).

Image Formation by Convex Lens

Object Position	Image Position	Size	Nature
At infinity	At focus F₂	Highly diminished	Real & Inverted
Beyond 2F₁	Between F₂ and 2F₂	Diminished	Real & Inverted
At 2F₁	At 2F₂	Same size	Real & Inverted
Between F₁ and 2F₁	Beyond 2F₂	Enlarged	Real & Inverted
At focus F₁	Image not formed (at infinity)
Between F₁ and O	Same side as object	Enlarged	Virtual & Erect

Concave Lens: Always produces a virtual, erect and diminished image regardless of object position. The image always forms on the same side as the object, between F₁ and O.

⑨	Lens Formula, Magnification & Power

Lens Formula

1/v − 1/u = 1/f

Note: different from mirror formula (subtraction, not addition)

Magnification

m = h’/h = v/u

m positive → virtual & erect; m negative → real & inverted

Power of a Lens

P = 1/f

SI unit: dioptre (D). f in metres. Convex: +ve; Concave: −ve

Understanding Dioptres

1 dioptre is the power of a lens with a focal length of exactly 1 metre. A lens with power +2.0 D has a focal length of +0.50 m (convex). A lens with power −2.5 D has a focal length of −0.40 m (concave). When multiple lenses are combined in contact, their individual powers simply add: P_total = P₁ + P₂ + P₃ + …

⑩	Worked Examples

EXAMPLE 1 — Mirror Focal Length

A spherical mirror has a radius of curvature of 30 cm. Find its focal length.

▶ Show Solution

Given: R = 30 cm

Formula: f = R/2

Solution: f = 30/2 = 15 cm

Conclusion: The focal length is 15 cm. F lies exactly midway between P and C.

EXAMPLE 2 — Convex Mirror Image

A convex mirror used in a vehicle has a radius of curvature of 3.00 m. A bus is 5.00 m away. Find the image position, nature and magnification.

▶ Show Solution

R = +3.00 m (convex → positive), so f = +1.50 m

u = −5.00 m (object in front of mirror → negative)

1/v = 1/f − 1/u = 1/1.50 − 1/(−5.00) = 1/1.50 + 1/5.00

1/v = (5.00 + 1.50)/7.50 = 6.50/7.50 → v = +1.15 m

m = −v/u = −(+1.15)/(−5.00) = +0.23

The image is 1.15 m behind the mirror. It is virtual, erect and 0.23 times the size of the object.

EXAMPLE 3 — Concave Mirror Image

An object 4.0 cm tall is placed 25.0 cm in front of a concave mirror of focal length 15.0 cm. Find the screen position and image size.

▶ Show Solution

h = +4.0 cm, u = −25.0 cm, f = −15.0 cm (concave → negative)

1/v = 1/f − 1/u = 1/(−15) − 1/(−25) = −1/15 + 1/25

1/v = (−5 + 3)/75 = −2/75 → v = −37.5 cm

h’ = −(v/u) × h = −(−37.5/−25) × 4 = −6.0 cm

Screen should be placed 37.5 cm in front of mirror. Image is 6.0 cm tall, real and inverted (enlarged).

EXAMPLE 4 — Speed of Light in Glass

Light enters glass with refractive index 1.50. If the speed of light in vacuum is 3×10⁸ m/s, find the speed in glass.

▶ Show Solution

n = c/v → v = c/n = (3×10⁸)/1.50

v = 2×10⁸ m/s — light slows to two-thirds its vacuum speed in glass.

EXAMPLE 5 — Concave Lens (Object Position)

A concave lens of focal length 15 cm forms an image 10 cm from the lens. Where is the object? Find the magnification.

▶ Show Solution

f = −15 cm, v = −10 cm (virtual image, same side as object)

1/u = 1/v − 1/f = 1/(−10) − 1/(−15) = −1/10 + 1/15

1/u = (−3+2)/30 = −1/30 → u = −30 cm

m = v/u = (−10)/(−30) = +1/3 = +0.33

Object is 30 cm from the lens. Image is virtual, erect and one-third the size of the object.

EXAMPLE 6 — Convex Lens (Tall Object)

A 2.0 cm tall object is placed 15 cm from a convex lens of focal length 10 cm. Find image position, size and nature.

▶ Show Solution

h = +2.0 cm, u = −15 cm, f = +10 cm (convex → positive)

1/v = 1/f + 1/u = 1/10 + 1/(−15) = 1/10 − 1/15 = (3−2)/30 = 1/30 → v = +30 cm

h’ = h × v/u = 2.0 × (30/−15) = −4.0 cm; m = −2

Image is 30 cm on the other side of the lens; 4.0 cm tall; real, inverted and enlarged (×2).

EXAMPLE 7 — Power of a Lens

A doctor prescribes a corrective lens of power +1.5 D. Find the focal length. Is it converging or diverging?

▶ Show Solution

P = +1.5 D → f = 1/P = 1/1.5 = +0.667 m = +66.7 cm

The focal length is approximately +66.7 cm. The positive sign indicates a convex (converging) lens.

EXAMPLE 8 — Combined Lens Power

Two lenses of power +2.0 D and +0.25 D are placed in contact. What is the combined focal length?

▶ Show Solution

P_total = P₁ + P₂ = 2.0 + 0.25 = 2.25 D

f = 1/2.25 ≈ 0.444 m ≈ 44.4 cm

The combined system behaves as a single convex lens of focal length ≈ 44.4 cm.

EXAMPLE 9 — Convex Mirror (Object Near Mirror)

An object is placed 10 cm from a convex mirror of focal length 15 cm. Find the image position and nature.

▶ Show Solution

u = −10 cm, f = +15 cm (convex mirror)

1/v = 1/f − 1/u = 1/15 − 1/(−10) = 1/15 + 1/10 = (2+3)/30 = 5/30 → v = +6 cm

Image is 6 cm behind the mirror. Virtual, erect and diminished. m = −v/u = −(+6)/(−10) = +0.6

EXAMPLE 10 — Finding Power from Focal Length

Find the power of a concave lens of focal length 2 m.

▶ Show Solution

f = −2 m (concave lens, negative focal length)

P = 1/f = 1/(−2) = −0.5 D

The power is −0.5 dioptres. The negative sign confirms it is a diverging (concave) lens.

📝 Practice Sets A–D

Practice Set A — Multiple Choice Questions

MCQ — Choose the most appropriate answer
1. Which material cannot be used to make a lens?	d) Clay
2. A concave mirror gives a virtual, erect and larger image. The object is:	d) Between P and F
3. To get a real image the same size as the object from a convex lens, place the object:	b) At 2F₁
4. No matter how far you stand, your image is erect. The mirror is:	d) Plane or convex
5. To read small dictionary letters, which lens is best?	c) Convex, f = 5 cm

Practice Set B — Short Answer Questions

Short Answer
1. Define the principal focus of a concave mirror.	The point on the principal axis through which rays parallel to the principal axis converge after reflection from a concave mirror.
2. Why is a convex mirror preferred as a rear-view mirror?	It always gives a virtual, erect and diminished image and provides a wider field of view than a plane mirror.
3. What is the meaning of refractive index n = 2.42 for diamond?	Light travels 2.42 times slower in diamond than in vacuum. Diamond is an extremely optically dense medium.
4. What does a magnification of +1 mean for a plane mirror?	The image is the same size as the object (not magnified or diminished) and is virtual and erect.

Practice Set C — Numerical Problems

Apply Formulae
C1. An object 5 cm tall is held 25 cm from a convex lens of f = 10 cm. Find image distance, size and nature.	v = +16.7 cm; h’ = −3.33 cm; real, inverted, diminished.
C2. A concave mirror produces a 3× enlarged real image of an object at 10 cm. Where is the image?	m = −3, u = −10 cm → v = 30 cm in front of mirror.
C3. An object 7 cm tall is 27 cm from a concave mirror of f = 18 cm. Find screen position and image size.	v = −54 cm; h’ = −14 cm; real, inverted and enlarged. Screen 54 cm in front of mirror.

Practice Set D — Higher Order Thinking

Analytical & Application Questions
D1. Half a convex lens is covered with black paper. Explain whether a complete image still forms.	Yes. A complete image still forms because every part of the lens refracts rays from the entire object. Covering half reduces brightness but not the image.
D2. A lens of power −2.0 D is used in spectacles. What kind of vision defect is being corrected?	Myopia (short-sightedness). A concave (negative power) lens is used to diverge incoming rays so the eye can focus on distant objects.
D3. A ray enters a glass slab at 45°. As it exits from the parallel face, explain the direction of the emergent ray.	The emergent ray is parallel to the incident ray but laterally displaced. The two refractions at the parallel faces are equal and opposite, so no net change in direction occurs.

📚 Chapter Summary

Reflection Angle of incidence = angle of reflection. All three rays coplanar. R = 2f for spherical mirrors. Mirror formula: 1/v + 1/u = 1/f.	Spherical Mirrors Concave: used in torches, shaving mirrors, solar furnaces. Convex: used in rear-view mirrors. Magnification m = −v/u.
Refraction Light bends at a media boundary due to change in speed. Snell’s Law: sin(i)/sin(r) = n₂₁ = constant. Entering denser medium → bends toward normal.	Refractive Index n = c/v. Higher n = optically denser = slower light. Diamond has highest common n (2.42). Optically denser ≠ more massive.
Lenses Convex: converging, +f. Concave: diverging, −f. Lens formula: 1/v − 1/u = 1/f. Magnification m = v/u.	Power of a Lens P = 1/f (f in metres). Unit: dioptre (D). Combined lenses: P = P₁ + P₂ + … Convex: +P, Concave: −P.

⚡ 8-Point Exam Quick-Check

#	Must-Know Fact
1	R = 2f for all spherical mirrors (small aperture approximation)
2	Mirror formula: 1/v + 1/u = 1/f \| Lens formula: 1/v − 1/u = 1/f
3	For mirrors: m = −v/u \| For lenses: m = +v/u
4	Concave mirrors: all signs negative (f, u, v all in front of mirror = negative)
5	Convex mirrors and concave lenses always produce virtual, erect, diminished images
6	Light in vacuum = 3×10⁸ m/s. Refractive index n = c/v. Higher n → slower speed
7	Power P = 1/f (f in metres). Unit is dioptre (D). P_total = P₁ + P₂ + …
8	Rectangular glass slab: emergent ray is parallel to incident ray but laterally displaced

This Grade 10 Science study guide covers Chapter 9: Light — Reflection and Refraction, including laws of reflection, spherical mirror types (concave and convex), image formation tables, the mirror formula, magnification, refraction of light, Snell’s law, refractive index, spherical lenses (convex and concave), lens formula, power of a lens in dioptres, and worked numerical examples. Ideal for CBSE Grade 10 students, Science Olympiad preparation, and annual examination revision. Topics include ray diagrams for mirrors and lenses, New Cartesian Sign Convention, and practical uses of concave and convex mirrors and lenses in everyday life.