MG SCHOOL SCIENCE • CLASS 10

Light: Reflection and Refraction

Complete chapter notes with definitions, laws, ray rules, image-formation tables, sign conventions and important formulae.

Class 10 ScienceChapter NotesStudy • Revise • Practise

1. Introduction to Light

Light is a form of electromagnetic energy that causes the sensation of vision and makes things visible to our eyes. It acts like a messenger carrying information about the world around us.

Common phenomena associated with light

Image formation by mirrors
The twinkling of stars in the night sky
The beautiful colours of a rainbow
Bending of light rays when passing through different media

Properties of light

Medium independentElectromagnetic waves do not require any physical medium to travel.

Rectilinear propagationLight tends to travel in straight lines.

Dual natureLight exhibits both wave and particle characteristics.

Shadow formationLight casts distinct shadows when obstructed by opaque objects.

Speed of lightMaximum in vacuum; its value is 3 × 10⁸ m/s.

2. Reflection of Light

When light encounters a surface, it bounces back into the same medium. Reflection of light is the phenomenon in which light rays strike a surface and change direction.

Laws of reflection

Angle equality: The angle of incidence (∠i) is always equal to the angle of reflection (∠r).
Planar coincidence: The incident ray, reflected ray and normal to the reflecting surface at the point of incidence all lie in the same plane.

∠i = ∠r First law of reflection

Real and virtual images

Real imageFormed when light rays actually meet after reflection or refraction. It can be obtained on a screen.

Virtual imageFormed when light rays only appear to meet when produced backwards. It cannot be obtained on a screen.

Image formed by a plane mirror

Virtual and erect.
Image size is exactly equal to object size.
Image is formed as far behind the mirror as the object is in front of it.
Laterally inverted.

Lateral inversion: The right side of an object appears as the left side in its image and vice versa. The word “AMBULANCE” is written in reverse on emergency vehicles so drivers ahead can read it correctly in their rear-view mirrors.

3. Spherical Mirrors

Spherical mirrors are mirrors whose reflecting surface forms part of a hollow glass sphere.

Concave mirrorReflecting surface is curved inwards (towards the centre of the sphere). It is a converging mirror.

Convex mirrorReflecting surface is curved outwards. It is a diverging mirror.

Common terms for spherical mirrors

Principal axis: Straight line passing through the pole and centre of curvature.
Pole (P): Centre of the reflecting surface of the spherical mirror.
Aperture (MN): Effective diameter of the reflecting surface.
Centre of curvature (C): Centre of the hollow sphere of glass of which the mirror forms a part.
Radius of curvature (R): Radius of that sphere; distance PC.
Principal focus (F): Point on the principal axis where rays parallel to the principal axis actually converge (concave) or appear to diverge from (convex) after reflection.
Focal length (f): Distance between pole (P) and principal focus (F).

f = R / 2 Focal length of a spherical mirror is half its radius of curvature.

Rules for ray diagrams in spherical mirrors

A ray parallel to the principal axis passes through the principal focus (concave mirror) or appears to diverge from the focus (convex mirror) after reflection.
A ray passing through or directed towards the principal focus emerges parallel to the principal axis after reflection.
A ray passing through or directed towards the centre of curvature (C) is reflected back along the same path.
A ray incident obliquely at the pole (P) reflects obliquely, making equal angles with the principal axis (∠i = ∠r).

Image formation by a concave mirror

Object position	Image position	Nature of image	Size of image
At infinity	At focus (F)	Real and inverted	Point-sized / highly diminished
Beyond C	Between F and C	Real and inverted	Diminished
At C	At C	Real and inverted	Same size as object
Between F and C	Beyond C	Real and inverted	Enlarged
At F	At infinity	Real and inverted	Highly enlarged
Between P and F	Behind the mirror	Virtual and erect	Enlarged

Uses of concave mirrors

Torches, searchlights and vehicle headlights to produce powerful parallel beams of light.
Dentists use them to see enlarged images of teeth (teeth placed between P and F).
Shaving mirrors to view a larger image of the face.
Large concave mirrors concentrate sunlight to generate heat in solar furnaces.

Image formation by a convex mirror

Object position	Image position	Nature of image	Size of image
At infinity	At focus (F) behind mirror	Virtual and erect	Point-sized
Between pole (P) and infinity	Between P and F behind mirror	Virtual and erect	Diminished

Uses of convex mirrors

Rear-view mirrors in vehicles because they provide an erect, diminished image and a wider field of view.
At blind turns and traffic merging points to facilitate viewing incoming traffic.
Security mirrors in shops and stores.

4. Sign Convention and Mirror Formula

New Cartesian sign convention for reflection

The object is always placed to the left of the mirror.
All distances parallel to the principal axis are measured from the pole (P).
Distances measured in the direction of incident light (along +X axis) are positive.
Distances measured against the direction of incident light (along −X axis) are negative.
Distances measured perpendicular to and above the principal axis (along +Y axis) are positive.
Distances measured perpendicular to and below the principal axis (along −Y axis) are negative.
Object distance (u) is always negative.
Focal length of a concave mirror is negative; focal length of a convex mirror is positive.

Mirror formula and magnification

1/v + 1/u = 1/f Mirror formula

m = hᵢ / hₒ = −v/u Magnification produced by a spherical mirror

Key rules for magnification (m)

Negative magnification: If m is negative, the image is real and inverted (concave mirror).
Positive magnification: If m is positive, the image is virtual and erect.
Unit magnification: If hᵢ = hₒ (m = 1), image size equals object size.
Magnitude: If |m| > 1, the image is enlarged; if |m| < 1, it is diminished.
Plane mirror: Magnification is always +1.
Convex mirror identification: If m is positive and less than 1 (0 < m < 1), the mirror is convex.
Concave mirror identification: If m is positive and greater than 1 (m > 1), the mirror is concave.

5. Refraction of Light

Refraction is the bending of a light ray as it passes obliquely from one transparent medium to another. It occurs due to a change in the speed (velocity) of light across different media.

Speed of light and media density

Maximum speed of light occurs in vacuum or air: c = 3 × 10⁸ m/s.
Light travels slower in optically denser media compared to optically rarer media.

Laws of refraction

The incident ray, refracted ray and normal to the interface of two transparent media at the point of incidence all lie in the same plane.
Snell’s law: The ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is constant for a given pair of media and colour of light.

sin i / sin r = constant (n₂₁) Snell’s law as given in the notes

Bending behaviour of light

Rarer → denserLight bends towards the normal (∠i > ∠r).

Denser → rarerLight bends away from the normal (∠i < ∠r).

Refractive index depends on the nature of the medium and the wavelength of light. It is maximum for violet light and minimum for red light.

Refractive index (n)

Refractive index measures how fast light propagates through a material. It is a dimensionless quantity.

n = c / v Absolute refractive index: speed of light in vacuum (c) divided by speed in the medium (v).

n₂₁ = v₁ / v₂ = n₂ / n₁ Relative refractive index of medium 2 with respect to medium 1.

n₁₂ = v₂ / v₁ = n₁ / n₂ Relative refractive index of medium 1 with respect to medium 2.

n₂₁ × n₁₂ = 1; therefore n₂₁ = 1 / n₁₂ Reciprocal relation.

6. Lenses

A lens is a transparent optical material bounded by two curved surfaces or one curved and one flat surface.

Convex (converging) lensThicker at the centre than at the edges; converging lens.

Concave (diverging) lensThinner at the centre than at the edges; diverging lens.

Key terminologies for lenses

Optical centre (O): Central point of a lens through which an incident light ray passes without deviation.
Principal axis: Line C₁C₂ passing through the optical centre and perpendicular to both surfaces of the lens.
Principal focus: A lens has two principal foci (F₁, F₂). Rays parallel to the principal axis converge at or appear to diverge from F₂.
Focal length (f): Distance between optical centre (O) and principal focus (F).
Aperture: Effective diameter of the circular outline of a spherical lens.

Rules for ray diagrams in lenses

A ray passing through the optical centre (O) proceeds completely undeviated through the lens.
A ray passing through or directed towards the first focus (F₁) emerges parallel to the principal axis after refraction.
A ray parallel to the principal axis passes through (convex lens) or appears to diverge from (concave lens) the second focus (F₂).

Image formation for a convex lens

Object position	Image position	Nature of image	Magnification (m)
At infinity	At focus (F₂)	Real, inverted, very small	m < 0, approaches 0
Between infinity and 2F₁	Between F₂ and 2F₂	Real, inverted, diminished	−1 < m < 0
At 2F₁	At 2F₂	Real, inverted, same size	m = −1
Between 2F₁ and F₁	Beyond 2F₂	Real, inverted, enlarged	m < −1
At F₁	At infinity	Real, inverted, highly enlarged	m < 0, very large magnitude
Between F₁ and optical centre O	On same side as object	Virtual, erect, enlarged	m > +1

Image formation for a concave lens

A concave lens always forms a virtual, erect and diminished image on the same side as the object (m > 0).

Object position	Image position	Nature of image	Magnification (m)
At infinity	At focus (F₁)	Virtual, erect, point-sized	m ≪ +1
In front of lens (any distance)	Between F₁ and optical centre O	Virtual, erect, diminished	0 < m < +1

Sign convention for lenses

Parameter / quantity	Real image	Virtual image
Object distance (u)	Negative (−)	Negative (−)
Image distance (v)	Positive (+)	Negative (−)
Object height (hₒ)	Positive (+)	Positive (+)
Image height (hᵢ)	Negative (−)	Positive (+)
Magnification (m)	Negative (−)	Positive (+)

7. Lens Formula, Power and Combination

Lens formula

The lens formula relates object distance (u), image distance (v) and focal length (f) of a lens.

1/f = 1/v − 1/u Lens formula

Rules for applying lens formula

Substitute known values with their proper algebraic sign conventions.
Do not assign a sign to the unknown variable; its sign will emerge automatically from the calculation.
A positive calculated image distance (v > 0) indicates an image on the opposite side of the lens (real image). A negative image distance (v < 0) indicates an image on the same side as the object (virtual image).

Magnification of lens

Magnification (M) of a lens is the ratio of image height (hᵢ) to object height (hₒ).

M = hᵢ / hₒ = v / u Lens magnification

Power of a lens

The power (P) of a lens is defined as the reciprocal of its focal length (f) expressed in metres.

P = 1 / f (in metres) Power formula

SI unit: Dioptre (D) or m⁻¹.
Power of a convex lens is positive (+D).
Power of a concave lens is negative (−D).

Combination of thin lenses

When two or more thin lenses are placed in contact with each other:

P = P₁ + P₂ + P₃ + … Total power

1/F = 1/f₁ + 1/f₂ + 1/f₃ + … Equivalent focal length

⚡ Quick Formula Revision

Spherical mirrorf = R/21/v + 1/u = 1/fm = −v/u

Refractionsin i / sin r = n₂₁n = c/vn₂₁ × n₁₂ = 1

Lens1/f = 1/v − 1/uM = v/uP = 1/f (metres)

Lenses in contactP = P₁ + P₂ + …1/F = 1/f₁ + 1/f₂ + …

Remember: Use the correct sign convention before substituting values in mirror and lens numericals. For lens power, focal length must be expressed in metres.

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