Class 10 Science Notes

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Light Reflection and Refraction Class 10 Notes

This chapter runs from a light ray striking a mirror to the same ray bending through a lens and splitting inside a prism. Every numerical in this topic is built on three relations: the mirror formula, the lens formula and the definition of refractive index. Learn the ray diagrams first and the numbers become bookkeeping.

Class:10Subject:ScienceUnit:IIICovers:CBSE 2024-25

6 Key Formulas

DWritten byDeep Narayan

UpdatedSeptember 2026

Key Concept Summary

State the mirror formula and the lens formula, and explain how they differ.

The mirror formula is 1/v + 1/u = 1/f and the lens formula is 1/v - 1/u = 1/f, with all distances measured from the pole or the optical centre under the New Cartesian sign convention. The magnification also differs, since a mirror gives m = -v/u while a lens gives m = v/u. Mixing these two formulas and their signs is the commonest error in numerical questions from this unit.

Reflection of light and spherical mirrors

Reflection of light is the bouncing back of light from a surface, and it obeys two laws: the angle of incidence equals the angle of reflection, and the incident ray, the reflected ray and the normal all lie in the same plane.A spherical mirror is a part of a sphere. A concave mirror curves inward like the inside of a spoon and can converge rays to form real images, while a convex mirror curves outward and always forms a virtual, erect and diminished image.

Pole P: the centre of the reflecting surface of the mirror
Principal axis: the line drawn through the pole and the centre of curvature
Centre of curvature C: the centre of the sphere of which the mirror is a part
Focus F: the point on the principal axis where parallel rays meet after reflection
Focal length f: the distance from the pole P to the focus F
Radius of curvature R: the distance from P to C, and R equals 2f

Key mirror terms

f = distance (P \to F), R = distance (P \to C) = 2 f

Two terms worth remembering

The focal length is measured from the pole, not from the centre of curvature, which is the most common confusion in diagrams.The focal length of a concave mirror is negative under the sign convention, so f = -R/2 for it and f = +R/2 for a convex mirror.Both focal length and radius of curvature must be written with the correct sign in a numerical.

Image formation by a spherical mirror

The size, position and nature of the image depend on where the object is placed. For a concave mirror the cases run from an object far beyond C right down to the mirror surface itself.Every answer should state the position, size and nature of the image, and should be supported by a ray diagram in which at least two rays from the top of the object are drawn.

Object beyond C: image between F and C, real, inverted and diminished
Object at C: image at C itself, real, inverted and of the same size
Object between C and F: image beyond C, real, inverted and magnified
Object at F: image at infinity, real and highly enlarged
Object between P and F: image behind the mirror, virtual, erect and magnified
Object on the mirror: image on the mirror, virtual, erect and highly diminished

Answer in a fixed order

For a mirror diagram, write position first, then size, then nature, and finish with the mirror type.The case the examiner checks most is the object between P and F, which gives a virtual, erect and magnified image behind the mirror.A convex mirror gives a virtual, erect and diminished image between P and F for every position of the object.

Mirror formula and magnification

Every numerical on mirrors uses the mirror formula together with the New Cartesian sign convention, in which all distances are measured from the pole and distances measured against the direction of the incident light are taken as negative.The magnification gives the ratio of the image size to the object size, and its sign also tells you whether the image is inverted or erect.

Mirror formula

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

Mirror magnification

m = - \frac{h _{i}}{h _{o}} = - \frac{v}{u}

Where marks are lost

Distances measured against the direction of the incident light must be taken as negative, so u is negative for a real object in front of the mirror.A negative m means the image is real and inverted, while a positive m means the image is virtual and erect.Do not use the lens formula with a mirror, since the two signs are deliberately different.

Refraction of light and refractive index

Refraction is the bending of light when it passes from one transparent medium to another because its speed changes there. It bends towards the normal on entering a denser medium such as glass and away from the normal on entering a rarer one such as air.Two laws of refraction govern the behaviour: the incident ray, the refracted ray and the normal lie in the same plane, and the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media. This constant is the refractive index.

Refraction is a change in the direction of light as it crosses a boundary
Refractive index n equals the speed of light in vacuum divided by its speed in the medium
For a glass slab, n also equals the real depth divided by the apparent depth
Light bends towards the normal in a denser medium and away from it in a rarer one
The pair of media must always be named, usually air to glass
The speed of light in vacuum is about three hundred thousand kilometres per second

Refractive index

n = \frac{c}{v} = \frac{speed in vacuum}{speed in medium} = \frac{real depth}{apparent depth}

Values worth memorising

The refractive index of glass is about 1.5 and that of diamond about 2.4, both measured for air to that medium.A higher refractive index means a greater bending towards the normal for the same angle of incidence.A coin at the bottom of a glass of water looks raised because its apparent depth is smaller than its real depth.

Spherical lenses, image formation and lens formula

A spherical lens is a portion of a transparent sphere bounded by two surfaces, one convex and one concave. A lens that is thicker in the middle than at the edges converges light and is called convex, while a lens thinner in the middle diverges light and is called concave.Image formation in a lens follows the same case analysis as in mirrors, but the lens formula uses a minus sign between the two reciprocals and the magnification is positive for an upright image.

Convex lens, object beyond 2F: real, inverted and diminished image between F and 2F
Object at 2F: image at 2F, real, inverted and of the same size
Object between F and 2F: image beyond 2F, real, inverted and magnified
Object at F: image at infinity, real and highly enlarged
Object inside F: image on the same side, virtual, erect and magnified
Concave lens: always a virtual, erect and diminished image on the same side as the object

Lens formula and magnification

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, m = \frac{h _{i}}{h _{o}} = \frac{v}{u}

Mirror versus lens

The mirror formula is 1/v + 1/u = 1/f, while the lens formula is 1/v - 1/u = 1/f.Mirror magnification is m = -v/u and lens magnification is m = v/u, since in a lens object and image are measured along the same reference.Mixing the two signs is the commonest numerical error, so write the formula out in full before substituting values.

Power of a lens

The power of a lens is the reciprocal of its focal length with the focal length expressed in metres, and it is measured in dioptre. A lens of power +1 dioptre has a focal length of 1 metre.The power is positive for a converging convex lens and negative for a diverging concave lens. When two thin lenses are placed in contact their powers simply add.

P equals 1 over f, with f in metres and P in dioptre
One dioptre equals one per metre
Sign: convex lens positive, concave lens negative
A convex lens of focal length 50 cm has a power of +2 D
A concave lens of focal length -50 cm has a power of -2 D
Powers of thin lenses in contact are added algebraically

Power of a lens

P = \frac{1}{f ( metres )}, 1 dioptre = 1 m^{- 1}

Unit trap

The focal length must be converted into metres before the power is calculated, so 50 cm becomes 0.5 m.Dropping the negative sign for a concave lens, or using centimetres directly, loses the final mark.Power has the unit of inverse length, so the answer must never be written in metres or dioptres per metre.

Prism, dispersion and scattering of light

A prism is a transparent optical device with two refracting faces that are not parallel to each other. A ray entering it is refracted twice and is deviated from its original path, always towards the base of the prism.White light is a mixture of seven colours, and because each colour bends by a different amount in glass, a prism spreads the light into a spectrum. This spreading is called dispersion, and the same effect produces a rainbow when sunlight is dispersed by water droplets.

A prism deviates a ray of light towards its base
The angle between the incident ray and the emergent ray is the angle of deviation
Violet bends the most and red the least in a glass prism
Dispersion is the splitting of white light into its component colours
Scattering is the redirection of light by fine particles, and it makes the sky blue
The eye's own lens disperses light, which is why colour is seen without any prism

Spectrum order and deviation

V I B G Y O R, δ = (i + e) - A

Scattering in daily life

The sky looks blue because short wavelengths such as violet and blue are scattered most by dust and air particles, and the eye is more sensitive to blue than to violet.The Sun appears white when seen from space because space is a vacuum and there is nothing there to scatter its light.The twinkling of stars and the sharp angle of a road signal light are further everyday uses of the same physics.

Quick Revision

Key formulas at a glance

Memorise these equations — direct application numericals and derivations in CBSE & JEE frequently hinge on these.

Mirror formula

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

All distances measured from the pole under the New Cartesian sign convention.

Mirror magnification

m = - \frac{h _{i}}{h _{o}} = - \frac{v}{u}

Negative m means a real and inverted image.

Lens formula

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

Note the minus sign, which distinguishes it from the mirror formula.

Lens magnification

m = \frac{h _{i}}{h _{o}} = \frac{v}{u}

Positive m means a virtual and erect image for a single lens.

Refractive index

n = \frac{c}{v} = \frac{speed in vacuum}{speed in medium} = \frac{real depth}{apparent depth}

Always stated for a named pair of media, such as air to glass.

Power of a lens

P = \frac{1}{f}, P in D when f is in m

Positive for a convex lens, negative for a concave lens.

Exam Strategy

How this chapter is asked

High-yield question patterns observed across CBSE boards, JEE Main & Advanced, and NEET.

Use the New Cartesian sign convention in every numerical and show it if the question carries a mark for the sign.
For image formation always write position, size and nature, and draw at least two rays from the top of the object.
The mirror formula has a plus sign, the lens formula a minus sign, and the two magnifications differ in sign as well.
Distances measured against the direction of the incident light are negative under the sign convention.
Convert every focal length into metres before calculating power, and keep the negative sign for a concave lens.
Learn the two famous cases together: object between P and F in a concave mirror and object inside F in a convex lens both give a virtual, erect and magnified image.
A convex mirror always gives a virtual, erect and diminished image between P and F, whatever the object position.
Refractive index must name the pair of media, and the value for glass is about 1.5.
For a prism, remember deviation towards the base, maximum deviation for violet and minimum for red.

FAQ

Frequently asked questions

Why does a convex mirror always form a diminished image?

A convex mirror curves outward, so rays striking it always appear to diverge from a focus behind the mirror. The image is therefore always virtual and erect, and since the object lies beyond the focus it is always smaller than the object. This is why convex mirrors are fitted as rear-view mirrors, since they show a much wider field of view than a plane mirror.

How is the refractive index of a glass slab measured?

The refractive index is the ratio of the speed of light in vacuum to the speed of light in the medium, which is a fixed property of the pair of media. For a slab it can also be found by comparing the real depth of an object with its apparent depth when viewed from above. A glass slab of refractive index 1.5 makes an object at 9 cm below its surface appear at 6 cm.

What happens to a ray of light when it travels from air into glass?

The ray slows down because glass is optically denser, and it bends towards the normal. The angle of refraction is therefore smaller than the angle of incidence. When the ray leaves the glass and returns to air it speeds up and bends away from the normal, so it travels parallel to the original incident ray but laterally displaced.

Why do we add the powers of lenses kept in contact?

When two thin lenses are placed in contact they behave like a single lens of combined power. The power of the combination is the algebraic sum of the individual powers, so a convex and a concave lens in contact can give any required resultant power. This is how a camera lens is made up of several elements, some converging and some diverging, to correct the image.

What is the difference between dispersion and scattering of light?

Dispersion is the splitting of white light into its component colours because each colour bends by a different amount while passing through a prism. Scattering is the redirection of light in many directions by fine particles in its path, and it makes the sky blue and distant objects hazy. Dispersion needs a transparent medium such as glass, whereas scattering happens wherever there are particles.

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