CBSE Class 12 Physics Revision Notes Chapter 10: Wave Optics

Wave optics explains the behaviour of light using wavefronts, superposition, interference, diffraction and polarisation. The chapter shows why light cannot always be understood through straight-line ray propagation.

Wave Optics studies the wave nature of light. It uses Huygens’ principle to explain reflection and refraction and the principle of superposition to explain interference.

Use these CBSE Class 12 Physics Revision Notes Chapter 10 for the 2026–27 session. Start with wavefronts and Huygens’ construction. Then revise coherent sources, Young’s experiment, single-slit diffraction and polarisation.

Key Takeaways

• Wavefront: A surface containing points that oscillate in the same phase.
• YDSE fringe width: β = λD/d gives the distance between consecutive bright or dark fringes.
• Single-slit minima: a sin θ = nλ gives the directions of diffraction minima.
• Malus’ law: I = I₀ cos² θ gives the intensity transmitted through an analyser.

Access Class 12 Physics Chapter 10 Wave Optics Notes in 30 Minutes

Divide the chapter into three revision blocks:

• First 10 minutes: Wavefronts, Huygens’ principle, reflection and refraction
• Next 10 minutes: Coherent sources, superposition and Young’s double-slit experiment
• Final 10 minutes: Single-slit diffraction, polarisation and Malus’ law

While revising, distinguish path difference from phase difference. Also remember that interference requires coherent sources, while polarisation proves that light is transverse.

Need help revising fringe conditions, diffraction patterns and Polaroid questions?
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Wavefront and Huygens’ Principle in Class 12 Physics Chapter 10 Notes

A wavefront is a surface containing points that vibrate in the same phase.

Every point on a wavefront has:

• The same phase
• A fixed phase difference of zero with other points on that wavefront
• The same stage of oscillation at a given instant

The direction in which wave energy travels is perpendicular to the wavefront.

Ray and Wavefront

A ray represents the direction of energy propagation.

A ray is always normal to the wavefront in an isotropic medium.

Types of Wavefront

The shape of a wavefront depends on the source and its distance from the observer.

Spherical Wavefront

A point source produces a spherical wavefront.

All points on the spherical surface are equally distant from the source and vibrate in the same phase.

Cylindrical Wavefront

A long narrow or linear source produces a cylindrical wavefront.

The wavefront spreads outward in the form of cylindrical surfaces.

Plane Wavefront

A small portion of a spherical wavefront appears plane at a large distance from the source.

Light from a distant star reaches Earth approximately as a plane wavefront.

Huygens’ Principle

Huygens’ principle is a geometrical method used to find the position and shape of a wavefront at a later time.

It is based on two ideas:

• Every point on a wavefront acts as a source of secondary wavelets.
• The forward envelope of these secondary wavelets gives the new wavefront.

If the wave speed is v, each secondary wavelet travels a distance vt in time t.

Huygens’ Construction

To construct the new wavefront:

1. Mark several points on the original wavefront.
2. Draw secondary wavelets of radius vt from each point.
3. Draw a common forward tangent to the wavelets.
4. The tangent surface gives the new wavefront.

Huygens’ construction predicts a backward wave as well. Huygens assumed that secondary wavelets have maximum amplitude in the forward direction and zero amplitude in the backward direction.

Reflection of Plane Waves in Class 12 Wave Optics Revision Notes

Huygens’ principle can be used to derive the laws of reflection.

Consider a plane wavefront incident on a reflecting surface at angle i.

Huygens’ Construction for Reflection

While one end of the wavefront reaches the reflecting surface, another end travels a certain distance.

During the same time:

• Secondary wavelets spread from the point that first reached the surface.
• A common tangent to these wavelets forms the reflected wavefront.

The incident and reflected rays are perpendicular to their respective wavefronts.

Laws of Reflection

The construction gives:

i = r

Therefore:

• The angle of incidence equals the angle of reflection.
• The incident ray, reflected ray and normal lie in the same plane.

The wave model and ray model give the same laws of reflection.

Reflection by Curved Surfaces

A plane wavefront falling on a concave mirror becomes a converging spherical wavefront after reflection.

The reflected wavefront converges towards the principal focus of the mirror.

Refraction of Plane Waves in CBSE Class 12 Physics Chapter 10 Notes

Refraction of plane wave occurs when a wavefront enters another medium and its speed changes.

The frequency remains unchanged during refraction, but speed and wavelength may change.

Refraction from One Medium to Another

Let:

• v₁ be the speed of light in medium 1.
• v₂ be the speed of light in medium 2.
• i be the angle of incidence.
• r be the angle of refraction.

Huygens’ construction gives:

sin i/sin r = v₁/v₂

Since:

n₁ = c/v₁

and:

n₂ = c/v₂

we get:

n₁ sin i = n₂ sin r

This is Snell’s law.

Refraction into a Denser Medium

When light enters a medium in which its speed is lower:

v₂ < v₁

Therefore:

r < i

The ray bends towards the normal.

The wavelength also decreases:

λ₂ < λ₁

Refraction into a Rarer Medium

When light enters a medium in which its speed is higher:

v₂ > v₁

Therefore:

r > i

The ray bends away from the normal.

Frequency and Wavelength During Refraction

The frequency of light does not change during refraction.

Using:

v = νλ

we get:

v₁/v₂ = λ₁/λ₂

Therefore:

λ₁/λ₂ = n₂/n₁

Critical Angle

When light travels from a denser medium to a rarer medium, the angle of refraction increases with the angle of incidence.

At the critical angle ic:

r = 90°

Therefore:

sin ic = n₂/n₁

Here, n₁ is the refractive index of the denser medium and n₂ is that of the rarer medium.

For i > ic, total internal reflection occurs.

Refraction by a Lens

A plane wavefront incident on a convex lens becomes a converging spherical wavefront.

The central part passes through a greater thickness of glass and is delayed more than the outer parts. The refracted wavefront then converges at the focus.

Principle of Superposition in Class 12 Physics Wave Optics Notes

The principle of superposition states that when two or more waves overlap, the resultant displacement is the vector sum of their individual displacements.

For two waves:

y = y₁ + y₂

The principle of superposition explains interference.

Phase Difference

Consider two waves:

y₁ = a₁ cos ωt

y₂ = a₂ cos(ωt + φ)

Here, φ is the phase difference.

Phase difference and path difference are related by:

φ = 2πΔx/λ

Therefore:

Δx = λφ/(2π)

Resultant Amplitude

The square of the resultant amplitude is:

A² = a₁² + a₂² + 2a₁a₂ cos φ

Since intensity is proportional to the square of amplitude:

I = I₁ + I₂ + 2√(I₁I₂) cos φ

This is the general expression for the intensity of two coherent waves.

Equal-Intensity Sources

If:

I₁ = I₂ = I₀

then:

I = 2I₀(1 + cos φ)

Using:

1 + cos φ = 2 cos²(φ/2)

we get:

I = 4I₀ cos²(φ/2)

Maximum and Minimum Intensity

For maximum intensity:

cos φ = 1

Therefore:

Imax = (√I₁ + √I₂)²

For minimum intensity:

cos φ = −1

Therefore:

Imin = (√I₁ − √I₂)²

For equal intensities:

Imax = 4I₀

Imin = 0

Coherent and Incoherent Sources in Wave Optics Class 12 Notes

Coherent sources produce waves of the same frequency with a constant phase difference.

For a stable interference pattern, the sources must be coherent.

Conditions for Coherent Sources

Coherent sources should have:

• The same frequency
• The same wavelength
• A constant phase difference
• Comparable amplitudes for clear fringes

Two independent lamps are generally not coherent because their phase difference changes rapidly with time.

Incoherent Sources

Sources with a rapidly changing phase difference are called incoherent sources.

For incoherent sources:

• No stable interference pattern appears.
• Maximum and minimum positions change rapidly.
• The observed intensity is the time-averaged sum.

Therefore:

I = I₁ + I₂

For two equal incoherent sources:

I = 2I₀

Producing Coherent Light Sources

Coherent sources are obtained by dividing light from one original source.

In Young’s experiment, two nearby slits receive light from the same source. They then act as coherent secondary sources.

Interference of Light in Wave Optics Revision Notes

Interference of light is the redistribution of intensity produced when two coherent light waves overlap.

Some points become bright due to constructive interference. Other points become dark due to destructive interference.

Constructive Interference

Constructive interference occurs when the waves arrive in the same phase.

The conditions are:

Path difference:

Δx = nλ

Phase difference:

φ = 2nπ

Here:

n = 0, 1, 2, 3, ...

For equal intensities:

Imax = 4I₀

Destructive Interference

Destructive interference occurs when the waves arrive in opposite phases.

The conditions are:

Path difference:

Δx = (n + 1/2)λ

Phase difference:

φ = (2n + 1)π

For equal intensities:

Imin = 0

Constructive and Destructive Interference Comparison

Interference redistributes energy. It does not create or destroy energy.

Young’s Double-Slit Experiment in Physics Chapter 10 Revision Notes

Young’s double-slit experiment provides clear evidence for the wave nature of light.

A monochromatic source illuminates two narrow slits S₁ and S₂ separated by distance d. The slits behave as coherent sources and produce alternate bright and dark fringes on a screen placed at distance D.

Experimental Arrangement

Let:

• d be the separation between the slits.
• D be the distance between the slits and screen.
• x be the distance of a point from the central line.
• λ be the wavelength of light.

The experiment uses:

D >> d

and:

D >> x

Path Difference in YDSE

The path difference at a point P is:

Δx = S₂P − S₁P

For small angles:

Δx = d sin θ

Since:

sin θ ≈ tan θ ≈ x/D

we get:

Δx = dx/D

Position of Bright Fringes

For constructive interference:

Δx = nλ

Therefore:

dxn/D = nλ

Hence:

xn = nλD/d

Here:

n = 0, ±1, ±2, ...

The central bright fringe corresponds to n = 0.

Position of Dark Fringes

For destructive interference:

Δx = (n + 1/2)λ

Therefore:

xn = (n + 1/2)λD/d

Here:

n = 0, ±1, ±2, ...

Fringe Width

The distance between two consecutive bright fringes or two consecutive dark fringes is called fringe width.

β = λD/d

Therefore, fringe width:

• Increases with wavelength
• Increases with screen distance
• Decreases with slit separation

Angular Fringe Width

Angular fringe width is:

βθ = λ/d

It is independent of screen distance.

Properties of YDSE Fringes

• Bright and dark fringes are equally spaced.
• All fringes have the same width.
• The central fringe is bright.
• Fringe width is the same for bright and dark fringes.
• The interference pattern is stable only for coherent sources.
• If one slit is closed, the interference pattern disappears.
• Increasing slit separation reduces fringe width.
• Increasing wavelength increases fringe width.

Effect of Medium on Fringe Width

If the complete arrangement is placed in a medium of refractive index μ:

λmedium = λair/μ

Therefore:

βmedium = λD/(μd)

Hence:

βmedium = βair/μ

The fringe width decreases in an optically denser medium.

Intensity in Young’s Experiment

For equal source intensities:

I = 4I₀ cos²(φ/2)

Using:

φ = 2πΔx/λ

we get:

I = 4I₀ cos²(πΔx/λ)

At the centre:

Δx = 0

Therefore:

I = 4I₀

Diffraction of Light in CBSE Class 12 Wave Optics Notes

Diffraction of light is the bending or spreading of light around the edges of an obstacle or through a narrow aperture.

It becomes significant when the size of the aperture or obstacle is comparable to the wavelength.

Why Diffraction Is Usually Not Observed

The wavelength of visible light is very small compared with everyday openings and obstacles.

Therefore, light generally appears to travel in straight lines. Diffraction becomes visible through very narrow slits.

Diffraction and Ray Optics

Diffraction places a limit on straight-line propagation.

Ray optics is a useful approximation when:

• The aperture is much larger than the wavelength.
• The obstacle dimensions are much larger than the wavelength.

Conservation of Energy

In a diffraction pattern, energy is redistributed.

Dark regions do not represent destroyed energy. The energy missing from dark regions appears in bright regions.

Single-Slit Diffraction in Chapter 10 Physics Notes

In single-slit diffraction, monochromatic light passes through a narrow slit of width a.

The pattern contains:

• A broad central bright maximum
• Dark minima on both sides
• Weaker secondary maxima between the minima

Condition for Diffraction Minima

For a slit of width a:

a sin θ = nλ

Here:

n = ±1, ±2, ±3, ...

For small angles:

sin θ ≈ θ

Therefore:

θn = nλ/a

Position of Minima on a Screen

If the screen is at distance D:

xn = nλD/a

Width of Central Maximum

The first minima occur at:

x = ±λD/a

Therefore, the width of the central maximum is:

W = 2λD/a

The angular width is:

Wθ = 2λ/a

Secondary Maxima

Secondary maxima occur approximately between consecutive minima.

Their intensity decreases as their distance from the centre increases.

Important Features of the Pattern

• The central maximum is the brightest.
• The central maximum is twice as wide as the secondary maxima.
• Secondary maxima become weaker away from the centre.
• Narrower slits produce wider diffraction patterns.
• Longer wavelengths produce wider patterns.

Interference and Diffraction in Class 12 Wave Optics Revision Notes

Both interference and diffraction result from the superposition of waves.

The difference mainly depends on the number and arrangement of contributing sources.

In a real double-slit experiment, the observed pattern is the interference pattern modified by diffraction from each slit.

Polarisation of Light in Wave Optics Class 12 Notes

Polarisation of light is the restriction of electric-field vibrations to one direction perpendicular to the direction of wave propagation.

Polarisation shows that light is a transverse wave.

Longitudinal waves cannot be polarised.

Transverse Nature of Light

In an electromagnetic wave:

• Electric field E is perpendicular to the direction of propagation.
• Magnetic field B is perpendicular to the direction of propagation.
• E and B are perpendicular to each other.

Light is commonly described using the direction of its electric field.

Unpolarised Light

In unpolarised light, the electric field changes randomly in all directions perpendicular to the direction of propagation.

Light from the Sun, bulbs and ordinary lamps is generally unpolarised.

Plane-Polarised Light

In plane-polarised light, the electric field oscillates in only one fixed direction.

It is also called linearly polarised light.

Unpolarised and Plane-Polarised Light

Polaroid and Malus’ Law in CBSE Class 12 Physics Chapter 10 Notes

A Polaroid is a material that allows one component of the electric field to pass and absorbs the perpendicular component.

Its transmitting direction is called the pass axis or transmission axis.

Polariser and Analyser

A Polaroid used to convert unpolarised light into plane-polarised light is called a polariser.

A second Polaroid used to study the polarised light is called an analyser.

Intensity Through One Polaroid

When unpolarised light of intensity I enters a Polaroid:

Ipolarised = I/2

Rotating a single Polaroid does not change the transmitted intensity of unpolarised incident light.

Malus’ Law

When plane-polarised light passes through an analyser:

I = I₀ cos² θ

This is Malus’ law.

Here:

• I₀ is the intensity incident on the analyser.
• θ is the angle between the transmission axes of the polariser and analyser.
• I is the transmitted intensity.

Important Malus’ Law Cases

When the axes are parallel, maximum intensity passes.

When the axes are perpendicular, no light ideally passes. The Polaroids are then called crossed Polaroids.

Three-Polaroid Arrangement

Suppose a third Polaroid is placed between two crossed Polaroids.

If the middle Polaroid makes angle θ with the first:

I = (I₀/4) sin² 2θ

The transmitted intensity is maximum when:

θ = 45°

This shows that inserting a third Polaroid between crossed Polaroids can allow some light to pass.

Uses of Polaroids

Polaroids are used in:

• Sunglasses
• Photographic cameras
• 3D cinema
• Windowpanes
• Glare reduction
• Controlling light intensity

Wave Optics Formula Notes

Important Terms in Class 12 Physics Chapter 10

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