Chapter 10 Wave Optics

NCERT Solutions Class 12 Physics Chapter 10 - Wave Optics

Physics in Class 12th-Rays will stand second to the newest shift in the way we view light, which is performed basically by implementing Wave Optics. Ray Optics treats light as a straight line path particle; this is, however, quite the counter when we evaluate the true nature of light wavelength. Here, we will learn the revolutionary Huygens' Principle that will help in explaining some optical phenomena like interference and diffraction, which Ray Optics alone could not do. The study will address a very fundamental question: Why does light bend around corners? How do different sources of light interact with each other and create patterns? Apart from being an integral part of CBSE Board Examinations, it is also an important area in competitive entrance examinations such as JEE and NEET.

NCERT developed a solution to help students visualize the wavefronts and phase differences as discussed in Class 12 Physics Chapter 10, i.e. Wave Optics. The solution flows in a logical manner from the geometric aspect of Huygens' construction through to the complex mathematics involved in Young's Double Slit Experiment.

1.0Class 12 Physics Chapter 10 Wave Optics: Key Concepts

Class 12 Physics Chapter 10, Wave Optics, explains the wave nature of light and the phenomena that cannot be explained using ray optics alone. The main concepts covered in this chapter include:

Huygens’ Principle: Explains wavefronts and secondary wavelets and how they help describe the propagation of light.
Reflection and Refraction Using Wave Theory: Explains the laws of reflection and refraction using Huygens’ wave theory and the change in speed of light in different media.
Coherent and Incoherent Addition of Waves: Covers the principle of superposition and the conditions required to produce a steady interference pattern.
Interference of Light and Young’s Double Slit Experiment: Explains constructive and destructive interference, fringe formation, and the derivation of fringe width in Young’s double slit experiment.
Diffraction of Light: Explains the bending and spreading of light when it passes through a narrow slit or around an obstacle, including the single-slit diffraction pattern.
Resolving Power of Optical Instruments: Explains the ability of telescopes and microscopes to distinguish between two closely spaced objects using Rayleigh’s criterion.
Polarisation of Light: Explains the transverse nature of light through polarisation, Brewster’s law, and the use of Polaroids.

2.0NCERT Solutions Class 12 Physics Chapter 10 Wave Optics : Detailed Solutions

SOLVED EXAMPLES

(a) When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency. Explain why ? (b) When light travels from a rarer to a denser medium, the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave? (c) In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity of light in the photon picture of light.

Sol.

(a) Reflection and refraction arise through interaction of incident light with the atomic constituents of matter. Atoms may be viewed as oscillators, which take up the frequency of the external agency (light) causing forced oscillations. The frequency of oscillation. Thus, the frequency of scattered light equals the frequency of incident light. (b) No. Energy carried by a wave depends on the amplitude of the wave, not on the speed of wave propagation. (c) For a given frequency, intensity of light in the photon picture is determined by the number of photons crossing per unit area per unit time.

Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?

Sol. Let $I_{0}$ be the intensity of polarised light after passing through the first polariser $P_{1}$ . Then the intensity of light after passing through second polariser $P_{2}$ will be, $I = I_{0} cos^{2} θ$ .

Where $θ$ is the angle between pass axes of $P_{1}$ and $P_{2}$ . Since $P_{1}$ and $P_{3}$ are crossed the angle between the pass axes of $P_{2}$ and $P_{3}$ will be $(\frac{π}{2} - θ)$ . Hence the intensity of light emerging from $P_{3}$ will be

$I = I_{0} cos^{2} θ cos^{2} (\frac{π}{2} - θ) = I_{0} cos^{2} θ sin^{2} θ = (\frac{I _{0}}{4}) sin^{2} 2 θ$

Therefore, the transmitted intensity will be maximum when $θ = π /4$

EXERCISE QUESTIONS WITH SOLUTIONS

Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of : (a) Reflected, and (b) Refracted light? Refractive index of water is 1.33. Sol. (a) In reflected light wavelength $λ = 589 nm$

$frequency v = \frac{c}{λ} = \frac{3 \times 1 0 ^{8}}{580 \times 1 0 ^{- 9}} = 5.1 \times 1 0^{14} Hz$

Speed of light $c = 3 \times 1 0^{8} m / s$ (b) In refracted light

$λ^{'} = \frac{λ}{μ} = \frac{589 nm}{1.33} = 442.8 nm$

frequency (v) remain same

$speed = \frac{c}{μ} = \frac{3 \times 1 0 ^{8}}{1.33} m / s = 2.26 \times 1 0^{8} m / s .$

What is the shape of the wave front in each of the following cases: (a) Light diverging from a point source. (b) Light emerging out of a convex lens when a point source is placed at its focus. (c) The portion of the wave front of light from a distant star intercepted by the Earth.

Sol. (a) Spherical wave front, because all such points which are equidistant from the point source will lie on a sphere. (b) Plane wave front, because the light emerges from the convex lens as a parallel beam for which the wave front is plane. (c) Plane wave front, because a small portion of a spherical wave front of very large radius is nearly planar.

(a) The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times 1 0^{8} ms^{- 1}$ ) (b) Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism? Sol. (a) Here $μ = 1.5$ ,

$c = 3 \times 1 0^{8} ms^{- 1}$

As $μ = \frac{c}{v}$ ∴ Speed of light in glass,

$v = \frac{c}{μ} = \frac{3.0 \times 1 0 ^{8}}{1.5} = 2.0 \times 1 0^{8} ms^{- 1}$

(b) No, speed of light is not independent of the colour (wavelength) of the light. The violet colour travels slower than the red light in a glass prism. This is because $μ_{v} > μ_{R}$ and $v = \frac{c}{μ}$ .

In a Young's double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment. Sol. Distance of fourth bright fringe from centre

$x_{n} 1.2 \times 1 0^{- 2} λ = \frac{n λ D}{d} \Rightarrow x_{4} = \frac{4 λ D}{d} = \frac{4 \times λ \times 1.4}{0.28 \times 1 0 ^{- 3}} = \frac{1.2 \times 1 0 ^{- 3} \times 0.28 \times 1 0 ^{- 3}}{4 \times 1.4} = 600 nm$

In Young's double-slit experiment using monochromatic light of wavelength $λ$ , the intensity of light at a point on the screen where path difference is $λ$ , is K units. What is the intensity of light at a point where path difference is $λ /3$ ? Sol. Intensity of any point is given by

$I^{'} = I_{1} + I_{2} + 2 I_{1} I_{2} cos θ$

Given : Intensity of light is I then $I^{'} = K$

$K = I + I + 2 I cos 2 π$

( ∵ path difference $λ$ ) $($ phase difference $= 2 π)$

$K = 4 I$

Now,

$I^{''} = I_{1} + I_{2} + 2 I_{1} I_{2} cos \frac{2 π}{3}$

( ∵ path difference $λ /3$ ) (phase difference $= 2 π /3$ )

$I^{''} = I + I - 2 I (\frac{1}{2}) = I$

from equation (i) → I = K/4

$I^{''} = I .. I^{''} = \frac{K}{4}$

A beam of light consisting of two wavelengths, 650 nm and 520 nm , is used to obtain interference fringes in a Young's double-slit experiment. (a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm. (b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide ? Sol. $D = 120 cm, d = 2 mm$ (a) Distance of third bright fringe from centre of screen.

$x_{n} = \frac{nλ D}{d} \Rightarrow x_{3} = \frac{3 λ D}{d} = \frac{3 \times 120 \times 1 0 ^{- 2} \times 6500 \times 1 0 ^{- 10}}{2 \times 1 0 ^{- 3}} = 1.17 \times 1 0^{- 3} m = 1.17 m$

(b) When bright fringe of different wavelength coincide to each other.

$\Rightarrow = = n_{1} λ_{1} = n_{2} λ \frac{n _{1}}{n _{2}} = \frac{λ _{2}}{λ _{1}} \frac{5200 A ˚}{6500 A ˚} \frac{4}{5}$

for minimum value of $n_{1} & n_{2}$ .

$so, x = \frac{n _{1} λ _{1} D}{d} = \frac{4 \times 6500 \times 1 0 ^{- 10} \times 120 \times 1 0 ^{- 2}}{2 \times 1 0 ^{- 3}} = 0.156 \times 1 0^{- 2} m = 0.156 cm$

3.0Class 12 Physics NCERT Solutions – Chapter-wise Links

Access NCERT Solutions for Class 12 Physics for all chapters, with exercise answers, key formulas, and step-by-step solutions to help students study each topic and solve questions.

Chapter Number	Chapterwise NCERT Solutions
Chapter 1	Electric Charges and Fields
Chapter 2	Electrostatic Potential and Capacitance
Chapter 3	Current Electricity
Chapter 4	Moving Charges and Magnetism
Chapter 5	Magnetism and Matter
Chapter 6	Electromagnetic Induction
Chapter 7	Alternating Current
Chapter 8	Electromagnetic Waves
Chapter 9	Ray Optics and Optical Instruments
Chapter 11	Dual Nature of Radiation and Matter
Chapter 12	Atoms
Chapter 13	Nuclei
Chapter 14	Semiconductor Electronics: Materials, Devices and Simple Circuits

4.0Key Features of NCERT Solutions for Class 12 Physics Chapter 10

Clear Wavefront Diagrams: The answers provide clear diagrams that illustrate spherical, cylindrical, and flat wavefronts. This makes it easier for children to recognise each category and comprehend their differences.
Phase and Path Difference: A thorough explanation of the connection between phase difference and path difference is provided. In Young's Double Slit Experiment, students can utilise these ideas to determine the locations of the bright and dark fringes.
Step-by-Step Derivations: Key derivations are presented step-by-step, including fringe width and the principles of refraction using wave theory. To make the formulas simpler to comprehend and apply, each computation is displayed in a transparent manner.
Comparison of Interference and Diffraction: The answers elucidate the distinctions between interference and diffraction. This aids pupils in answering comparison-based questions on CBSE exams and preventing confusion between these two wave phenomena.
Important Physics Terms: Key terms such as monochromatic light, coherent sources, superposition, interference, and diffraction are explained using simple and correct definitions. This helps students use the right terms while writing answers in board examinations and practising questions for competitive exams.

NCERT Solutions Class 12 Physics Chapter 10 - Wave Optics

Physics in Class 12th-Rays will stand second to the newest shift in the way we view light, which is performed basically by implementing Wave Optics. Ray Optics treats light as a straight line path particle; this is, however, quite the counter when we evaluate the true nature of light wavelength. Here, we will learn the revolutionary Huygens' Principle that will help in explaining some optical phenomena like interference and diffraction, which Ray Optics alone could not do. The study will address a very fundamental question: Why does light bend around corners? How do different sources of light interact with each other and create patterns? Apart from being an integral part of CBSE Board Examinations, it is also an important area in competitive entrance examinations such as JEE and NEET.

NCERT developed a solution to help students visualize the wavefronts and phase differences as discussed in Class 12 Physics Chapter 10, i.e. Wave Optics. The solution flows in a logical manner from the geometric aspect of Huygens' construction through to the complex mathematics involved in Young's Double Slit Experiment.

1.0Class 12 Physics Chapter 10 Wave Optics: Key Concepts

Class 12 Physics Chapter 10, Wave Optics, explains the wave nature of light and the phenomena that cannot be explained using ray optics alone. The main concepts covered in this chapter include:

Huygens’ Principle: Explains wavefronts and secondary wavelets and how they help describe the propagation of light.
Reflection and Refraction Using Wave Theory: Explains the laws of reflection and refraction using Huygens’ wave theory and the change in speed of light in different media.
Coherent and Incoherent Addition of Waves: Covers the principle of superposition and the conditions required to produce a steady interference pattern.
Interference of Light and Young’s Double Slit Experiment: Explains constructive and destructive interference, fringe formation, and the derivation of fringe width in Young’s double slit experiment.
Diffraction of Light: Explains the bending and spreading of light when it passes through a narrow slit or around an obstacle, including the single-slit diffraction pattern.
Resolving Power of Optical Instruments: Explains the ability of telescopes and microscopes to distinguish between two closely spaced objects using Rayleigh’s criterion.
Polarisation of Light: Explains the transverse nature of light through polarisation, Brewster’s law, and the use of Polaroids.

2.0NCERT Solutions Class 12 Physics Chapter 10 Wave Optics : Detailed Solutions

SOLVED EXAMPLES

(a) When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency. Explain why ? (b) When light travels from a rarer to a denser medium, the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave? (c) In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity of light in the photon picture of light.

Sol.

(a) Reflection and refraction arise through interaction of incident light with the atomic constituents of matter. Atoms may be viewed as oscillators, which take up the frequency of the external agency (light) causing forced oscillations. The frequency of oscillation. Thus, the frequency of scattered light equals the frequency of incident light. (b) No. Energy carried by a wave depends on the amplitude of the wave, not on the speed of wave propagation. (c) For a given frequency, intensity of light in the photon picture is determined by the number of photons crossing per unit area per unit time.

Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?

Sol. Let $I_{0}$ be the intensity of polarised light after passing through the first polariser $P_{1}$ . Then the intensity of light after passing through second polariser $P_{2}$ will be, $I = I_{0} cos^{2} θ$ .

Where $θ$ is the angle between pass axes of $P_{1}$ and $P_{2}$ . Since $P_{1}$ and $P_{3}$ are crossed the angle between the pass axes of $P_{2}$ and $P_{3}$ will be $(\frac{π}{2} - θ)$ . Hence the intensity of light emerging from $P_{3}$ will be

$I = I_{0} cos^{2} θ cos^{2} (\frac{π}{2} - θ) = I_{0} cos^{2} θ sin^{2} θ = (\frac{I _{0}}{4}) sin^{2} 2 θ$

Therefore, the transmitted intensity will be maximum when $θ = π /4$

EXERCISE QUESTIONS WITH SOLUTIONS

Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of : (a) Reflected, and (b) Refracted light? Refractive index of water is 1.33. Sol. (a) In reflected light wavelength $λ = 589 nm$

$frequency v = \frac{c}{λ} = \frac{3 \times 1 0 ^{8}}{580 \times 1 0 ^{- 9}} = 5.1 \times 1 0^{14} Hz$

Speed of light $c = 3 \times 1 0^{8} m / s$ (b) In refracted light

$λ^{'} = \frac{λ}{μ} = \frac{589 nm}{1.33} = 442.8 nm$

frequency (v) remain same

$speed = \frac{c}{μ} = \frac{3 \times 1 0 ^{8}}{1.33} m / s = 2.26 \times 1 0^{8} m / s .$

What is the shape of the wave front in each of the following cases: (a) Light diverging from a point source. (b) Light emerging out of a convex lens when a point source is placed at its focus. (c) The portion of the wave front of light from a distant star intercepted by the Earth.

Sol. (a) Spherical wave front, because all such points which are equidistant from the point source will lie on a sphere. (b) Plane wave front, because the light emerges from the convex lens as a parallel beam for which the wave front is plane. (c) Plane wave front, because a small portion of a spherical wave front of very large radius is nearly planar.

(a) The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times 1 0^{8} ms^{- 1}$ ) (b) Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism? Sol. (a) Here $μ = 1.5$ ,

$c = 3 \times 1 0^{8} ms^{- 1}$

As $μ = \frac{c}{v}$ ∴ Speed of light in glass,

$v = \frac{c}{μ} = \frac{3.0 \times 1 0 ^{8}}{1.5} = 2.0 \times 1 0^{8} ms^{- 1}$

(b) No, speed of light is not independent of the colour (wavelength) of the light. The violet colour travels slower than the red light in a glass prism. This is because $μ_{v} > μ_{R}$ and $v = \frac{c}{μ}$ .

In a Young's double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment. Sol. Distance of fourth bright fringe from centre

$x_{n} 1.2 \times 1 0^{- 2} λ = \frac{n λ D}{d} \Rightarrow x_{4} = \frac{4 λ D}{d} = \frac{4 \times λ \times 1.4}{0.28 \times 1 0 ^{- 3}} = \frac{1.2 \times 1 0 ^{- 3} \times 0.28 \times 1 0 ^{- 3}}{4 \times 1.4} = 600 nm$

In Young's double-slit experiment using monochromatic light of wavelength $λ$ , the intensity of light at a point on the screen where path difference is $λ$ , is K units. What is the intensity of light at a point where path difference is $λ /3$ ? Sol. Intensity of any point is given by

$I^{'} = I_{1} + I_{2} + 2 I_{1} I_{2} cos θ$

Given : Intensity of light is I then $I^{'} = K$

$K = I + I + 2 I cos 2 π$

( ∵ path difference $λ$ ) $($ phase difference $= 2 π)$

$K = 4 I$

Now,

$I^{''} = I_{1} + I_{2} + 2 I_{1} I_{2} cos \frac{2 π}{3}$

( ∵ path difference $λ /3$ ) (phase difference $= 2 π /3$ )

$I^{''} = I + I - 2 I (\frac{1}{2}) = I$

from equation (i) → I = K/4

$I^{''} = I .. I^{''} = \frac{K}{4}$

A beam of light consisting of two wavelengths, 650 nm and 520 nm , is used to obtain interference fringes in a Young's double-slit experiment. (a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm. (b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide ? Sol. $D = 120 cm, d = 2 mm$ (a) Distance of third bright fringe from centre of screen.

$x_{n} = \frac{nλ D}{d} \Rightarrow x_{3} = \frac{3 λ D}{d} = \frac{3 \times 120 \times 1 0 ^{- 2} \times 6500 \times 1 0 ^{- 10}}{2 \times 1 0 ^{- 3}} = 1.17 \times 1 0^{- 3} m = 1.17 m$

(b) When bright fringe of different wavelength coincide to each other.

$\Rightarrow = = n_{1} λ_{1} = n_{2} λ \frac{n _{1}}{n _{2}} = \frac{λ _{2}}{λ _{1}} \frac{5200 A ˚}{6500 A ˚} \frac{4}{5}$

for minimum value of $n_{1} & n_{2}$ .

$so, x = \frac{n _{1} λ _{1} D}{d} = \frac{4 \times 6500 \times 1 0 ^{- 10} \times 120 \times 1 0 ^{- 2}}{2 \times 1 0 ^{- 3}} = 0.156 \times 1 0^{- 2} m = 0.156 cm$

3.0Class 12 Physics NCERT Solutions – Chapter-wise Links

Access NCERT Solutions for Class 12 Physics for all chapters, with exercise answers, key formulas, and step-by-step solutions to help students study each topic and solve questions.

Chapter Number	Chapterwise NCERT Solutions
Chapter 1	Electric Charges and Fields
Chapter 2	Electrostatic Potential and Capacitance
Chapter 3	Current Electricity
Chapter 4	Moving Charges and Magnetism
Chapter 5	Magnetism and Matter
Chapter 6	Electromagnetic Induction
Chapter 7	Alternating Current
Chapter 8	Electromagnetic Waves
Chapter 9	Ray Optics and Optical Instruments
Chapter 11	Dual Nature of Radiation and Matter
Chapter 12	Atoms
Chapter 13	Nuclei
Chapter 14	Semiconductor Electronics: Materials, Devices and Simple Circuits

4.0Key Features of NCERT Solutions for Class 12 Physics Chapter 10

Clear Wavefront Diagrams: The answers provide clear diagrams that illustrate spherical, cylindrical, and flat wavefronts. This makes it easier for children to recognise each category and comprehend their differences.
Phase and Path Difference: A thorough explanation of the connection between phase difference and path difference is provided. In Young's Double Slit Experiment, students can utilise these ideas to determine the locations of the bright and dark fringes.
Step-by-Step Derivations: Key derivations are presented step-by-step, including fringe width and the principles of refraction using wave theory. To make the formulas simpler to comprehend and apply, each computation is displayed in a transparent manner.
Comparison of Interference and Diffraction: The answers elucidate the distinctions between interference and diffraction. This aids pupils in answering comparison-based questions on CBSE exams and preventing confusion between these two wave phenomena.
Important Physics Terms: Key terms such as monochromatic light, coherent sources, superposition, interference, and diffraction are explained using simple and correct definitions. This helps students use the right terms while writing answers in board examinations and practising questions for competitive exams.

Frequently Asked Questions

Which Wave Optics topics are covered in NCERT Solutions Class 12 Physics Chapter 10?

Huygens’ Principle or Young’s Double Slit Experiment — what should I study from NCERT Solutions Chapter 10?

How do NCERT Solutions Class 12 Physics Chapter 10 explain the formation of bright and dark fringes in Young’s Double Slit Experiment?

Is diffraction the same as interference in NCERT Solutions Class 12 Physics Chapter 10?

Can NCERT Solutions Class 12 Physics Chapter 10 explain polarisation of light?

Are NCERT Solutions Class 12 Physics Chapter 10 Wave Optics useful for JEE and NEET preparation?

Join ALLEN!

NCERT Solutions Class 12 Physics Chapter 10 - Wave Optics

1.0Class 12 Physics Chapter 10 Wave Optics: Key Concepts

2.0NCERT Solutions Class 12 Physics Chapter 10 Wave Optics : Detailed Solutions

SOLVED EXAMPLES

EXERCISE QUESTIONS WITH SOLUTIONS

3.0Class 12 Physics NCERT Solutions – Chapter-wise Links

4.0Key Features of NCERT Solutions for Class 12 Physics Chapter 10

Table of Contents

Frequently Asked Questions

Which Wave Optics topics are covered in NCERT Solutions Class 12 Physics Chapter 10?

Huygens’ Principle or Young’s Double Slit Experiment — what should I study from NCERT Solutions Chapter 10?

How do NCERT Solutions Class 12 Physics Chapter 10 explain the formation of bright and dark fringes in Young’s Double Slit Experiment?

Is diffraction the same as interference in NCERT Solutions Class 12 Physics Chapter 10?

Can NCERT Solutions Class 12 Physics Chapter 10 explain polarisation of light?

Are NCERT Solutions Class 12 Physics Chapter 10 Wave Optics useful for JEE and NEET preparation?

Join ALLEN!

NCERT Solutions Class 12 Physics Chapter 10 - Wave Optics

1.0Class 12 Physics Chapter 10 Wave Optics: Key Concepts

2.0NCERT Solutions Class 12 Physics Chapter 10 Wave Optics : Detailed Solutions

SOLVED EXAMPLES

EXERCISE QUESTIONS WITH SOLUTIONS

3.0Class 12 Physics NCERT Solutions – Chapter-wise Links

4.0Key Features of NCERT Solutions for Class 12 Physics Chapter 10

Table of Contents