NCERT Class 12 Physics Chapter 10 Notes Wave Optics - Download PDF

Wave Optics is all about the behavior of light as a wave. In this chapter, you will be taught significant concepts such as wavefronts, young double slit experiment polarization and Huygens' principle. The notes are made amazingly easy to learn, with key formulas for rapid revision. Ideal for boards and entrance examinations such as JEE and NEET.

The wave theory of light was introduced for the first time by a Dutch scientist in 1678 to describe the behavior of light. It explained reflection and refraction based on the concept that light moves in waves. Students will learn these fundamentals in a easy manner in Class 12 Wave Optics notes. The notes are also provided in PDF form, which is easily revisable at any time, anywhere.

Also, students can refer,

• NCERT Notes Class 12 Physics
• NCERT Solutions for Class 12 Physics Chapter 10 Wave Optics
• NCERT Exemplar Class 12 Physics Chapter 10 Solutions Wave Optics

NCERT Class 12 Physics Chapter 10 Notes

• WaveFront:

A light source is a spot that radiates noise in all directions. In a homogeneous medium, the disturbance hits all of the medium's particles in phase, which is all placed at the same distance from the light source, and so every particle must vibrate in phase with each other at all times. The wavefront is the location of all medium particles that are vibrating in the same phase at any given time.

Wavefronts can be one of the following sorts, depending on the shape of the light source:

1. Spherical wavefront

2. Cylindrical wavefront

Spherical WaveFront: A spherical wavefront is created by a point source of light. This is due to the fact that the locus of all equidistant points from the point source is a sphere.

Cylindrical WaveFront: A cylindrical wavefront is produced when the light source is linear (such as a slit). Every equidistant point from the linear source is located on the surface of a cylindrical

Plane WaveFront: If a wavefront is a small component of a spherical or cylindrical wavefront originating from a distant source, it will appear plane. As a result, it's known as a plane wavefront

Huygens' Principle

Huygens' principle is a geometrical construction that can be used to calculate the new position of a wavefront at a later time from its current position. Or, to put it another way, this principle provides a means for determining how light spreads out in a material.

It is founded on the following assumptions:

1. All of the locations on a given or primary wavefront operate as a source of secondary wavelets, which, like the primary light source, sends out disruption in all directions.

2. The envelope of the secondary wavelets at any instant is the new position of the wavefront (called secondary wavefront).

Principle of Superposition
Suppose there are two sources of waves $S_1$ and $S_2$.

Now, the two waves from $S_1$ and $S_2$ meet at some point (say $P$ ). Then, according to principle of superposition net displacement at $P$ (from its mean position) at any time is given by

$y=y_1+y_2$
Based on principle of superposition means two or more than two waves meet at one point or several points and at every point net displacement is $y=y_1+y_2$ or $y=y_1+y_2+y_3$ etc.

Resultant Amplitude
1. Consider the superposition of two sinusoidal waves of same frequency (means sources are coherent) at some point. Let us assume that the two waves are travelling in the same direction with same velocity. The equation of the two waves reaching at a point can be written as

$y_1=A_1\sin (kx-\omega t)$

and

$y_2=A_2\sin (kx-\omega t+\varphi )$
$\begin{array}{rl}A& =\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \varphi }\\ \tan \theta & =\frac{A\sin \theta }{A\cos \theta }=\frac{A_2\sin \varphi }{A_1+A_2\cos \varphi }\end{array}$

2. The above result can be obtained by graphical method also. Assume a vector ${\mathbf{A}}_1$ of length $A_1$ to represent the amplitude of first wave.

Resultant Intensity
In the previous chapter, we have read that intensity of a wave is given by

$I=\frac{1}{2}\rho {\omega }^2{A}^{2}v\text{ or }I\propto A^2$

So, if $\rho ,\omega$ and $v$ are same for the both interfering waves then Eq. (i) can also be written as

$I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$
Here, proportionality constant $(I\propto A^2)$ cancels out on right hand side and left hand side.

Phase difference (ϕ): The difference between the phases of two waves at a given place is known as phase difference.

i.e.,

$y_1=a_1\sin \omega t$

and

$y_2=a_2\sin (\omega t+\varphi )$

so phase difference = ϕ

Path difference (Δ): The difference in path lengths of two waves meeting at a place is referred to as path difference.

$\mathrm{\Delta }=\frac{\lambda }{2\pi }\times \varphi$

T.D. (Time Difference): T.D. (Time Difference) is the time difference between two waves meeting at a place. = $\frac{T}{2\pi }\times \varphi$

If we have two waves y₁=a₁sinωt and where y₂=a₂sin(ωt+ϕ),a₁ and a₂ =Individual amplitudes, ϕ= phase difference I₁and I₂= Intensities of Individual waves.

Coherent sources:

Coherent sources of light are light sources that emit continuous light waves of the same wavelength, frequency, and phase (or with a constant phase difference).

• Interference of light:

Interference of light is a phenomenon where two or more light waves superimpose to form a new wave pattern. It occurs when coherent light waves (same frequency and constant phase difference) overlap.

• Types of Interference:

• Constructive Interference: When crest meets crest and trough meets trough → Bright fringes.

• Destructive Interference: When crest meets trough → Dark fringes.

Young’s Double Slit Experiment (YDSE)

When monochromatic light (single wavelength) falls on two narrow slits S₁ and S₂ that are very close together, they act as two coherent sources, and the waves from these two sources superimpose on each other, an interference pattern appears on the screen. In this experiment, bright and dark bands alternated on the screen. Fringes are the name given to these bands.

d is the distance between the slits.

D be the distance between the slits and the screen.

$\lambda =$ Monochromatic light emanating from the source's wavelength.

1. At the central position Φ=0^o or Δ=0 the Central fringe will always be bright

2. A slit's fringe pattern will be brighter than a point's fringe pattern.

3. If the slit widths are mismatched, the minima will not be fully dark. As a result, uniform illumination occurs over a wide area.

4. When one slit is lit with red light and the other with blue light, no interference pattern appears on the screen.

• Path difference:

The path difference between interfering waves that collide at point P on the screen is given by

$x=\frac{yd}{D}=d\sin \theta$

where x be the position of point P from central maxima

For maxima at P:

$x=n\lambda n=0,\pm 1,\pm 2\dots$.

And for minima at P:

$x=\frac{(2n-1)\lambda }{2}n=0,\pm 1,\pm 2\dots$

• Diffraction of Light

The phenomenon of light bending around the corners of an obstacle/aperture with a size equal to the wavelength of light.

Types of Diffraction

1. Fresnel Diffraction

• Source and screen are at a finite distance.
• No lenses are used.
• Wavefronts are spherical or cylindrical.
• The diffraction pattern changes with the distance between the screen and the obstacle.
• Example: Light bending around the edge of a razor blade.

2. Fraunhofer Diffraction

• Source and screen are at infinite distance (or made so with lenses).

• Lenses are used to make wavefronts plane.

• Diffraction pattern is sharp and fixed.

• Commonly used for studying diffraction in labs.

• Example: Diffraction pattern through a single slit using a laser and lenses.

Comparison Between Interference and Diffraction

• Unpolarized light:

Unpolarized light is light that has electric field oscillations in all directions in a plane perpendicular to its propagation. The horizontal and vertical components of light oscillation are separated.

• Polarized light:

Plane or polarized light is light that has just one plane of oscillations.

The plane of oscillation is the plane in which polarized light oscillates.

The plane perpendicular to the plane of oscillation is the plane of polarization.

Light can be polarized by passing through particular crystals like tourmaline or Polaroid.

• Polarization by Scattering:

When a beam of white light is transmitted through a material with particles of the same size as the wavelength of the light, the beam is scattered. This scattered light will propagate perpendicular to the incidence direction and will be plane-polarized (as detected by the analyzer). This is known as scattering polarization.

Polarization of Light by Reflection

When a beam of white light is transmitted through a material with particles of the same size as the wavelength of the light, the beam is scattered. This scattered light will propagate perpendicular to the incidence direction and will be plane-polarized (as detected by the analyzer). This is known as scattering polarization.

• Polaroid:

A Polaroid is the name of the device that produces plane-polarized light. It is based on the selective absorption principle. It's also more powerful than the tourmaline crystal.

A thin layer of ultramicroscopic quinine iodide sulphate crystals with optic axes parallel to one another is also known as it.

Only light oscillations that are parallel to the transmission axis can travel through a Polaroid.

Unpolarized light is incident on a polarizer, which is a crystal or Polaroid. An analyzer is a crystal or polaroid on which polarized light is incident.

Malus Law

The square of the cosine of the angle between the analyzer’s plane of transmission and the plane of the polarizer will vary the intensity of polarized light passing through an analyzer. This is referred to as the Malus law.

$\begin{array}{rl}& I=I_0{\cos }^2\theta \\ & A^2=A_0{}^2{\cos }^2\theta \Rightarrow A=A\cos \theta \\ & \theta =0^{\circ },I=I_0,A=A_0\\ & \theta ={45}^{\circ },I=\frac{I_0}{2},A=\frac{A_0}{\sqrt{2}}\\ & \theta ={90}^{\circ },I=0,A=0\end{array}$

• Brewster’s law

When unpolarized light is reflected from a clear medium (with refractive index=μ), the reflected light will be totally plane-polarized at a specific angle of incidence (known as the angle of polarization θ_p). Brewster's law is the name for this rule.

$\mu =\tan {\theta }_p$

• Resolvong Power:

If two-point objects are near together, their image diffraction patterns will likewise be close together and overlap.

The minimum distance between two objects that can be seen independently by the object instrument is known as the instrument's limit of resolution.

• Resolving power of Microscope:

R.P. of microscope = $\frac{2\mu \sin \theta }{\lambda }$

• Resolving power of Telescope:

R.P of telescope = $\frac{1}{d\theta }=\frac{D}{1.22\lambda }$

Where D is the aperture of the telescope

Importance of NCERT Class 12 Physics Chapter 10 Notes

• NCERT Wave Optics class 12 notes are essential for comprehending wave phenomena.
• These class 12 physics chapter 10 notes provide a comprehensive review of the chapter's main topics.
• They are beneficial for CBSE Class 12 board exams because they correspond to the CBSE Class 12 Physics Syllabus.
• CBSE class 12 physics ch 10 notes also serve as valuable resources for competitive exams such as VITEEE, BITSAT, JEE Core, NEET
• The ch 10 physics class 12 notes provide a condensed version of the main concepts, making it easier for students to review and comprehend the material.
• Physics class 12 chapter 10 notes pdf, which allows for offline study and convenient access.

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