PhysicsKund Physics class 9 to 12 NCERT, JEE - NEET

Polarisation of Light Notes Class 12 PDF | NCERT, Board, NEET & JEE Polarisation Polarisation is an important property of light that proves light is a transverse wave. It is possible only in transverse waves because their vibrations occur perpendicular to the direction of propagation. Definition: Polarisation is the phenomenon in which the vibrations of a transverse wave are restricted to one direction (or one plane) perpendicular to the direction of propagation. Important Points: Only transverse waves can be polarised. Longitudinal waves cannot be polarised. Polarisation proves the transverse nature of light. Transverse Wave A transverse wave is a wave in which the particles of the medium vibrate perpendicular to the direction of propagation. For a wave travelling along the x-axis , the particles may vibrate along the y-axis or z-axis . Remember: The direction of vibration is always perpendicular to the direction of propagation. y-Polarised Wa...

Interference of Light Interference of light is the phenomenon in which two or more coherent light waves superpose and redistribute light intensity in space, producing regions of maximum and minimum intensity. Principle of Superposition The phenomenon of interference is based on the Principle of Superposition, which states: When two or more light waves overlap at a point, the resultant displacement at that point is equal to the vector sum of the displacements produced by the individual waves. Conditions for Sustained Interference The sources must be coherent. The waves must have the same frequency or wavelength. The phase difference between the waves should remain constant. The amplitudes should be nearly equal for clear interference patterns. Types of Interference 1. Constructive Interference Constructive interference occurs when two waves meet in the same phase. The resultant amplitude becomes maximum, producing maximum intensity. Condition: $\Delta = n...

State and explain Malus' law. The intensity of the plane polarised light transmitted through the analyser varies as the square of the cosine of the angle between the plane of transmission of the analyser and the plane of the polariser. Let $E$ be the amplitude of the light transmitted by the polariser and $\theta$ be the angle between the planes of the polariser and the analyser. Resolve $E$ into two components: (i) $E \cos \theta$ along $OP$ (i.e. parallel to the plane of transmission of analyser) (ii) $E \sin \theta$ along $OV$ (i.e. perpendicular to the plane of transmission of analyser). Only $E \cos \theta$ component is transmitted through the analyser. We know that, Intensity  $\propto (\text{Amplitude})^2$ i.e. $I \propto E^2$ Intensity of the transmitted light through the analyser is given by, $I \propto (E \cos \theta)^2 \quad \text{i.e.} \quad I = k E^2 \cos^2 \theta.$ But $k E^2 = I_0 \quad \text{i.e., the intensity of the incident polarised light}$ $I = I_0 \cos^2 \thet...

Viewing Single Slit Diffraction Pattern Diffraction pattern due to single slit can be easily seen by using an electric lamp with straight filament preferably and two razor (shaving) blades.  The shaving blades are held to form a narrow slit just near the eyes. Effort is made to see the filament through the slit. Bright and dark fringes are observed with slight adjustment of the width of slit. A single blade can also show diffraction of light. A slit made in aluminium foil can also be used for the purpose. Slit made by two fingers can also be used to observe diffraction of light.

The diffraction pattern due to a single slit obtained on a screen is shown in Angular width of a central maximum :   It is defined as the angle between the directions of the first minima on two sides of the central maximum. That is, angular width of central maximum is $2\theta$. The direction of the first minima on either side of the central maximum is given by $\theta = \frac{\lambda}{d} \quad \cdots (i) $ which is called half angular width of central maximum. Therefore, angular width of central maximum $= 2\theta = \frac{2\lambda}{d} \quad \cdots (ii)$ Linear width of central maximum :  Let $D$ be the distance of the screen from the centre $C$ of the slit. The linear distance of the first minima from the centre $O$ of the screen is given by $\because \text{ Arc } = \text{ angle } \times \text{ radius}$ $x = \theta D \quad $ $x = \frac{\lambda}{d} D = \frac{\lambda D}{d} \quad [\text{Using eqn. } (i)] $ The width of central maximum is equal to the linear distance between firs...

Describe diffraction of light at a single slit. Explain the formation of pattern of fringes on screen. Also, use the variation of intensity with diffraction angle $\theta$ to explain why the intensity of secondary maxima decreases with the order of maxima. Solution:  Let a diverging light from a monochromatic source S be made parallel after refraction through convex lens $L_1$. The refracted light forms a plane wavefront WW'. This plane wavefront WW' is incident on the slit AB of width $d$. According to Huygens' principle, each point of slit AB acts as a source of secondary disturbance or wavelets. Convex lens $L_2$ helps in converging the parallel beam of light. Now consider a point O equidistant from points A and B on the screen which is placed at a distance D from the slit AB. The secondary wavelets from A and B reach the point O in the same phase covering the same distance so constructive interference takes place at O. In other words, O is the position of central maximu...

Derive an expression for fringe width in Young's double slit experiment. State the factors on which fringe width depends.What is the shape of interference fringes obtained in Young's double slit experiment Dark and bright bands in the interference pattern are called interference fringes. Consider two coherent sources $S_1$ and $S_2$ separated by a distance $d$. Let $D$ be the distance between the screen and the plane of slits $S_1$ and $S_2$. Light waves emitted from $S_1$ and $S_2$ reach point O on the screen after travelling equal distances. So, path difference and hence phase difference between these waves is zero. Therefore, $S_1$ and $S_2$ meet at O in phase and hence constructive interference takes place at O. Thus, O is the position of the central bright fringe. Let the waves emitted by $S_1$ and $S_2$ meet at point P on the screen at a distance $y$ from the central bright fringe. The path difference between these waves at P is given by $ \Delta x = S_2P - S_1P \quad \cd...

Wavefronts Patterns for Mirrors, Lens and Prism (a) Wavefronts Patterns for Concave mirror : A plane wavefront is reflected as a converging wavefront from a concave mirror. When a point source of light is at the focus of the concave mirror, then diverging spherical wavefronts fall on the concave mirror. (b) Wavefronts Patterns for Prism : A plane wavefront incident on a prism emerges out as a plane wavefront from the prism. (c) Wavefronts Patterns for Convex lens : A plane wavefront emerges out of a convex lens as a converging wavefront. Let a point source of light be at the focus of a convex lens such that diverging spherical wavefronts fall on the convex lens. The refracted wavefront will be a plane wavefront. (d) Wavefronts Patterns for Concave lens : A concave lens takes a plane wavefront and transforms it into a diverging spherical wavefront. (e) Wavefronts Patterns for Convex mirror : A convex mirror takes a plane wavefront and reflects it as a...

Huygens' Principle: Understanding Wave Propagation Huygens' Principle is a fundamental concept in optics that helps us understand how light and other waves propagate through a medium. It provides a geometrical way to determine the new position of a wavefront at any given instant, knowing its position at an earlier time. Statement of Huygens' Principle Huygens' Principle can be stated in three key postulates: Each Point on a Wavefront Acts as a Source: Every point on an existing wavefront serves as a source of secondary wavelets. These wavelets spread out in all directions with the speed of the wave in that medium. The initial wavefront is the locus of all points vibrating in the same phase. Secondary Wavelets Propagate: These newly generated secondary wavelets are spherical in shape (in a homogeneous medium) and travel outwards with the same velocity as the original wave. The New Wavefront is the Forward Envelope: The new position of the wavefront at...

Wavefront and Types of Wavefronts :  Define wavefront. Discuss various types of wavefronts namely spherical wavefronts, cylindrical wavefronts and plane wavefronts. Definition of Wavefront :  Wavefront is defined as the locus of all the particles of a medium vibrating in the same phase at a given instant. The shape of a wavefront depends upon the shape of the source of disturbance. Types of Wavefronts :  (a) Spherical wavefront (SWF):  If the source of disturbance is a point source (O), then the wavefront is spherical. A point source of light emits waves which spread outward in all directions. If the medium is homogeneous, then after time $t$ seconds, the wave or disturbance will travel a distance equal to $vt$(sphere radius), from the point source in all directions. In means, the particles of the medium lying on the surface of the sphere of radius $vt$ will get disturbed at the same moment i.e., all these particles will vibrate in the same phase. In this case, the s...

Notes : Class 12 Physics Chapter 10 Wave Optics - Physics Kund Wave Front and Its Types Huygens' Principle Reflection and Refraction of Plane Waves Using Huygens' Principle Wavefront Patterns for Mirror, Lens and Prism Coherent and Incoherent Addition of Waves Interference Young's Double Slit Experiment and Expression for Fringe Width Diffraction Due to a Single Slit Width of Central Maximum Polarisation   Malus' Law

Coherent and Incoherent Addition of Waves  When two identical vibrating needles are allowed to oscillate in phase when they just touch the free surface of water in the tank at points $S_1$ and $S_2$. These needles generate two waves, each of amplitude $A$ at any instant. Phase difference between their displacement does not change with time. Consider a point $P$ such that $S_1P = S_2P$. At this point, resultant displacement is the sum of the individual displacements $y_1$ and $y_2$ of the two waves respectively. $y = y_1 + y_2 \quad \dots (i)$ $But \quad y_1 = y_2 = A \sin \omega t$ $\therefore \quad y = 2A \sin \omega t$ where $2A$ is the amplitude of the resultant wave. Now, intensity, $I \propto (\text{amplitude})^2$ $\therefore$ resultant intensity, $\quad I = K(2A)^2 = 4KA^2 = 4I_0$ $I_0 = KA^2$ is the intensity of wave produced by each source.  Thus, the intensity of the resultant wave at any point on the perpendicular bisector of $S_1S_2 = 4I_0$. Now, consider another po...

Derivation : Law of Reflection and Refraction by Huygens Principle (Snell's law)   Derivation of Laws of Refraction (Snell's law) from Huygens' Principle  (i) Plane wavefront refracted in denser medium :  AB is an incident wavefront striking the interface XY at point A. Refractive index of medium II is greater than refractive index of medium I, $n_2>n_1$. Let $v_1$ be speed of light in medium I and $v_2$ be the speed in medium II ($v_2 < v_1$). According to Huygens' principle, every point on incident wavefront AB acts as a source of disturbance. Time in which wavelet reaches from B to C is given by $t = \frac{BC}{v_1} \quad \text{i.e.,} \quad BC = v_1 t$ Draw AD = $v_2 t$ to get a point on the secondary spherical wavefront originating from point A on the incident wavefront. Join CD. Therefore, CD is the refracted wavefront. $\frac{BC}{AD} = \frac{v_1}{v_2} \quad \dots (i)$ In $\triangle BAC, \quad BC = AC \sin i$  and In $\triangle ACD, \quad AD= AC \sin r...